High-Accuracy Positioning in Urban Environments Using Single

remote sensing
Article
High-Accuracy Positioning in Urban Environments
Using Single-Frequency Multi-GNSS RTK/MEMSIMU Integration
Tuan Li 1 , Hongping Zhang 1, *, Zhouzheng Gao 2,3 , Qijin Chen 1 and Xiaoji Niu 1
1
2
3
*
GNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, China;
tuanli@whu.edu.cn (T.L.); chenqijin@whu.edu.cn (Q.C.); xjniu@whu.edu.cn (X.N.)
School of Land Science and Technology, China University of Geosciences, 29 Xueyuan Road,
Beijing 100083, China; zhouzhenggao@whu.edu.cn
German Research Centre for Geosciences (GFZ), Telegrafenberg, 14473 Postsdam, Germany
Correspondence: hpzhang@whu.edu.cn
Received: 18 December 2017; Accepted: 26 January 2018; Published: 30 January 2018
Abstract: The integration of Global Positioning System (GPS) real-time kinematics (RTK) and
an inertial navigation system (INS) has been widely used in many applications, such as mobile mapping
and autonomous vehicle control. Such applications require high-accuracy position information. However,
continuous and reliable high-accuracy positioning is still challenging for GPS/INS integration in
urban environments because of the limited satellite visibility, increasing multipath, and frequent
signal blockages. Recently, with the rapid deployment of multi-constellation Global Navigation
Satellite System (multi-GNSS) and the great advances in low-cost micro-electro-mechanical-system
(MEMS) inertial measurement units (IMUs), it is expected that the positioning performance could
be improved significantly. In this contribution, the tightly-coupled single-frequency multi-GNSS
RTK/MEMS-IMU integration is developed to provide precise and continuous positioning solutions in
urban environments. The innovation-based outlier-resistant ambiguity resolution (AR) and Kalman
filtering strategy are proposed specifically for the integrated system to resist the measurement outliers
or poor-quality observations. A field vehicular experiment was conducted in Wuhan City to evaluate
the performance of the proposed algorithm. Results indicate that it is feasible for the proposed
algorithm to obtain high-accuracy positioning solutions in the presence of measurement outliers.
Moreover, the tightly-coupled single-frequency multi-GNSS RTK/MEMS-IMU integration even
outperforms the dual-frequency multi-GNSS RTK in terms of AR and positioning performance for
short baselines in urban environments.
Keywords: multi-GNSS (GPS/BeiDou/GLONASS); real-time kinematic (RTK); MEMS-IMU;
tightly-coupled integration; urban environments; fault detection and exclusion
1. Introduction
High-accuracy positioning is an issue for many applications, such as machine control, unmanned
aerial vehicles, mobile mapping, etc. For outdoor environments, Global Positioning System (GPS)
real-time kinematics (RTK) has been proven to be a reliable and efficient tool because it can provide
centimeter-level positioning after correctly resolving the carrier-phase integer ambiguities. Research
has shown that rapid ambiguity resolution (AR) can be achieved in open sky conditions with
dual-frequency GPS receivers [1], but the high-cost of dual-frequency receivers definitely makes
many potential applications impossible.
Generally, the single-frequency GPS RTK has a low AR success rate and reliability [2,3]. With the
rapid development of multi-GNSS [4], the performance of single-frequency RTK can be improved
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significantly due to the increasing satellite visibility and better spatial geometry, as it was studied in
GPS/BDS [1,5,6], GPS/GLONASS [3], GPS/BDS/GLONASS [7], and BDS/GALILEO/QZSS/GPS [8].
In this research, the combination of three main satellite navigation systems, namely the U.S. GPS,
Russia’s GLObal NAvigation Satellite System (GLONASS), and the Chinese BeiDou navigation satellite
system (BDS), will be considered to enhance the positioning capabilities of single-frequency RTK
in urban environments. Currently, both GPS and GLONASS have full constellations of thirty-two
and twenty-four medium earth orbit (MEO) satellites, respectively. The Chinese BDS has begun to
provide position, velocity, and timing service in the Asia-Pacific region since the end of 2012, with the
constellation of five geostationary earth orbit (GEO) satellites, five inclined geo-synchronous orbit
(IGSO) satellites, and four MEO satellites [4]. Different from the code division multiple access (CDMA)
modulation that is adopted by GPS and BDS, GLONASS uses the frequency division multiple access
(FDMA) modulation, i.e., different frequencies for different satellites [2,9]. This FDMA modulation
makes GLONASS AR difficult due to the carrier phase inter-frequency bias (IFB) caused by the
analog hardware delay and the digital signal processing [10]. The IFB cannot be eliminated in the
double-differenced (DD) process like GPS or BDS, thus preventing the integer ambiguity resolution.
Recent research has shown that the IFB can be pre-calibrated or estimated in real-time, which makes
GLONASS AR possible [11,12].
In recent years, there has been increasing demand for high-accuracy positioning in urban
environments. However, the RTK performance degrades in such environments due to the frequent
signal blockages and multipath, even with multiple constellations. In order to provide continuous
high-accuracy positioning solutions, GNSS is often integrated with INS due to their complementary
characteristics [13–16]. Actually, the GPS/INS integrated system has been used in many applications
that require high-accuracy position, velocity, and attitude information [14,17]. In the last few years,
some researchers have investigated the positioning performance of GPS/INS integration in urban
environments [18–20]. These studies were mainly based on pseudo-range and Doppler observations
and only meter-level positioning accuracy could be obtained. With the rapid advances in MEMS
inertial sensor technology, the low-cost GNSS/INS integration becomes increasingly attractive and
suitable for many applications [21,22]. Recently, MEMS-IMUs have been integrated with low-cost GPS
receivers to provide an accurate and reliable navigation solution in urban environments [23–25].
Since the GNSS measurements are easily contaminated with large multipath errors, especially
for code measurements, the fault detection and exclusion (FDE) algorithm is necessary for integrated
GNSS/INS system working in urban environments. Some FDE algorithms have been developed
for the GPS/INS system in the literature. For example, quality control for an integrated navigation
system using innovations and recursive filtering is proposed in [26]. An innovation-based detection,
identification, and adaptation (DIA) procedure in an integrated navigation system is presented in [27].
In [28], a snapshot innovation method is used for improved positioning in foliage environments.
Hewitson et al. extended the GNSS receiver autonomous integrity monitoring (RAIM) algorithm to
the integrated GNSS/INS systems [29]. Even though these methods are effective to detect and isolate
faulty measurements, a highly-reliable FDE algorithm is still needed, especially for carrier-phase-based
high-accuracy positioning in GNSS-challenged environments.
Although the positioning performance in urban environments has been investigated in some
previous studies, they mainly focused on the integration of GPS-only and INS, and few investigated
the centimeter-level positioning capabilities in urban environments by combining the multi-GNSS data
and low-cost MEMS-IMU data. In this contribution, we investigate the feasibility of high-accuracy
positioning in urban environments by using the tightly-coupled integration of single-frequency
GPS/BDS/GLONASS RTK and INS. The outlier-resistant AR and Kalman filtering strategy are
proposed specifically for the tightly-coupled integration to resist the measurement outliers. A field
vehicular experiment was conducted in Wuhan City to evaluate the AR and positioning performance of
the proposed algorithm. Comparisons will be conducted with respect to the single- and dual-frequency
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multi-GNSS RTK. In addition, the positioning drifts during real GNSS signal outages instead of
simulated outages will be evaluated.
The paper is organized as follows: Section 2 presents the tightly-coupled multi-GNSS RTK/INS
integration models including the INS dynamic model, measurement model, and single-epoch
ambiguity resolution with inertial aiding. The innovation-based outlier-resistant AR and Kalman
filtering strategy is also given in this section. Next, the field experiment and data processing strategies
are described in Section 3. The corresponding results and discussion are presented in Section 4, followed
by a summary of the work and conclusions in Section 5.
2. Methods
2.1. Tightly-Coupled GPS/BDS/GLONASS RTK/INS Integration Model
In this research, the Extended Kalman Filter (EKF) is used to implement the tightly-coupled
multi-GNSS RTK/INS integration. The EKF directly fuses the multi-GNSS data and IMU data to obtain
optimal estimates of the integrated system state. In order to show the tightly-coupled integration
algorithm, the INS dynamic model, the measurement model and the single-epoch AR with inertial
aiding will be introduced in this section.
2.1.1. INS Dynamic Model
In this research, the INS dynamic model is constructed as the ψ-angle error model [30]. In this
model, the error analysis is done with respect to the computer (c) frame that is locally levelled at the
computed position. The ψ-angle error model can be described as:



.c
c × δrc + δvc
δr = −ωec
c + ωc × δvc + δgc + c p δfb
δv = fc × ψ − 2ωie
ec
b
.


c + ωc × ψ − c p δωb
ψ = − ωie
ec
ib
b
.
.
.c
(1)
.
where δr, δv and ψ denote the time derivative of position, velocity, and attitude error vectors,
c is the angular rate of e-frame (i.e., Earth-centered, Earth-fixed (ECEF)) with respect
respectively; ωie
c is the angular rate of c-frame with
to the inertial (i) frame, projected to the computer (c) frame; ωec
c
respect to e-frame, projected to c-frame; δg is the gravity error vector projected in the c-frame;
b denote the inertial sensor errors; C p is the rotation matrix from the body (b) frame
δfb and δωib
b
(i.e., forward-right-down (FRD)) to the platform (p) frame.
In order to improve the navigation performance of low-cost MEMS inertial sensors, the IMU
errors including the bias and scale factor of both the gyroscope and accelerometer are augmented into
the filter state and estimated on-line. In the implementation of GNSS/INS integration algorithms, they
are generally modeled as first-order Gauss-Markov process [31]. Therefore, the complete error state
vector can be described as:
h
X = (δrc ) T
(δvc )T ψ T bTg bTa sTg sTa
iT
(2)
where δrc and δvc are position and velocity errors in the navigation frame (i.e., north-east-down (NED)),
respectively; ψ is the attitude error; bg denotes the gyro bias error; ba denotes the accelerometer bias
error; sg and sa are the scale factor errors of the gyro and accelerometer, respectively.
2.1.2. Measurement Model
In the single-frequency GPS/BDS/GLONASS RTK positioning, the code and carrier phase
observations on f 1 frequency (herein GPS L1: 1575.42 MHz; BDS B1: 1562.098 MHz; GLONASS
L1: 1602.006 + k × 0.5625 MHz, where k is the corresponding satellite frequency number) will be
used together. Since there is no frequency overlap in the three GNSS systems, the double-differencing
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(DD) formulation should be applied within the individual GNSS system, i.e., one reference satellite
per system [5]. This is a loosely-coupled way to combine observations from different GNSS systems.
The double-differenced code and carrier-phase observation equations of a single GNSS system are
given as follows in units of range, and the time stamps are omitted for brevity:
∇∆PR = ∇∆ρ + ∇∆T + ∇∆I + ∇∆ε ρ
(3)
λ∇∆ϕ = ∇∆ρ + ∇∆T − ∇∆I + λ∇∆N + ∇∆ε ϕ
(4)
where ∇∆(·) denotes the DD operator; PR and ϕ are code and carrier phase observations, respectively;
ρ is the geometric distance in units of meters between the receiver and satellite; T and I denote
the tropospheric and ionospheric delay, respectively; λ and N are carrier phase wavelength and
integer ambiguity, respectively; ε ρ and ε ϕ are the measurement noise and un-modeled residual error
(multipath, etc.) of code and carrier phase observations, respectively. Specifically, for GLONASS carrier
phase observations, λ∇∆ϕ and λ∇∆N could be written as follows:
λ∇∆ϕ = λk ∆ϕk − λr ∆ϕr
(5)
λ∇∆N = λk ∆N k − λr ∆N r = λk ∇∆N kr + (λk − λr )∆N r
(6)
where the superscripts k and r denote the non-reference and reference satellite, respectively; ∆(·)
represents the single-differenced (SD) operator. In Equation (6), the SD ambiguity can be estimated
with the SD pseudo-range observations [32]. As the observation of low-elevation satellite is generally
noisier, the elevation-dependent weight model is adopted to determine the a priori variance for GNSS
observations [33]:
(
σ02 , ele ≥ π/6
2
σ =
(7)
(σ0 / sin(ele))2 , else
where σ0 is the un-differenced observation standard deviation (STD) at zenith, and ele is the
elevation angle.
For RTK positioning of short baseline, the tropospheric term T and ionospheric term I in
Equations (3) and (4) can be neglected. The remaining unknown parameters that need to be estimated
are the baseline increment vector and integer ambiguities. For single-frequency GPS/BDS/GLONASS
RTK, the linearized DD observation with unknown parameters can be described in matrix form
as follows:
"
# "
#"
# "
#
ερ
H 0n × n
δpr
∇∆PR − ∇∆r0
=
−
(8)
εϕ
H
Λ
∇∆N
λ∇∆ϕ − ∇∆r0
with
iT
H G HC H R
Λ = diag ΛG ΛC Λ R
H=
N=
h
h
NG
NC
NR
iT
(9)
(10)
(11)
where n is the total number of DD ambiguities; δpr is the baseline increment vector; ∇∆r0 denotes the
computed DD ranges with approximate rover coordinates and satellite positions; the superscripts ‘G’,
‘C’, ‘R’ represent GPS, BDS and GLONASS, respectively; H is the design matrix containing the relative
receiver-satellite geometry; Λ is the diagonal matrix that contains the wavelengths of f 1 frequencies
from the GPS, BDS and GLONASS satellites.
For the tightly-coupled integration, the measurement model in the discrete-time form can be
expressed as
Zk = Hk Xk + Vk
(12)
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where Hk is the design matrix, and Zk is the measurement vector with the following formula:
"
Zk =
#
∇∆ρ̂ I NS − ∇∆PR,GNSS
∇∆ρ̂ I NS − λ∇∆ϕGNSS
(13)
where the subscripts “INS” and “GNSS” represent the INS-predicted ranges and GNSS observations,
respectively. The INS-predicted ranges are calculated using the INS-updated position and satellite positions.
Since the IMU measurement center and the GNSS antenna phase center cannot be installed at
the same place, the lever-arm offset should be considered when fusing the two different kinds of data.
The lever-arm correction can be described in the e-frame as:
reGNSS = reI MU + Cen Cnb `bGNSS
(14)
where reGNSS and reI MU are position coordinates in the e-frame for the GNSS rover receiver and IMU
center, respectively; Cen is the rotation matrix form the n-frame to the e-frame; Cnb is the rotation matrix
form the b-frame to the n-frame; `bGNSS denotes the lever-arm offset vector in the b-frame. After the
error perturbation analysis, the position error term between the IMU and GNSS antenna can be written
as [34]:
h
i
δreGNSS ≈ δreI MU + Cen Cnb `bGNSS × ψ
(15)
where × denotes the cross-product operator. Considering that the position error term in the system
state vector is expressed in the n-frame, the final design matrix Hk in (12) can be derived from (3), (4),
(9), (13), and (15) as:
h
h
i
i
Hk = H·Cen 0n×3
H·Cen · Cnb `bGNSS ×
0n×12
(16)
2.1.3. Single-Epoch Ambiguity Resolution with Inertial Aiding
Differential carrier-phase based centimeter-level positioning relies on the correct integer ambiguity
resolution, but there are still challenges for reliable ambiguity resolution in urban environments,
especially for single-frequency RTK. For the tightly-coupled RTK/INS integration, a priori information
from INS can be used to reduce the search space of integer ambiguities, and then improve the AR
reliability [35]. In this research, the INS predicted position information is used as a virtual measurement.
Assuming that the observation equation is linearized at the INS predicted position, and then the virtual
observation equation from INS predicted position can be written as:
ε I NS =
h
I3 × 3
03 × n
i
"
δpr
∇∆N
#
− 03×1
(17)
where I3×3 is the identity matrix. Combining the above equation and (8), the unknown parameters
and their corresponding covariance can be obtained through the weighted least-squares estimation:
T
B WB
"
δpr
∇∆N
#
= BT WL
(18)
with:


B=
H
H
I3×3

0n × n

λIn×n , W = diag Wρ
03×n

Wϕ
WINS

∇∆PR − ∇∆r0


, L =  λ∇∆ϕ − ∇∆r0 
03×1
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where Wρ , Wϕ, and WINS are the inverse of the covariance matrices of the code, carrier phase, and INS
virtual measurements, respectively. Further, the coefficient matrix of the normal Equation (18) can be
derived as follows:
"
#
HT Wρ H + HT WϕH + WINS λHT Wϕ
T
B WB =
(19)
λWρ
λ 2 Wρ
Generally, the strength of the normal equation is weak if the code and carrier phase observations
are used only because the code measurements are imprecise. With the term WINS in the top-left corner
of the above equation, the strength will be enhanced and then the accuracy of the float solution can be
improved. Since the precision of INS predicted position is high in the short-term period, this virtual
measurement will definitely improve the AR performance.
Once the real-valued ambiguities and their corresponding variance-covariance (VC) matrix are
obtained, the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method is performed
to obtain the integer-valued ambiguities [36]. Then, the ambiguity validation test is performed to
determine whether the searched ambiguities should be accepted or not. The validation test is very
crucial, as incorrect ambiguity resolution will lead to unacceptable positioning result. In practice,
the data-driven ratio-test and model-driven bootstrapped success rate are used together for ambiguity
validation [37,38], which will be adopted in this research as well.
2.2. Innovation-Based Outlier-Resistant Ambiguity Resolution and Kalman Filtering Strategy
In order to keep the optimality of the system state, faulty measurements should be excluded before
the Kalman updates. In urban environments, the code and carrier phase observations are susceptible
to multipath errors, especially for the code measurements. In the tightly-coupled RTK/INS integration,
large code multipath errors will bias the estimates of the float ambiguities dramatically and then reduce
the probability of correctly fixing the ambiguities. To reduce the effects of measurement outlier on the
parameter estimation, the observation variance should be inflated properly for those with outliers.
Under normal operating condition, the measurement innovation sequence of Kalman filtering
should be normally distributed with zero mean. When discrepancies in innovation sequence are found,
the faulty measurements are detected. In this research, the following innovation-based inflating factor
γii is constructed to model the measurements [39]:
νek,i ≤ k0
1,
e
ν
| k,i |
k1 −k0
γii =
×
, k0 < νek,i ≤ k1
k
e
0
k
−
ν

1 | k,i |


∞, νek,i > k1




(20)
where k0 and k1 are two constants, usually chosen as 2.0–3.0 and 4.5–8.5, respectively; νek,i is the i-th
normalized measurement innovation at epoch k, which can be written as:
νek,i = q
Vk,i
(Hk Pk,k−1 HkT + Rk )i,i
(21)
where Vk,i is the i-th measurement innovation at epoch k; Pk,k−1 is the time update of covariance matrix
in the Kalman filtering; Rk is the measurement covariance matrix. In Equation (20), γii is equal to
one if the measurement is normal; when the measurement is outlying, γii is infinite, i.e., this gross
measurement will be eliminated; when the normalized value is between k0 and k1 , the effect of this
measurement on the parameter estimation will be reduced.
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Since the DD measurements are correlated mathematically, the inflated measurement covariance
matrix should preserve the original correlation. Therefore, the following equivalent covariance matrix
should be used in the measurement update:
γ11 σ12

..
Rk = 
.
γn1 σn1


· · · γ1n σ1n

..
..

.
.
2
· · · γnn σn
(22)
γii γ jj
(23)
with:
γij =
p
where γij is the inflating factor of the covariance at i-th row and j-th column.
In the ambiguity resolution process, the outlier-resistant scheme will be applied to model the
code measurements so that the effects of the abrupt measurement errors on the float ambiguities can
be eliminated. In the measurement update stage of Kalman filter, the outlier-resistant filtering will be
activated again to model the code or ambiguity-fixed carrier phase observations in case of wrongly
accepted ambiguities. With the outlier-resistant ambiguity estimation and filtering, the unbiased float
ambiguities and system states can be achieved; otherwise, the system states may become biased or
even make the integration filter diverged. Obviously, the two-step outlier-resistant scheme is easy to
implement in the framework of RTK/INS integration and little extra computation is required.
2.3. Overview of Multi-GNSS RTK/INS Tightly-Coupled Integration with Innovation-Based FDE
According to the description above, an overview of the proposed multi-GNSS RTK/INS integration
with innovation-based FDE is shown in Figure 1. After the system initialization, the compensated
raw IMU outputs are used in the INS mechanization to provide high data-rate position, velocity and
attitude (PVA) information. In the process of INS mechanization, the second-order coning correction
term, the rotational and sculling motion effect are considered to weaken their influences on the attitude
and velocity update [40,41].
Once the multi-GNSS data from base and rover receivers are available, the double-differenced
code and carrier phase observations will be formed within the individual GNSS system. Then,
the outlier-resistant ambiguity resolution with INS aiding will be used to resist the code measurement
outliers. The LAMBDA method is employed for ambiguity resolution, and a validation process will be
used to confirm the correctness of the fixed ambiguities. If the searched ambiguities pass the validation
test, the precise ambiguity-fixed carrier phase measurements will be used to update the tightly-coupled
integration filter; otherwise, the code observations should be used at this epoch. The measurement
inputs of the integration filter is the difference between INS-derived DD ranges and DD code or
carrier-phase observations. In the EKF update phase, the outlier-resistant filtering is applied again to
model the potential code measurement outlier or the ambiguity-fixed carrier phase measurement in
case the incorrectly-fixed ambiguities are accepted. Since the output rate of IMU data is much higher
than that of GNSS data, the standalone INS mode will process the IMU data epoch-by-epoch when the
GNSS data is not available.
Finally, the estimated IMU sensor errors including the biases and scale factors of the gyroscope
and accelerometer are fed back to compensate the errors of raw IMU data. Meanwhile, the navigation
solution provided by INS mechanization is updated with the estimated PVA errors from the
integration filter.
measurement in case the incorrectly-fixed ambiguities are accepted. Since the output rate of IMU data
is much higher than that of GNSS data, the standalone INS mode will process the IMU data epochby-epoch when the GNSS data is not available.
Finally, the estimated IMU sensor errors including the biases and scale factors of the gyroscope
and accelerometer are fed back to compensate the errors of raw IMU data. Meanwhile, the navigation
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by INS mechanization is updated with the estimated PVA errors from the8 of 21
integration filter.
n
PINS
∇Δϕ
∇ΔP
Figure
1. Implementation
innovation-based outlier-resistant
resolution
and and
Kalman
Figure
1. Implementation
of of
thethe
innovation-based
outlier-resistantambiguity
ambiguity
resolution
Kalman
filtering for the tightly-coupled integration of multi-GNSS RTK and MEMS-IMU.
filtering for the tightly-coupled integration of multi-GNSS RTK and MEMS-IMU.
3. Field Test Description and Data Processing Strategy
3. Field Test Description and Data Processing Strategy
In order to evaluate the performance of the proposed robust single-frequency multi-GNSS
In
order to evaluate
the performance
of the proposed
robusttest
single-frequency
RTK/MEMS-IMU
integration
in urban environments,
a field vehicular
was carried out inmulti-GNSS
Wuhan
City, China on integration
12 June 2015.in
The
trajectory,
as shown in
2a, is about
7.0was
km in
the north-south
RTK/MEMS-IMU
urban
environments,
a Figure
field vehicular
test
carried
out in Wuhan
7.2 km
in the
east-west
direction.
A range
of scenarios
was incorporated
in north-south
the test
City, direction
China onand
12 June
2015.
The
trajectory,
as shown
in Figure
2a, is about
7.0 km in the
route,
including
relatively
open-sky
condition,
under
trees
and
overpasses,
and
sub-dense
direction and 7.2 km in the east-west direction. A range of scenarios was incorporated in theurban
test route,
including relatively open-sky condition, under trees and overpasses, and sub-dense urban canyon
with high buildings (Figure 2b). Figure 2c shows the test platform and equipment used in this paper.
The inertial data from MEMS grade IMU (POS1100), which consists of three MEMS gyroscopes and
three quartz accelerometers, was used in this research. The tactical-grade IMU (POS310) with three
fiber optic gyroscopes (FOGs) was used to provide the reference solutions. Both of the two IMUs are
provided by Wuhan MaiPu Space Time Technology Company (Wuhan, China), and their output rate
are 200 Hz. Their main performance specifications are shown in Table 1.
A Trimble NetR9 multi-GNSS receiver (Sunnyvale, CA, USA), as the reference station, was located
on the rooftop of the GNSS Research Center at Wuhan University to collect raw GNSS data. The rover
receiver (Trimble BD982 OEM board) was fixed on the vehicle during the driving test. The lever
arm offset between the phase center of the rover GNSS antenna and the IMU measuring center was
accurately measured in advance. In the experiment, the sampling rate of multi-GNSS data in the base
and rover station was set to 1 Hz. As shown in Figure 2d, the field test took about 45 min and the
vehicle stayed static in the first several minutes.
In the data processing, broadcast ephemeris are used to provide satellite clocks and orbits for GPS,
BDS, and GLONASS. As the baseline separation is less than 7 km, the tropospheric and ionospheric
delay are not considered. Empirically, a priori standard deviations for the un-differenced GPS, BDS,
and GLONASS carrier phase observation at the zenith are set to 3 mm. The values for code observations
of GPS, BeiDou MEO/IGSO, BeiDou GEO, and GLONASS satellites are 0.35 m, 0.35 m, 0.5 m, and 0.5 m,
respectively. In terms of the ambiguity validation, the predefined success rate is set to 0.99, and the
critical ratio value is 3.0 for the GPS-only and 2.0 for the combined GNSS system. The main reason why
smaller ratio value is applied to the combined GNSS system is that it provides much better satellite
geometry and model strength for reliable AR than the single GNSS system [42].
located on the rooftop of the GNSS Research Center at Wuhan University to collect raw GNSS data.
The rover receiver (Trimble BD982 OEM board) was fixed on the vehicle during the driving test. The
lever arm offset between the phase center of the rover GNSS antenna and the IMU measuring center
was accurately measured in advance. In the experiment, the sampling rate of multi-GNSS data in the
base
station
was set to 1 Hz. As shown in Figure 2d, the field test took about 45 min9 and
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the vehicle stayed static in the first several minutes.
(a)
(b)
VN
VE
VD
Velocity (m/s)
10
5
0
-5
-10
-15
2500
3000 3500 4000 4500 5000
GPS Time - 43,5000 (sec)
(c)
5500
(d)
Figure
2. Test
description of
the land
land vehicle
vehicle experiment
China. (a)
Figure 2.
Test description
of the
experiment on
on 12
12 June
June 2015
2015 in
in Wuhan,
Wuhan, China.
(a) Test
Test
trajectory;
(b)
typical
scenarios;
(c)
platform
and
equipment;
and
(d)
vehicle
speed
in
the
field
test.
trajectory; (b) typical scenarios; (c) platform and equipment; and (d) vehicle speed in the field test.
Table 1. Performance specifications of the IMU sensors in the experiment.
Table 1. Performance specifications of the IMU sensors in the experiment.
IMU
Grade
IMU
Grade
POS310
Tactical
POS310
Tactical
POS1100
MEMS
POS1100
MEMS
Dimensions (mm)
Dimensions (mm)
151 × 120 × 101
151
× 120
81.8
× 68××101
70
81.8 × 68 × 70
Bias
Random Walk
Bias
Random Walk Velocity
Angular
Gyro.
Acce.
Gyro.
Acce.
(°/ )
(mGal) Angular
(°/√
) Velocity
( √/ /√ )
√
(◦ /h)
(mGal)
(◦ / h)
(m/s/ h)
0.5
300
0.05
0.10
0.510.0
300
0.05
0.10
1500
0.33
0.18
10.0
1500
0.33
0.18
In the data processing, broadcast ephemeris are used to provide satellite clocks and orbits for
4.
Results
GPS, BDS,and
andDiscussion
GLONASS. As the baseline separation is less than 7 km, the tropospheric and
4.1. Satellite Availability
The satellite availability in sub-dense urban environments is investigated at first for the GPS (G),
BDS (C) and GLONASS (R). As shown in Figure 3, the PRN numbers between 1 and 32 are for the
GPS satellites, between 33 and 67 for the BDS, and between 68 and 91 for the GLONASS. Currently,
the constellations of GPS and GLONASS consist of MEO satellites only, whereas the BDS constellation
is comprised of GEO, IGSO, and MEO satellites. In this field test, there are four GEO satellites (C33,
C35, C36, and C37) and five IGSO satellites (C38–C42) tracked, but no MEO satellites were tracked.
It can be seen that some satellites’ tracking conditions are very poor due to the high buildings and
overpasses in the urban environments wherein the longest partial GNSS outage lasted about 2 min
with only 1–2 satellites tracked. Obviously, the multi-GNSS provides many more available satellites
than the GPS only, which will definitely bring benefits for RTK positioning in urban environments.
BDS (C) and GLONASS (R). As shown in Figure 3, the PRN numbers between 1 and 32 are for the
GPS satellites, between 33 and 67 for the BDS, and between 68 and 91 for the GLONASS. Currently,
the constellations of GPS and GLONASS consist of MEO satellites only, whereas the BDS
constellation is comprised of GEO, IGSO, and MEO satellites. In this field test, there are four GEO
satellites (C33, C35, C36, and C37) and five IGSO satellites (C38–C42) tracked, but no MEO satellites
were tracked. It can be seen that some satellites’ tracking conditions are very poor due to the high
Remote Sens. 2018,
10, 205
10 of 21
buildings
and overpasses in the urban environments wherein the longest partial GNSS outage lasted
about 2 min with only 1–2 satellites tracked. Obviously, the multi-GNSS provides many more
available satellites than the GPS only, which will definitely bring benefits for RTK positioning in
The number
of satellites and the corresponding position dilution of precision (PDOP) of GPS,
urban environments.
◦ cut-off(PDOP)
number
of satellites
the corresponding
of GPS,
GPS + BDS (G The
+ C),
and GPS
+ BDSand
+ GLONASS
(G +position
C + R) dilution
with a of
15precision
elevation
angle in the
GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) with a 15° cut-off elevation angle in the
rover station are depicted in Figure 4a,b, respectively.
rover station are depicted in Figure 4a,b, respectively.
It can be seen
4 that
thethe
satellite
and
PDOP
can
be improved
It can from
be seenFigure
from Figure
4 that
satelliteavailability
availability and
PDOP
can be
improved
visibly byvisibly by
using the combined
GPS/BDS
and
GPS/BDS/GLONASS
systems.
According
to
the
from
using the combined GPS/BDS and GPS/BDS/GLONASS systems. According to the statisticsstatistics
from
Figure
4,
the
average
number
of
satellites
of
GPS,
GPS
+
BDS,
and
GPS
+
BDS
+
GLONASS
are
6.0,
Figure 4, the average number of satellites of GPS, GPS + BDS, and GPS + BDS + GLONASS are 6.0, 12.3,
12.3, and 16.5, and the corresponding average PDOPs are 3.12, 2.05, and 1.71, respectively. Compared
and 16.5, and
the corresponding average PDOPs are 3.12, 2.05, and 1.71, respectively. Compared with
with the GPS, the PDOP improvements of the multi-GNSS are about 34.3–45.2%. Obviously, the
the GPS, the
PDOP
improvements
the multi-GNSS
are about are
34.3–45.2%.
Obviously,
the average
average
number
of available of
satellites
in urban environments
less than that
in open-sky
number ofconditions.
available satellites in urban environments are less than that in open-sky conditions.
90
80
Satellite PRN number
70
GLONASS: [68, 91]
BeiDou: [33, 67]
GPS: [1, 32]
60
50
40
30
20
10
0
3000
3500
4000
4500
GPS Time - 43,5000 (sec)
5000
Remote Sens. 2018, 10, x FOR PEER REVIEW
10 of 22
Figure 3. Satellite availability of GPS (1 ≤ PRN ≤ 32), BeiDou (33 ≤ PRN ≤ 67), and GLONASS
Figure 3. Satellite availability of GPS (1 ≤ PRN ≤ 32), BeiDou (33 ≤ PRN ≤ 67), and GLONASS (68
(68 ≤ PRN ≤ 91) with a 15◦ cut-off elevation angle.
≤ PRN ≤ 91) with a 15° cut-off elevation angle.
GPS
G+C
GPS
G+C+R
25
G+C
G+C+R
30
20
PDOP
Number of satellites
30
15
10
20
10
5
0
2500
3000
3500
4000
4500
GPS Time - 43,5000 (sec)
5000
3000
3500
4000
4500
GPS Time - 43,5000 (sec)
(a)
5000
(b)
Figure 4. The number of available satellites and PDOP of GPS (G), GPS/BDS (G + C), and
Figure 4. The number of available satellites and PDOP of GPS (G), GPS/BDS (G + C), and GPS/BDS/
GPS/BDS/GLONASS (G + C + R) with a 15° cut-off elevation angle in the rover station. (a) Number of
GLONASS (G + C + R) with a 15◦ cut-off elevation angle in the rover station. (a) Number of satellites;
satellites; and (b) PDOP.
and (b) PDOP.
4.2. Multi-GNSS RTK/INS Integration with Innovation-Based FDE
4.2. Multi-GNSS RTK/INS Integration with Innovation-Based FDE
One of the key issues for GNSS-based high-accuracy positioning in urban environments is the
fault
detection
exclusion
because the GNSS
observations
are more likely
to contain
measurement
One of
the keyand
issues
for GNSS-based
high-accuracy
positioning
in urban
environments
is the
outliers.
As
the
code
measurements
can
have
very
large
multipath
error,
they
should
be
detected
and
fault detection and exclusion because the GNSS observations are more likely to contain
measurement
excluded in the data processing. As stated previously, the measurement innovations of Kalman
outliers.
As the code measurements can have very large multipath error, they should be detected
filtering should be distributed with zero mean and there will be discrepancies for those
and excluded in the data processing. As stated previously, the measurement innovations of Kalman
measurements with outliers. Figure 5 depicts the code innovations for all available GPS + BDS +
filtering
should be distributed with zero mean and there will be discrepancies for those measurements
GLONASS satellites with a 15° cut-off elevation angle. It can be seen that very large code
with outliers.
Figure
5 depicts
the code
innovations
forare
alldetected
availableinGPS
+ BDS +filter’s
GLONASS
satellites
measurement
outliers
(shown
in three
red circles)
the Kalman
innovation
sequence of DD code observation. A zoom-in window is given to show the spread of those code
innovations with small magnitudes. It shows that most of the code innovations are within ±2 m, but
there are still small discrepancies. There is no doubt that these code measurements with abrupt
outliers will affect ambiguity resolution and positioning accuracy if no effective measures are taken.
4
Figure 4. The number of available satellites and PDOP of GPS (G), GPS/BDS (G + C), and
GPS/BDS/GLONASS (G + C + R) with a 15° cut-off elevation angle in the rover station. (a) Number of
satellites; and (b) PDOP.
4.2. Multi-GNSS RTK/INS Integration with Innovation-Based FDE
One of the key issues for GNSS-based high-accuracy positioning in urban environments is the
Remote Sens. 2018,
10,detection
205
fault
and exclusion because the GNSS observations are more likely to contain measurement
11 of 21
outliers. As the code measurements can have very large multipath error, they should be detected and
excluded in the data processing. As stated previously, the measurement innovations of Kalman
filteringelevation
should be angle.
distributed
with
there
willcode
be discrepancies
for those
with a 15◦ cut-off
It can
bezero
seenmean
thatand
very
large
measurement
outliers (shown
measurements with outliers. Figure 5 depicts the code innovations for all available GPS + BDS +
in three red circles)
are detected in the Kalman filter’s innovation sequence of DD code observation.
GLONASS satellites with a 15° cut-off elevation angle. It can be seen that very large code
A zoom-in window
is given
show
of are
those
codein innovations
with
small magnitudes.
measurement
outliers to
(shown
in the
threespread
red circles)
detected
the Kalman filter’s
innovation
of DD
observation.
A zoom-in
window is
show
the spread
of those
code
It shows thatsequence
most of
thecode
code
innovations
are within
±given
2 m, tobut
there
are still
small
discrepancies.
innovations with small magnitudes. It shows that most of the code innovations are within ±2 m, but
There is no doubt
that these code measurements with abrupt outliers will affect ambiguity resolution
there are still small discrepancies. There is no doubt that these code measurements with abrupt
and positioning
accuracy
no effective
measures
are taken.
outliers
will affectifambiguity
resolution
and positioning
accuracy if no effective measures are taken.
4
2
0
-2
-4
20
Code Innovation (m)
Zoom in
0
-20
-40
Large Outlier
-60
-80
3000
3500
4000
4500
GPS Time - 43,5000 (sec)
5000
Figure 5. Kalman filter’s innovation sequence of double-differenced code observation for all available
GPS + BDS + GLONASS satellites with a 15◦ cut-off elevation angle. Each color denotes a different
satellite pair. The points in three red circles are very large code measurement outliers.
Remote Sens. 2018, 10, x FOR PEER REVIEW
11 of 22
Figure 6 givesFigure
an example
about
the effects
code measurement
outlier
the estimation of float
5. Kalman filter’s
innovation
sequence of
of double-differenced
code observation
for allon
available
GPS + BDS + GLONASS satellites with a 15° cut-off elevation angle. Each color denotes a different
ambiguities. It shows
the ambiguity biases with and without innovation-based FDE in the presence
satellite pair. The points in three red circles are very large code measurement outliers.
of one code measurement outlier on a GLONASS satellite whose code innovation is –19.8 m (given
Figure 6 gives
example about
the effects
of code as
measurement
outlier onbetween
the estimation
by the integration filter).
The an
ambiguity
bias
is defined
the difference
theofestimated float
float ambiguities. It shows the ambiguity biases with and without innovation-based FDE in the
ambiguity and presence
its trueofinteger
value. If the
ambiguity
biassatellite
is closer
zero,
it is more
one code measurement
outlier
on a GLONASS
whoseto
code
innovation
is –19.8likely to fix the
m
(given
by
the
integration
filter).
The
ambiguity
bias
is
defined
as
the
difference
between
the
ambiguity correctly. It can be seen that the ambiguity biases are within 0.15 cycles, except
the satellite
estimated float ambiguity and its true integer value. If the ambiguity bias is closer to zero, it is more
with the outlier likely
(about
0.26
cycles),
when
the
innovation-based
FDE
strategy
is
applied.
By
comparison,
to fix the ambiguity correctly. It can be seen that the ambiguity biases are within 0.15 cycles,
except theare
satellite
withlarger
the outlier
(about 0.26
cycles),
when
innovation-based
FDE strategy
is is even more
the ambiguity biases
much
without
FDE
and
thethemaximum
ambiguity
bias
applied. By comparison, the ambiguity biases are much larger without FDE and the maximum
than 0.6 cycles, ambiguity
which will
prevent correct ambiguity fixing.
bias is even more than 0.6 cycles, which will prevent correct ambiguity fixing.
0.7
Ambiguity bias (cycle)
0.6
0.5
With FDE
Without FDE
Satellite with outlier
0.4
0.3
0.2
0.1
0
3 14 16 26 29 32 33 37 38 39 40 41 42 69 75 77 78 79 87
Satellite PRN number
Figure 6. Ambiguity biases with and without innovation-based FDE in the presence of one code
Figure 6. Ambiguity
biases
and without
FDE
in the
of one code
measurement
outlierwith
on a GLONASS
satellite innovation-based
at epoch 439,618 s (The PRN
number
is 69presence
with an
elevation
and the DDsatellite
code innovation
given 439,618
by the integration
is −19.8
m). is 69 with an elevation
measurement outlier
onofa21.4°,
GLONASS
at epoch
s (Thefilter
PRN
number
of 21.4◦ , and theInDD
innovation
given
by the integration
filter
is presence
−19.8 m).
ordercode
to verify
the feasibility
of high-accuracy
positioning
in the
of measurement
outliers, Figure 7 shows the root-mean-square (RMS) of code innovations of the tightly-coupled
GPS/BDS/GLONASS/INS integration and the AR fixing differences with and without innovationbased FDE. The epochs whose AR fixing difference is equal to zero (shown in red) means that the
fixing states of these epochs are the same, i.e., both fixed or float. The epochs that can be fixed only
with FDE are depicted with green circles. It can be seen that the ambiguity-fixed solution can be
obtained in some cases even though a large code measurement outlier is present. Clearly, the
innovation-based FDE strategy is effective to resist the code measurement outliers and, thus, improve
the ambiguity resolution performance.
Remote Sens. 2018, 10, 205
12 of 21
In order to verify the feasibility of high-accuracy positioning in the presence of measurement
outliers, Figure 7 shows the root-mean-square (RMS) of code innovations of the tightly-coupled
GPS/BDS/GLONASS/INS integration and the AR fixing differences with and without innovation-based
FDE. The epochs whose AR fixing difference is equal to zero (shown in red) means that the fixing
states of these epochs are the same, i.e., both fixed or float. The epochs that can be fixed only with FDE
are depicted with green circles. It can be seen that the ambiguity-fixed solution can be obtained in
some cases even though a large code measurement outlier is present. Clearly, the innovation-based
FDE strategy is effective to resist the code measurement outliers and, thus, improve the ambiguity
resolution performance.
Since the ambiguity is resolved in the single-epoch mode, the integrated filter will be insensitive
to the frequent cycle slips in urban environments. In the filter’s measurement update stage,
the outlier-resistant Kalman filtering strategy will be applied for the code or ambiguity-fixed
carrier-phase measurements. For carrier-phase based high-accuracy positioning, the ambiguity-fixed
Remote Sens. 2018, 10, x FOR PEER REVIEW
12 of 22
carrier phase residual can indicate the correctness of ambiguity resolution and positioning accuracy.
Figures 8 and 9 show
18the DD carrier phase residual and the corresponding RMS of all the available
satellites of the tightly-coupled
GPS/BDS/GLONASS/INS integration,
respectively.
RMS of code
innovation
Remote Sens. 2018, 10, x FOR PEER REVIEW
12 of 22
Both fixed or float
(with and without FDE)
RMSFixed
of codeonly
innovation
with FDE
18
14
16
12
RMS of code innovation (m)
and AR fixing difference
RMS of code innovation (m)
and AR fixing difference
16
10
12
8
10
6
8
4
2
Both fixed or float
(with and without FDE)
Fixed only with FDE
14
6
4
2
0
0
3000 3000
3500
4000
3500
4000
45004500
GPSTime
Time --43,5000
(sec)
GPS
43,5000
(sec)
5000
5000
Figure 7. RMS of code innovations for the tightly-coupled GPS/BDS/GLONASS/INS integration and
Figure 7. RMS of code innovations for the tightly-coupled GPS/BDS/GLONASS/INS integration and
the AR fixing
difference with
without
FDE.
Figure 7. RMS of code
innovations
forandthe
tightly-coupled
GPS/BDS/GLONASS/INS integration and
the AR fixing difference with and without FDE.
the AR fixing difference with and without FDE.
0.06
L1 Carrier Phase Residual (m)
L1 Carrier Phase Residual (m)
0.06
0.04
0.04
0.02
0.02
0
0
-0.02
-0.04
-0.02
-0.04
-0.06
-0.08
-0.06
3000
3500
4000
4500
GPS Time - 43,5000 (sec)
5000
Figure 8. DD carrier phase residual for the tightly-coupled GPS/BDS/GLONASS/INS integration.
-0.08
Each color denotes a different satellite pair. (Measurement noise, multipath, and atmospheric delay
are included).
3000
3500
4000
4500
5000
GPS
- 43,5000
(sec) are below 10 cm for all the
It can be seen from Figure 8 that the
DDTime
carrier
phase residuals
available satellites and most of them are within ±2 cm. The obvious discrepancies of some residuals
Figure
8. be
DD
carrier
for the tightly-coupled
GPS/BDS/GLONASS/INS
may
mainly
duephase
to the residual
un-modeled
effects. The corresponding
RMSs of carrierintegration.
phase
Figure 8. DD carrier
phase
residual
for themultipath
tightly-coupled
GPS/BDS/GLONASS/INS
integration.
Each residuals
color denotes
a different
satellite
(Measurement
multipath,
and
atmospheric
are below
20 mm, except
forpair.
one BDS
IGSO satellitenoise,
and one
GLONASS
satellite
(shown indelay
Each colorare
denotes
a
different
satellite
pair.
(Measurement
noise,
multipath,
and
atmospheric
delay
Figure 9). The relatively large residuals of these two satellites may be caused by low-elevation
included).
are included). multipath.
It can be seen from Figure 8 that the DD carrier phase residuals are below 10 cm for all the
available satellites and most of them are within ±2 cm. The obvious discrepancies of some residuals
may be mainly due to the un-modeled multipath effects. The corresponding RMSs of carrier phase
residuals are below 20 mm, except for one BDS IGSO satellite and one GLONASS satellite (shown in
Figure 9). The relatively large residuals of these two satellites may be caused by low-elevation
multipath.
Remote Sens. 2018, 10, 205
13 of 21
It can be seen from Figure 8 that the DD carrier phase residuals are below 10 cm for all the available
satellites and most of them are within ±2 cm. The obvious discrepancies of some residuals may be
mainly due to the un-modeled multipath effects. The corresponding RMSs of carrier phase residuals
are below 20 mm, except for one BDS IGSO satellite and one GLONASS satellite (shown in Figure 9).
The relatively large residuals of these two satellites may be caused by low-elevation multipath.
Remote Sens. 2018, 10, x FOR PEER REVIEW
13 of 22
RMS of carrier phase residual (mm)
30
25
20
15
10
5
0
3 14 16 26 29 31 32 33 35 36 37 38 39 40 41 42 69 75 77 78 79 87 88
Satellite PRN number
Figure 9. RMS of the DD carrier phase residual for the tightly-coupled GPS/BDS/GLONASS/INS
integration.
Figure 9. RMS of the
DD carrier phase residual for the tightly-coupled GPS/BDS/GLONASS/
INS integration. 4.3. Single-Epoch Ambiguity Resolution and Positioning
In order to assess the AR and positioning performance of the single-frequency multi-GNSS
RTK/INS tightly-coupled integration algorithm in urban environments, the reference trajectory was
4.3. Single-Epoch Ambiguity
Resolution and Positioning
generated firstly by using the measurements of a tactical-grade POS310 IMU and dual-frequency
GPS/BDS/GLONASS data in the tightly-coupled RTK/INS integration mode with Rauch-Tung-
In order to assess
the
and[43].
positioning
performance
ofenvironments,
the single-frequency
multi-GNSS
Striebel
(RTS)AR
smoothing
Since frequent loss-of-lock
occurs in urban
we focus on
the single-epoch ambiguity resolution and positioning performance in this research. This method has
RTK/INS tightly-coupled
integration algorithm in urban environments, the reference trajectory
the advantage that the positioning results are insensitive to the cycle slips. The ambiguity resolution
and positioning
performance
of singleand dual-frequency RTK
and multi-GNSS) willPOS310 IMU and
was generated firstly
by using
the
measurements
of(single
a GPS
tactical-grade
also be investigated and their results will be compared with the solution of the tightly-coupled singledual-frequency GPS/BDS/GLONASS
thethetightly-coupled
RTK/INS
integration mode with
frequency RTK/INS integration.data
In orderin
to show
difference of RTK with and
without INS aiding,
the positioning results of the tightly-coupled RTK/INS integration are excluded at those epochs when
Rauch-Tung-Striebelthe
(RTS)
smoothing [43]. Since frequent loss-of-lock occurs in urban environments,
GNSS-only solution is not available (e.g., the number of satellites is less than four for GPS).
We first evaluate
the AR and positioning
performance
GPS, GPS + BDS (G
+ C), and GPS
we focus on the single-epoch
ambiguity
resolution
andof the
positioning
performance
in this research.
+ BDS + GLONASS (G + C + R) with a customary cut-off elevation angle of 15°. Figure 10 shows the
This method has the
advantage
that
the
positioning
results
are
insensitive
to
the cycle slips.
time series of position difference in the north, east, and vertical directions for single-frequency RTK
(GPS, G + C, G + C + R, top two rows), dual-frequency RTK (GPS, G + C, G + C + R, middle two rows),
The ambiguity resolution
and positioning performance of single- and dual-frequency RTK (single GPS
and single-frequency RTK/INS integration (GPS, G + C, G + C + R, bottom two rows). The correctlyfixedalso
solutions,
solutions,
float solutions
are shown
red, and grey,with the solution of
and multi-GNSS) will
be incorrectly-fixed
investigated
andandtheir
results
will inbegreen,
compared
respectively. The zoom-in windows are provided for both the horizontal (north, east) scatterplots and
the tightly-coupled single-frequency
RTK/INS
integration.
Insolutions.
order The
to correctness
show the
vertical (down) time series to
show the details
of the correctly-fixed
of difference of RTK
ambiguity fixing is checked according to the positioning difference between the fixed solution and
with and without INS
aiding,
the
positioning
results
of
the
tightly-coupled
RTK/INS
integration are
the reference solution. If the position difference is larger than 0.1 m in the north or east components,
or 0.15 m
in the vertical
direction, the integer
ambiguitiesis
willnot
be considered
as incorrectly
excluded at those epochs
when
the GNSS-only
solution
available
(e.g., fixed.
the number of satellites is
It can be seen from Figure 10 that the AR and positioning performance of single-frequency GPSless than four for GPS).
only RTK is very poor, indicating that it is difficult to use single-frequency GPS RTK for highaccuracy kinematic positioning in urban environments. The addition of BDS increases the AR
We first evaluate
the ARdramatically,
and positioning
performance
the GPS,
+ BDS
(G + C), and GPS
performance
and the inclusion
of GLONASSof
together
further GPS
improves
the
withathecustomary
single-frequency cut-off
GPS RTK, elevation
the dual-frequency
GPS RTK
+ BDS + GLONASS performance.
(G + C +Compared
R) with
angle
of can
15◦ . Figure 10 shows
obviously improve the positioning performance due to the doubled observations on another
the time series of position
difference
inis worse
the than
north,
east, andmulti-GNSS
vertical
directions
for single-frequency
frequency, but
its performance
the single-frequency
RTK.
Therefore, better
satellite availability from multi-GNSS brings benefits for single-frequency RTK in urban
RTK (GPS, G + C, Genvironments.
+ C + R,Significantly,
top twotherows),
dual-frequency
RTK
(GPS,
G
+
C,
AR and positioning performance of dual-frequency multi-GNSS G + C + R, middle
RTK
are
further
improved
with
a
substantial
decrease of ambiguity-float
two rows), and single-frequency RTK/INS
integration
(GPS, G +solutions
C, Gin+comparison
C + R, bottom two rows).
with the single-frequency multi-GNSS RTK.
The correctly-fixed solutions, incorrectly-fixed solutions, and float solutions are shown in green,
red, and grey, respectively. The zoom-in windows are provided for both the horizontal (north, east)
scatterplots and vertical (down) time series to show the details of the correctly-fixed solutions.
The correctness of ambiguity fixing is checked according to the positioning difference between the
fixed solution and the reference solution. If the position difference is larger than 0.1 m in the north
or east components, or 0.15 m in the vertical direction, the integer ambiguities will be considered as
incorrectly fixed.
It can be seen from Figure 10 that the AR and positioning performance of single-frequency
GPS-only RTK is very poor, indicating that it is difficult to use single-frequency GPS RTK for
high-accuracy kinematic positioning in urban environments. The addition of BDS increases the AR
performance dramatically, and the inclusion of GLONASS together further improves the performance.
Compared with the single-frequency GPS RTK, the dual-frequency GPS RTK can obviously improve the
positioning performance due to the doubled observations on another frequency, but its performance
is worse than the single-frequency multi-GNSS RTK. Therefore, better satellite availability from
Remote Sens. 2018, 10, 205
14 of 21
multi-GNSS brings benefits for single-frequency RTK in urban environments. Significantly, the AR and
positioning performance of dual-frequency multi-GNSS RTK are further improved with a substantial
decrease of ambiguity-float solutions in comparison with the single-frequency multi-GNSS RTK.
The results from Figure 10 also show that the ambiguity resolution and positioning performance
of the single-frequency multi-GNSS RTK/INS integration can be significantly improved with fewer
ambiguity-float solutions than the corresponding single- and dual-frequency RTK solutions. Compared
with single-frequency GPS RTK, the corresponding tightly-coupled GPS RTK/INS integration has
only small improvements in AR performance, but the accuracy and stability of the ambiguity-float
position series improves significantly due to the short-term accuracy and strong constraints of the INS.
For kinematic positioning in urban environments, this is one of the most important advantages of the
integrated GNSS/INS system. In case of RTK positioning, the ambiguity-float position error can be
large because it mainly depends on the quality and precision of the code measurements.
In Table 2, we provide the corresponding statistical information in terms of RMS of position
difference of the float and correctly-fixed single-epoch solution, positioning availability and fixing rate
of GPS, GPS + BDS, and GPS + BDS + GLONASS. The position availability, i.e., the percentage of all
epochs that the RTK positioning, is available to the total number of epochs. The AR fixing rate for full
ambiguity resolution was computed by:
PFR =
number o f correctly f ixed epochs
total number o f epochs
(24)
For the single-epoch-based kinematic positioning, this fixing rate directly reflects the high-accuracy
positioning availability.
It can be seen from Table 2 that the positioning availability is increased from 85.5% of the GPS
to 91.8% of the GPS + BDS and 92.4% of the GPS + BDS + GLONASS, respectively. The fixing rate
of the single-frequency GPS RTK is only 0.1%. By comparison, the fixing rate of single-frequency
GPS + BDS and GPS + BDS + GLONASS RTK increases to 25.1% and 44.7%, respectively. Obviously,
the dual-frequency multi-GNSS RTK greatly improves the AR performance with fixing rates of 75.8%
and 76.7% for the GPS + BDS and GPS + BDS + GLONASS systems, respectively. The dual-frequency
GPS-only RTK has a low fixing rate of 10.4% due to the poor satellite geometry (mean number of
satellites is 6.0). The single-frequency multi-GNSS RTK/INS integration shows better AR performance
with fixing rate of 86.1% for both the GPS + BDS and GPS + BDS + GLONASS system. This means
that centimeter-level positioning accuracy is available over 86% of the time in the field test with the
tightly-coupled single-frequency multi-GNSS RTK/INS integration. Similar to the dual-frequency
GPS-only RTK, the fixing rate of single-frequency GPS RTK/INS integration is also very low (only 5.8%).
Table 2. The positioning availability (PA, %), RMS of positioning differences (north, east, down)
of the float and correctly-fixed single-epoch solution, and fixing rate PFR (%) for different system
configurations with a 15◦ cut-off elevation angle.
System
G
PA
G+C
85.5
G+C+R
91.8
92.4
RMS (cm)
N
E
D
FR
N
E
D
FR
N
E
D
FR
L1 RTK
Fixed/Float
0.35
105.9
0.45
97.2
1.58
179.0
0.1
1.27
74.42
2.21
76.27
2.09
180.9
25.1
0.35
83.54
0.38
86.67
1.13
188.9
44.7
L1 + L2 RTK
Fixed/Float
0.72
91.19
0.74
90.88
1.47
147.1
10.4
0.57
81.66
0.62
95.23
1.59
170.9
75.8
0.57
86.83
0.56
91.90
1.41
143.9
76.7
L1 + INS
Fixed/Float
1.60
58.40
1.60
34.94
1.45
85.61
5.8
0.55
23.54
0.65
37.35
1.79
53.61
86.1
0.53
16.44
0.57
27.78
1.50
44.81
86.1
The results from Table 2 also show that the RMSs of the position differences of the correctly-fixed
solutions for the GPS, GPS + BDS, and GPS + BDS + GLONASS are all within 3 cm in the north,
Remote Sens. 2018, 10, 205
15 of 21
east, and vertical directions. Noticeably, the RMSs of the float solutions of the tightly-coupled
single-frequency RTK/INS integration are much smaller than that of the single- and dual-frequency
RTK. We also notice that some RMS values of the L1-RTK fixed solutions are smaller than that of
L1/L2-RTK. The main reason for this is that the fixing rate of L1-RTK is much lower and the majority
of these fixed solutions are obtained under relatively good observation conditions with small PDOP
and multipath error. Therefore, the precision of these fixed solutions can be very high and the RMS
value of them is smaller.
Similarly,
the reason why some RMS values of L1/L2-RTK
float solutions
Remote Sens. 2018,
10, x FOR PEER REVIEW
15 of 22
is greater than that
of L1 RTK is that the percentage of L1/L2 float solutions is much lower and the
multipath error. Therefore, the precision of these fixed solutions can be very high and the RMS value
of them isof
smaller.
Similarly,
the reason
why some RMS
valuespoor
of L1/L2-RTK
solutions
is greatersatellites. Overall,
observation condition
these
epochs
is generally
very
withfloat
fewer
visible
than that of L1 RTK is that the percentage of L1/L2 float solutions is much lower and the observation
the L1 RTK can obtain
fixed
solutions
in
good
condition
while
L1/L2
RTK
can
condition of these epochs is generally very poor with fewer visible satellites. Overall, the L1obtain
RTK can fixed solutions in
obtain
fixed
solutions
in
good
condition
while
L1/L2
RTK
can
obtain
fixed
solutions
in more
more challenged cases.
challenged cases.
0.05
0
0
-5
0
5
East(m)
0
-10
3000
4000
5000
3000
-0.05
-0.05 0 0.05
-5
-5
North(m)
2
3000
5000
0
-0.05
-0.05 0 0.05
2
3000
0
3000
4000
5000
GPS Time - 43,5000 (sec)
0
-2
-0.05
-0.05 0 0.05
-5
0
5
East(m)
0
-10
5000
3000
4000
5000
L1 G+C+R+INS(15°)
2
L1 G+C+INS(15°)
0
-0.05
-0.05 0 0.05
0
East(m)
5000
0
0
-5
0.05
-2
-2
4000
0.05
5
0.05
0
-0.05
10
4000
0
0.05
0
-0.05
2
-2
0
5
East(m)
0
-10
Down (m)
0.05
0
-0.05
2
3000
L1+L2 G+C+R(15°)
-0.05
-0.05 0 0.05
2
0.05
0
East(m)
0
-5
L1 GPS+INS(15°)
-2
-2
Down (m)
4000
0
0.05
0
0.05
0
-0.05
10
0
-10
5
-5
0
5
East(m)
Down (m)
Down (m)
0.05
0
-0.05
10
-10
5000
Down (m)
0
North(m)
0.05
0
4000
0
5
East(m)
0
L1+L2 G+C(15°)
North(m)
North(m)
L1+L2 GPS(15°)
5
0
-0.05
-0.05 0 0.05
0.05
0
-0.05
10
0
-10
0.05
0
-5
0
5
East(m)
Down (m)
Down (m)
0.05
0
-0.05
10
North(m)
-5
5
-0.05
-0.05 0 0.05 -5
-0.05
-0.05 0 0.05 -5
-5
0.05
0
-0.05
10
Down (m)
5
North(m)
0
0.05
-0.05
-0.05 0 0.05
0.05
0
-0.05
2
3000
4000
5000
GPS Time - 43,5000 (sec)
0
0
-2
-2
2
Down (m)
0.05
0
North(m)
North(m)
5
L1 G+C+R(15°)
North(m)
L1 G+C(15°)
L1 GPS(15°)
0
East(m)
2
0
-2
3000
4000
5000
GPS Time - 43,5000 (sec)
Figure 10. Time series of position difference in the north, east, and vertical directions for GPS
(1st column), GPS + BDS (G + C, 2nd column) and GPS + BDS + GLONASS (G + C + R, 3rd column) with
a 15◦ cut-off elevation angle. The top two rows are single-frequency RTK (GPS, G + C, and G + C + R).
The middle two rows are dual-frequency RTK (GPS, G + C, and G + C + R). The bottom two rows are
the single-frequency RTK/INS integration (GPS, G + C, and G + C + R). The correctly-fixed solutions
are shown in green, incorrectly-fixed solutions in red, and float solutions in grey. A zoom-in window is
provided to show the details of the correctly fixed solutions in the horizontal (north, east) and vertical
(down) time-series. Note the different scale for the tightly-coupled RTK/INS integration.
Remote Sens. 2018, 10, 205
16 of 21
For the high-accuracy positioning in urban environments, the measurements are easily affected
by multipath outliers, especially for those from low-elevation satellites. These measurement outliers
will make reliable AR impossible and bias the final positioning result. With the greatly increased
observations from multi-GNSS, the high-accuracy positioning with higher cut-off elevation angles
becomes possible. Therefore, we also investigate the positioning capabilities of the combined GPS,
BeiDou, and GLONASS systems with elevation cut-off angles of 25◦ , 30◦ , and 35◦ .
Figure 11 shows the time series of the position differences in the north, east, and vertical directions
for single-frequency RTK (1st column), dual-frequency RTK (2nd column), and single-frequency
RTK/INS integration (3rd column), respectively. The first two rows are for a 25◦ cut-off elevation,
while the middle two rows and last two rows are for elevation cut-off angles of 30◦ and 35◦ , respectively.
The results from Figure 11 indicates that the AR and positioning performance of dual-frequency
GPS/BDS/GLONASS RTK are much better than that of the corresponding single-frequency RTK,
especially under the higher cut-off elevation angle. Meanwhile, the performance of the dual-frequency
multi-GNSS RTK does not degrade obviously with the increasing cut-off elevation angles, while this is
not the case for the single-frequency multi-GNSS RTK. In comparison with dual-frequency multi-GNSS
RTK, the performance of the tightly-coupled single-frequency multi-GNSS RTK/INS integration is
improved further with fewer ambiguity-float solutions and a smaller positioning error. Generally,
the quality of the measurements from high-elevation satellites are better than that from low-elevation
satellites. However, the position error of ambiguity-float RTK can also be very large with high elevation
cut-off angles.
Table 3 shows the corresponding AR and positioning performance of the combined GPS, BDS,
and GLONASS system with elevation cut-off angles of 25◦ , 30◦ , and 35◦ . It includes the fixing rate and
RMSs of positioning differences of the float and correctly-fixed single-epoch solution.
It can be seen from Table 3 that the fixing rate of single-frequency GPS + BDS + GLONASS
RTK is 36.1% with a 25◦ cut-off elevation angle, and it drops to 20.3% with a 30◦ cut-off elevation
angle and to only 14.7% with a 35◦ cut-off elevation angle. By comparison, the dual-frequency
GPS + BDS + GLONASS RTK achieves much higher AR fixing rates of 77.7%, 74.3%, and 71.5%
for cut-off elevation angles of 25◦ , 30◦ , and 35◦ , respectively. For the tightly-coupled single-frequency
GPS + BDS + GLONASS RTK/INS integration, further improvements of 8.5%, 10.3%, and 10.7% can
be obtained with cut-off elevation angles of 25◦ , 30◦ , and 35◦ , respectively.
The results in Table 3 also indicate that centimeter-level poisoning accuracy is available once
the ambiguities are correctly fixed. The RMSs of position differences of the correctly-fixed solutions
with three different cut-off elevation angles are all within 3 cm in the north-east-down components.
The RMSs of the ambiguity-float solutions of the tightly-coupled RTK/INS integration are all within 1 m
in the north, east, and vertical directions. By contrast, the RMSs of the corresponding ambiguity-float
RTK solutions can reach more than 2 m in the vertical direction.
Table 3. RMSs of positioning difference (north, east, down) of the float and correctly-fixed
single-epoch solution and fixing rate PFR (%) of the GPS + BDS + GLONASS system with higher
cut-off elevation angles.
Cut-off (◦ )
25
30
35
RMS (cm)
N
E
D
FR
N
E
D
FR
N
E
D
FR
L1 RTK
Fixed/Float
0.35
78.44
0.44
88.31
1.33
206.3
36.1
0.41
81.30
0.52
87.39
1.95
223.9
20.3
0.46
81.14
0.54
87.75
2.07
226.4
14.7
L1 + L2 RTK
Fixed/Float
0.50
82.56
0.56
100.9
1.56
183.5
77.7
0.60
102.8
0.73
102.5
2.28
221.2
74.3
0.55
107.9
0.76
103.4
2.60
230.4
71.5
L1 + INS
Fixed/Float
0.54
20.35
0.62
32.28
1.75
43.03
86.2
0.76
35.47
0.78
50.04
2.51
67.94
84.7
0.78
36.00
0.77
47.65
2.37
67.59
82.2
Remote Sens. 2018, 10, 205
17 of 21
Remote Sens. 2018, 10, x FOR PEER REVIEW
17 of 22
0
-5
-0.05
-0.05 0 0.05
-5
0
5
East(m)
0
-10
-5
0.05
0
-0.05
10
0
-10
5000
0
0
-0.05
-0.05 0 0.05
-5
-5
3000
4000
-0.05
-0.05 0 0.05
-5
Down (m)
0.05
0
-0.05
10
0
-10
0
5
East(m)
0
-0.05
-0.05 0 0.05
-5
0
5
East(m)
3000
4000
5
0.05
0
0
-5
0
5
East(m)
-1
-1
3000
3000
4000
5000
GPS Time - 43,5000 (sec)
4000
5000
0
0
0.05
0
-0.05
2
-10
0
-0.05
-0.05 0 0.05
0
1
East(m)
L1 G+C+R+INS(35°)
1
0.05
0.05
0
-0.05
10
3000
4000
5000
GPS Time - 43,5000 (sec)
5000
0
-1
-1
0
1
4000
0
-2
5000
-0.05
-0.05 0 0.05
-5
3000
0.05
0
-0.05
2
0
0
East(m)
L1 G+C+R+INS(30°)
1
0.05
Down (m)
-5
-2
5000
L1+L2 G+C+R(35°)
North(m)
0
0
-0.05
-0.05 0 0.05
0
Down (m)
North(m)
0.05
0
-10
5000
L1 G+C+R(35°)
5
0.05
0.05
0
-0.05
10
0
-10
5
-5
0
5
East(m)
Down (m)
Down (m)
0.05
0
-0.05
10
4000
North(m)
0.05
North(m)
North(m)
5
3000
L1+L2 G+C+R(30°)
L1 G+C+R(30°)
0
-1
-1
0.05
0
-0.05
2
0
5
East(m)
Down (m)
4000
0.05
0
-0.05
-0.05 0 0.05
North(m)
3000
0
-5
Down (m)
Down (m)
0.05
0
-0.05
10
0.05
0
North(m)
0
5
Down (m)
0.05
North(m)
North(m)
5
L1 G+C+R+INS(25°)
1
L1+L2 G+C+R(25°)
L1 G+C+R(25°)
-0.05
-0.05 0 0.05
0
East(m)
1
0
-2
3000
4000
5000
GPS Time - 43,5000 (sec)
Figure
11.11.
Time
series
of position
differences
in the
east, and
directions
for single-frequency
Figure
Time
series
of position
differences
innorth,
the north,
east,vertical
and vertical
directions
for singleRTK
(G + C RTK
+ R, (G
1st +column),
RTK (G +RTK
C + R,
and single-frequency
frequency
C + R, 1stdual-frequency
column), dual-frequency
(G 2nd
+ C +column),
R, 2nd column),
and single◦ , 30◦ , and 35◦ ).
RTK/INS
integration
(G + C + R,(G
3rd
column)
higher
cut-off
angles (25
frequency
RTK/INS integration
+C
+ R, 3rdwith
column)
with
higherelevation
cut-off elevation
angles
(25°, 30°,
The
correctly-fixed
solutions
are
shown
in
green,
incorrectly-fixed
solutions
in
red,
and
float
solutions
and 35°). The correctly-fixed solutions are shown in green, incorrectly-fixed solutions in red, and
float
in solutions
grey. A zoom-in
is given istogiven
show
details
of the
solutions
in grey. Awindow
zoom-in window
to the
show
the details
of correctly-fixed
the correctly-fixed
solutionsininthe
the horizontal
east)vertical
and vertical
(down)
time-series.
the different
scale
fortightly-coupled
the tightlyhorizontal
(north,(north,
east) and
(down)
time-series.
Note Note
the different
scale for
the
coupled integration.
RTK/INS integration.
RTK/INS
epoch solution and fixing rate
elevation angles.
Cut-off (°)
25
RMS (cm)
N
E
D
L1 RTK
0.35
0.44
1.33
Fixed/Float
Remote Sens. 2018,
10, 205 78.44 88.31 206.3
L1 + L2 RTK
0.50
0.56
1.56
Fixed/Float
82.56
100.9
183.5
L1 + INS
0.54
0.62
1.75
Fixed/Float
32.28
43.03
4.4. Position Drift
Error 20.35
for Multi-GNSS
(%) of the GPS + BDS + GLONASS system with higher cut-off
30
N
E
D
0.41
0.52
1.95
36.1
81.30
87.39
223.9
0.60
0.73
2.28
77.7
102.8
102.5
221.2
0.76
0.78
2.51
86.2
35.47
50.04
67.94
RTK/INS
Integration
after
FR
FR
N
0.46
20.3
81.14
0.55
74.3
107.9
0.78
84.7
36.00
the End
of
35
E
D
FR
0.54
2.07
14.7
87.75
226.4
0.76
2.60
71.5
103.4
230.4
0.77
2.37
82.2
47.65 Outages
67.59
GNSS
18 of 21
4.4. Position
Driftapplications,
Error for Multi-GNSS
Integration
after the End
of GNSS
Outages
For most
dynamic
it is RTK/INS
inevitable
for vehicles
to go
through
the overpasses, trees
and tunnels, etc.
In
these
conditions,
the
satellite
signals
may
lose
lock
frequently
no matter
For most dynamic applications, it is inevitable for vehicles to go through the overpasses,
treesthe single
and
tunnels,
etc.
In
these
conditions,
the
satellite
signals
may
lose
lock
frequently
no
matter
the
single
GPS or the multi-GNSS is used. The frequent signal loss makes the GNSS data processing more
GPSespecially
or the multi-GNSS
used. The frequent
signal
loss makes thepositioning.
GNSS data processing
complicated,
for theiscarrier-phase
based
high-accuracy
Figure more
12 shows the
complicated, especially for the carrier-phase based high-accuracy positioning. Figure 12 shows the
GNSS outage
(it
cannot
provide
RTK
solutions)
durations
during
the
driving
test
for
the
combined
GNSS outage (it cannot provide RTK solutions) durations during the driving test for the combined
◦
GPS, BDS, and
system system
with awith
15 acut-off
elevation
angle.
windows
GPS, GLONASS
BDS, and GLONASS
15° cut-off
elevation
angle.Three
Three zoom-in
zoom-in windows
are are given
to show the
of duration
the outage duration
the longest
outage
lasts
morethan
than 22 min and
to show thegiven
magnitude
of magnitude
the outage
whereinwherein
the longest
outage
lasts
more
min and some others are within 10 s.
some others
are within 10 s.
Outage duration (seconds)
120
100
80
60
40
20
6
4
2
0
10
5
0
4050410041504200
3000 3100 3200
8
6
4
2
0
-2
4700 4800 4900
0
3000
3500
4000
4500
GPS Time - 43,5000 (sec)
5000
5500
Figure 12. GNSS outage durations during the driving test for the combined GPS, BDS, and GLONASS
Figure 12. GNSS outage durations during the driving test for the combined GPS, BDS, and GLONASS
system with a 15° cut-off elevation angle.
system with a 15◦ cut-off elevation angle.
Since the high-precision position information during the long outages is not available in the real
experiments, the maximum position error is used to evaluate the positioning performance in the data
Since the high-precision position information during the long outages is not available in the real
analysis. Generally, the position errors reach the maximum at the end of outages and the accurate
experiments,
the maximum
position
error
is used by
to applying
evaluatebackward
the positioning
in the data
reference
position at this
epoch can
be obtained
smoothing.performance
Table 4 shows all
the outage durations
and theerrors
corresponding
maximum
positionat
drift
analysis. Generally,
the position
reach the
maximum
theerrors.
end of outages and the accurate
reference position at this epoch can be obtained by applying backward smoothing. Table 4 shows all
Table 4. The GNSS outage durations in the field test and the corresponding maximum position drift
the outage durations
errors. and the corresponding maximum position drift errors.
Outage Items
#1
#2
0.4
6.2
7.1
9.4
#3
#3
#4
#5
#6
0.9
15.3
4.8
16.1
9
523.5
1739.3
#6
2817.3
3352.1
127
#7
#8
#9
#10
#11
#12
#13
6.8
6.7
1.5
0.3
14.7 4.2
#9
#10
8.7
1.4
1.4
11.0
2 16.2 2 4.7
#11
Table 4. The GNSS
outage
the corresponding
position
Duration
(s) durations
4
3 in the
6 field
2 test
9 and127
4
6
2 maximum
2
7
2
4 drift errors.
Outage Items MAX (cm)#1
Duration (s)
MAX (cm)
North
East
Down
3D
4
0.4
6.2
7.1
9.4
North
East
#2
Down
3D 3
1.2
0.4
1.6
2.0
1.2
0.4
1.6
2.0
6
5.6
9.3
#4
5.5
12.22
5.6
9.3
5.5
12.2
1.9
1.7
1.4
2.9
1.9
1.7
1.4
2.9
#5
0.9
15.3
4.8
16.1
523.5
1739.3
2817.3
3352.1
1.9
1.1
#7
6.9
7.24
1.9
1.1
6.9
7.2
5.8
14.6
1.1
15.7
7.1
1.5
2.3
67.6
#8
5.8
14.6
1.1
15.7
7.1
1.5
2.3
7.6
6.8
0.3
8.7
11.0
3.2
3.2
1.7
4.8
7
#12
#13
2
4
6.7
14.7
1.4
16.2
1.5
4.2
1.4
4.7
3.2
3.2
1.7
4.8
It can be seen from Table 4 that the maximum drift at the longest outage duration is up to 5.235,
17.393, and 33.521 m in the north, east, and vertical components. It is also clear that the position drift
becomes larger when the outage duration increases. It is mainly due to the uncompensated IMU errors
and these errors will lead to the rapid growth of position drift for MEMS inertial sensors. Generally,
centimeter-level positioning accuracy can be obtained when the outage duration is within 4 s for
the POS1100 MEMS grade IMU. This capability to provide high-accuracy navigation results within
short-term outages is meaningful for some navigation applications.
5. Conclusions
Carrier-phase-based high-accuracy positioning in urban environments is still a challenging task,
even using high-cost dual-frequency receivers. In this contribution, the tightly-coupled integration of
Remote Sens. 2018, 10, 205
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the single-frequency multi-GNSS RTK and low-cost MEMS-IMU was developed to provide reliable
and continuous high-accuracy positioning in GNSS-challenged environments. The outlier-resistant
AR and Kalman filtering strategy was proposed specifically for the integration algorithm to resist
the measurement outliers. A field vehicular test was carried out to investigate the high-accuracy
positioning capabilities of the proposed algorithm in urban environments. Comparisons in terms of
AR and positioning performance have been conducted with respect to the single- and dual-frequency
multi-GNSS RTK. The following conclusions can be drawn based on the presented results and analysis
in this research.
In urban environments, the satellite tracking condition is poor due to the frequent loss-of-lock
of the satellite signal, and the degraded satellite availability poses serious challenges to positioning,
especially for the single GPS system. The GNSS observations are susceptible to outliers in such
environments. Therefore, the fault detection and exclusion is definitely required for reliable positioning;
otherwise, the reliable ambiguity resolution is impossible when measurement outliers are in the
GNSS data. The proposed outlier-resistant ambiguity resolution and Kalman filtering strategy
are suitable for the tightly-coupled integration algorithm and effective to improve the ambiguity
resolution performance. By applying an outlier-resistant ambiguity resolution and filtering strategy,
the ambiguity-fixed solutions can be obtained even though the measurements are contaminated with
large outliers.
The AR and positioning performance of GPS is very poor in urban environments, even using the
dual-frequency RTK. As expected, the multi-GNSS can greatly improve the positioning performance
due to the increased satellite availability and better spatial geometry structure. The fixing rate
of single-frequency GPS RTK increases from 0.1% to 25.1% and 44.7% of the GPS/BDS and
GPS/BDS/GLONASS RTK, respectively. The dual-frequency RTK can obtain much better results than
the corresponding single-frequency RTK with fixing rates of 10.4%, 75.8%, and 76.7% for the GPS,
GPS/BDS, and GPS/BDS/GLONASS, respectively. The performance can be further improved by the
single-frequency multi-GNSS RTK/MEMS-IMU tightly-coupled integration with fewer ambiguity-float
solutions and smaller positioning error than the corresponding dual-frequency multi-GNSS RTK.
The corresponding fixing rate for the GPS, GPS/BDS, and GPS/BDS/GLONASS are 5.8%, 86.1%,
and 86.1%, respectively. Additionally, the position errors of ambiguity-float RTK are large even with
a higher cut-off elevation angle because it mainly relies on the relatively imprecise code measurements.
By contrast, the ambiguity-float solution of the RTK/INS tightly-coupled integration is more stable
and accurate due to the strong constraint from the INS in the short-term period.
The results also show that high-accuracy positioning is feasible with limited performance loss
for the single-frequency GPS/BDS/GLONASS/INS integration when higher cut-off elevation angles
are applied in urban environments. Its AR fixing rate is 86.2%, 84.7%, and 82.2% when the cut-off
elevation angles are set to 25◦ , 30◦ , and 35◦ , respectively. Compared with the high-cost dual-frequency
RTK, the tightly-coupled integration of single-frequency multi-GNSS and low-cost MEMS-IMU are
promising and preferred for some applications in urban environments.
For long outage durations, it is difficult to obtain centimeter-level positioning accuracy during
the GNSS outage. Therefore, other aiding sensors and methods will be considered in the future to
further improve the high-accuracy positioning capabilities. In addition, suitable methods should be
developed to model the multipath error on the carrier phase.
Acknowledgments: We would like to thank the anonymous reviewers for their valuable comments and critical
remarks, which greatly improved the quality of the manuscript. This work is supported in part by the National
Key Research and Development Program of China (nos. 2016YFB0501800, 2016YFB0501803 and 2016YFB0501804),
in part by the National High Technology Research and Develop Program of China (no. 2015AA124002) and,
in part, by the National Natural Science Foundations of China ( no. 41404029).
Author Contributions: Tuan Li and Hongping Zhang conceived the initial idea; Tuan Li designed the experiment
and implemented the software for this contribution; Tuan Li analyzed the data and wrote the main manuscript;
Zhouzheng Gao and Qijin Chen helped with the data analysis; and Hongping Zhang and Xiaoji Niu helped with
the writing. All authors reviewed the manuscript.
Remote Sens. 2018, 10, 205
20 of 21
Conflicts of Interest: The authors declare no conflict of interest.
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