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Texas Instruments Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP Application notes
Disclaimer: This document was part of the DSP
Solution Challenge 1995 European Team Papers. It
may have been written by someone whose native
language is not English. TI assumes no liability for the
quality of writing and/or the accuracy of the
information contained herein.
Implementing a Digital Tracker for
Monopulse Radar Using the TMS320C40
DSP
Authors: G. Aubree, P. Longepe, N. Pourrain,
L. Fourdan
EFRIE, France
December 1995
SPRA301
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CONTACT INFORMATION
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Contents
Abstract ..............................................................................................................................7
Product Support on the World Wide Web ......................................................................8
Introduction........................................................................................................................9
Overall Description......................................................................................................... 11
Operating Modes ........................................................................................................ 11
Step One: Acquisition......................................................................................... 11
Step Two: Tentative Tracking ............................................................................ 12
Step Three: Confirmed Tracking........................................................................ 13
Deviation Computations ............................................................................................. 13
Acquisition Mode ................................................................................................ 13
Tentative Tracking Mode ................................................................................... 14
Confirmed Tracking Mode.................................................................................. 15
Matrix Conversion....................................................................................................... 16
Spherical to Cartesian Conversion .................................................................... 17
Cartesian to Spherical Conversion .................................................................... 17
Alpha-Beta Filters ....................................................................................................... 18
Smoothing the Cartesian Coordinates............................................................... 18
Optimal Target Tracking..................................................................................... 20
Algorithms and Hardware.............................................................................................. 22
General Algorithm for Tracking .................................................................................. 22
Hardware Specifications............................................................................................. 23
Pedestal.............................................................................................................. 23
DMA Memories................................................................................................... 25
Conclusion ...................................................................................................................... 26
Figures
Figure 1. Acquisition Mode .................................................................................................. 11
Figure 2. Tentative Tracking Mode ...................................................................................... 12
Figure 3. Confirmed Tracking Mode .................................................................................... 13
Figure 4. Alpha-Beta Filter Schematic ................................................................................. 19
Figure 5. Tracking Algorithm Block Diagram ....................................................................... 23
Figure 6. One Potentiometer Device ................................................................................... 24
Figure 7. Two Potentiometer Device ................................................................................... 24
Implementing a Digital Tracker for
Monopulse Radar Using the
TMS320C40 DSP
Abstract
This project AXIR_B (Digital Tracker) corresponds to a PCB that
performs the following main tasks.
‰
‰
‰
Deviation calculus and coordinates transformations.
Tracking and smoothing the rectangular (X, Y, Z) coordinates.
Interfacing with the pedestal and the Radar Manager.
The Digital Tracker operates different algorithms during the three
modes of the AXIR. The three modes of the AXIR radar are
acquisition process, tentative tracking, and confirmed tracking.
The Digital Tracker communicates through dual access memory
with AXIR_A (Doppler processing) and AXIR_C (Radar Manager)
projects.
The input data used by the Digital Tracker corresponds to four
beams, 16 ranges bins, and three Doppler filters. From this data
the Digital Tracker calculates the deviations in elevation, azimuth,
and range and transforms them into rectangular errors. Three
Alpha-Beta filters are used to smooth the coordinates and to
calculate the derivatives (predicted X, Y, Z, dX/dt, dY/dt, dZ/dt).
From this trajectory data, the loops are completed via the reverse
matrix conversion calculating the azimuth and elevation voltages
to the benefit of the pedestal motors. The predicted range is used
to generate the early and late range gates.
The Radar Manager is responsible for updating the Alpha-Beta
coefficents.
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
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SPRA301
This project is based on a PCB using one Texas Instruments
(TI) TMS320C40 digital signal processor(DSP).
This document was an entry in the 1995 DSP Solutions
Challenge, an annual contest organized by TI to encourage
students from around the world to find innovative ways to use
DSPs. For more information on the TI DSP Solutions Challenge,
see TI’s World Wide Web site at www.ti.com.
The submission package for the TI DSP Solutions Challenge
included:
‰
‰
‰
This current paper.
A disk containing the C sources and assembler programs.
The AXIR demonstration program.
Product Support on the World Wide Web
Our World Wide Web site at www.ti.com contains the most up to
date product information, revisions, and additions. New users
must register with TI&ME before they can access the data sheet
archive. TI&ME allows users to build custom information pages
and receive new product updates automatically via email
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Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
Introduction
AXIR is a concept of low-cost Automatic Xband Instrumentation
Radar especially designed for the TI DSP Solutions Challenge.
This concept is based around four projects. The idea was to
demonstrate that is possible to quickly design a small intelligent
radar, including expert and adaptive digital signal processing,
made up of less than 8 TMS320C4x/TMS320C5x chips.
The objective cost is under 80,000 $ for the entire radar. This
includes the pedestal, antenna, transmitter, RF front-end, signal
processing, and display. The AXIR is basically a monopulse
Doppler ground base radar. Numerous AXIR civilian applications
include:
‰
‰
‰
‰
‰
‰
Tracking of meteo-sounders,
Cloud doppler analysis for meteo purposes,
Short range air control radar for parallel runways or difficult
access airports,
Detecting wind-shear and bursts,
Trajectory control for piloting schools, aerobatics sporting
events, and aero clubs,
General low-cost instrumentation radar (radar cross section
evaluation, tutorial radar for universities, and private air
tracking).
The digital signal processor is composed of four printed circuit
boards, corresponding to one of four separate projects submitted
to the TI DSP Solutions Challenge by four distinct teams from the
same university sharing the same advising professor. The four
projects are named:
a) Front-end/Doppler Processing
b) Digital Tracker (AXIR B)
c) Adaptive Radar Manager
d) Test Simulator/Display Control.
AXIR features modern technology for the other subsystems. The
antenna is planar monopulse, printed on three layers. The
transmitter, the Stalo, and the RF homodyne front-end are 100%
solid-state. All the circuits and the processor are located at the
back of the planar array antenna.
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
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SPRA301
The pedestal uses low-cost modern technology developed for
robotic applications. The flat antenna is free to rotate 360° both in
azimuth and elevation, which is not common. A standard PC,
running Microsoft Windows/MS-DOS, was used for the operator
remote control, graphics display, monitoring, and recording. A
radio link was managed between the sensor and the operator
desk.
This project was developed by three undergraduate students in
preparation for a radar course. It has been a practical exemplify of
their signal processing course.
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Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
Overall Description
Operating Modes
AXIR, the tracking radar, operates sequentially in the following
three modes:
‰
‰
‰
Acquisition
Tentative Tracking
Confirmed Tracking
Step One: Acquisition
Once a target is spotted by the radar’s operator, the radar
searches to acquire it (see Figure 1). The magnitudes of the
upper, lower, right and left four squinted beams are accumulated
individually for the three Doppler filters and for the sixteen range
gates. Each channel is compared to a threshold. If one result is
trespassing this level, the target is declared present in the cell
providing the largest number.
Figure 1. Acquisition Mode
AXIR
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
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SPRA301
Step Two: Tentative Tracking
Several Doppler measurements (coherent bursts) are operated
with at least 3 different Pulse Repetition Intervals (PRI) in order to
solve the range-Doppler ambiguities (see Figure 2). The objective
of this step is to evaluate the coherence of the unfolded range
measurements and Doppler frequencies. During this mode, the
angular deviations are computed and are used by the Alpha-Beta
filters with a short time constant.
Figure 2. Tentative Tracking Mode
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Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
Step Three: Confirmed Tracking
In this mode, the target is completely acquired (see Figure 3). The
bandwidths of the servo-loops are progressively reduced up to a
certain limit. As the trajectory is perfectly smoothed, the Doppler
frequency is calculated by the Radar Manager and only the central
Doppler filter is used for the calculus of the deviations.
Figure 3. Confirmed Tracking Mode
Deviation Computation
Acquisition Mode
The Digital Tracker calculates the sums of the four beams
individually for the 16 range bins and for the 3 Doppler filters.
SUM ( R, f ) =
B1( R, f ) + B 2( R, f ) + B 3( R, f ) + B 4( R, f )
(1)
where R is the range bin index (1 to 16), f is the Doppler index (1
to 3), B1, B2, B3, and B4 are respectively the upper, right, lower,
and left receiving antenna channels. The two dimensions array
SUM( ) is transmitted to the Radar Manager for thresholding
(Th1).
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
13
SPRA301
Tentative Tracking Mode
The Digital Tracker evaluates the same array SUM( ) according to
formula 1. The Radar Manager governs successive coherent
measurements changing the Pulse Repetition Frequency (PRF).
The "target present" booean is determined by the central range
gates and the threshold (Th2). Side range bins are accumulated to
give the ambient noise level used to determine Th2. Concerning
the angular and range deviations, the principles are used to
compute ratios DIF (difference) over SUM.
In this mode, the feed back loops are closed and the Alpha-Beta
coefficients are upgraded by the Radar Manager. It is also
necessary to supply the radar with great precision in the calculus
of the different deviations. It must work on the four beams of the
radar with three IIR Doppler filters and three range bins. The 6, 7
and 8 range bins are also centered precisely in the range gate
windows by the Radar Manager. The calculus of deviation in
azimuth, elevation, and range are given by the following
equations:
Ecart Azimuth
2
EAz =
8
∑∑ B4
f =0 R =6
2
8
2
8
(R, f ) − ∑∑ B2 (R, f )
f =0 R =6
2
8
∑∑ B4 (R, f ) + ∑∑ B2 (R, f )
f =0 R =6
f =0 R =6
Ecart Elevation
2
EEI =
8
∑∑ B1
f =0 R =6
2
8
2
8
(R, f ) − ∑∑ B3 (R, f )
f =0 R =6
2
8
∑∑ B1 (R, f ) + ∑∑ B3 (R, f )
f =0 R=6
f =0 R =6
Range
N=
(B 2(0,6) + B 4(0,6))⋅ ( −1) + (B2(0,7) + B 4(0,7) )⋅ (0) + (B2(0,8) + B4(0,8) )⋅ (+1)
8
∑ B2(0, R) + B4(0, R)
R =6
The new value for R is R = Ro + N * 75 meters. It is the Radar
Manager which calculates this value and sends it back to the
Digital Tracker. It is still needful to provide the calculus with the
three lIR Doppler filters. These three filters will help the radar
locate the exact position of the target and to compensate for the
Doppler effect.
14
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
If the tentative tracking mode is conclusive, the radar will pass to
the next step, the confirmed tracking mode.
Confirmed Tracking Mode
Indeed, like the position of the target is well-known in the tentative
tracking mode, it could be sure that the Doppler effect will not
work this time. It isn’t necessary to check it any more. The
equations are:
Ecart Azimuth
8
EA =
∑ B4(0, r) −
r =7
8
8
∑ B2(0, r )
r =7
8
∑ B4(0, r) + ∑ B2(0, r )
r =7
r =7
Ecart Elevation
EA =
8
8
r =7
8
r =7
8
r =7
r =7
∑ B1(0, r ) − ∑ B3(0, r)
∑ B1(0, r) + ∑ B3(0, r)
Range
N=
(B2(0,7) + B4(0,7) )⋅ (−1) + (B2(0,8) + B4(0,8))⋅ ( +1)
8
∑ B2(0, r ) + B4(0, r)
r =7
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
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SPRA301
Matrix Conversion
Notation
θ = Azimuth
ϕ = Elevation
Z
P
x
0
phi
theta
North
East
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Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
Spherical to Cartesian
Spherical to Cartesian Conversion (Total Difference)
The dXm, dYm, and dZm coordinates are obtained with the
following equations:
dX = cos ϕ . sin θ .dρ − ρ . sin θ . sin ϕ .dϕ + ρ . cos ϕ . cos θ .dθ
dY = cos ϕ . cosθ .dρ − ρ . cosθ . sin ϕ .dϕ − ρ . cos ϕ . cosθ .dθ
dZ = sin ϕ .dρ + ρ . cos ϕ .dϕ
Where:
dθ = dAz = dLat /(cos(El )) is the azimuth deviation.
dρ = dR is the range deviation.
Spherical to Cartesian Conversion (in Position)
X = ρ . cos ϕ . sin θ ( East )
Y = ρ . cos ϕ . cos θ ( North )
Z = ρ . sin ϕ
( Altitude)
By using these two algorithms it is possible to settle the Xm, Ym,
and Zm coordinates; using the following algorithm:
dAz = dLat/cos(El);
Convert_Polar_To_Cartesian_Diff ( dAz, dEl, dR, &dXm, &dym,
&dZm);
Convert_Polar_To_Cartesian_Pos ( AZ, El, R, &Xa, &Ya, &Za);
Xm = Xa + dXm;
Ym = Ya + dYm;
Zm = Za + dZm;
Cartesian to Spherical Conversion
Cartesian to Spherical Conversion (Total Difference)
This function is used to send filtered deviations from the AlphaBeta filters to the pedestal encoders.
dθ =
y.dx − x.dy
2
x +y
2
dϕ =
2
2
( x + y ).dz − z.( x.dx + y.dy )
2
2
2
( x + y + z ).
2
x +y
2
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
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SPRA301
dρ =
x.dx + y.dy + z.dz
2
+y
x
2
+z
2
Cartesian to Polar Conversion (Position)
This function is used to send the El, AZ and R coordinates to the
Radar Manager (AXIR_C).
2
2
2
ρ = x +y +z
( Radar Range)
ϕ = arc sin( Z / ρ ) ( Elevation)
θ = arc tan( X / Y ) ( Azimuth )
Alpha-Beta Filters
Smoothing the Cartesian Coordinates
The X, Y, and Z signals of the trajectory target are used to control
the engines of the radar. First, the coordinates must be smoothed
to remove noise in order to accurately compute the targets
trajectory. There is an Alpha-Beta target tracker filter for each of
the three coordinates. The DSP implements these filters with a
simple recursive procedure. The recursive procedure can estimate
the position and velocity of a two state, one dimensional motion
based on position measurements.
The structure of Alpha-Beta target tracker is well known. It is
based on the error estimation of a position vector measurement.
For example, if we suppose that the velocity of the X variable is
constant, we can predict the position at time sample k+ 1.
Prediction: Xp( k + 1) = X ( k ) + T . V ( k )
However, if the target manoeuverability is not null we can update
this prediction by adding a pourcentage of the error.
Update: X ( k + 1) = Xp( k + 1) + Alpha.[ z ( k + 1) − Xp( k + 1)]
where, z(k+1) is the position measurement and Alpha is the first
tracking parameter.
The same principle is used to attenuate the velocity noise.We
have just to divide the error by the sampling periode.
V ( k + 1) = V ( k ) + ( Beta / T ).[ z (k + 1) − Xp( k + 1)]
These equations can be represented by the schematic shown in
Figure 4.
18
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
Figure 4. Alpha-Beta Filter Schematic
Alpha
InP
V1
+
V2
OutP
+
P
Z1
+
P
(Predicted
Position)
V3
Beta/T
V4
OutV
+
P'
Z1
T
V5
The predict position is V1 = In – P, it is multiplying by the Alpha
coefficent to give V2 and by Beta to give V4. The output OutP is
the filtered position which is equal to the true position P plus the
Error V2:
OutP = P + V 2
The same principle is used for the filtered velocity:
OutV = V 4 + V 5
Where V4 is the velocity error and V5 is the velocity at the time;
T-1.
We can also deduce the Z transformed formulas:
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
19
SPRA301
OutP
In
=
Alpha − ( Alpha − Beta ).Z
−1
−1
1 − ( 2 − Alpha − Beta ).Z − ( Alpha − 1) Z
−2
and,
OutV
In
−1
=
Beta.(1 − Z )
−1
1 − ( 2 − Alpha − Beta ).Z − ( Alpha − 1) Z
−2
Now, the algorithm for implementation in the DSP can be
deduced.
Beginning period
P = V3 + V5
V1 = In - P
V2 = Alpha V1
V4 = Beta V1
OutP = P + V2
OutV = V4+ V5
V3 = OutP
V5 = OutV
Next period
Optimal Target Tracking
How to choose the parameters Alpha and Beta?
The main object of this target tracking device is to use the
possibility to change Alpha and Beta during confirmed tracking.
Thus, the unknown target manuvers must influence the AlphaBeta parameters by increasing swiftness or stability according as
the target is accelerating or not. The solution of the target tracking
is given by the tracking index, which characterizes the generalized
tracking solution. The tracking index is proportional to the ratio of
position uncertainty due to the target maneuverability and the
sensor measurement. A simple solution to increase the speed of
the filter in the acquisition mode is to use the evolutive coefficients
Alpha (n) and Beta(n).
Evolutive coefficients with time index ( n = 1, 2, 3...)
Example: Alpha (n ) = 2( 2n − 1) /( n( n + 1))
Example: Beta (n ) = 6 /(n ( n + 1))
20
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
The predict position is V1 = In - P; it is multiplying by the Alpha
coefficient to give V2 and by Beta to give V4. The output OutP is
the filtered position, which is equal to the true position P, plus the
Error V2.
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
21
SPRA301
Algorithms and Hardware
General Algorithm for Tracking
If target parameters correspond to the fixed threshold, track is
maintained and smoothed. Moreover, waveform ( DCP, PRI ) are
continuously optimized. The project_C (Radar Manager) optimized
the Alpha-Beta parameters according to trajectory variations. The
goal of this project is to supply project_C with the trajectory filtered
elevation, azimuth and range coordinates. These coordinates are
calculated by addition of the sidesteps dXm, dYm and dZm with
the position coordinates Xm, Ym and Zm, which are received from
the pedestal.
As a result of the Cartesian variation of a plane being generally
lower than the polar variation, the tracking stage is calculated in
rectangular coordinates. This enables the filters to smooth more
regularly.
If (Mode is Confirmed):
{
1) Read the values of 6 and 7 range squares in the Dual Access
RAM.
2) Calculate the azimuth and lateral deviation.
3) Convert these spherical deviations into the Cartesian
differentials dXm, dYm, dZm.
4) Read the values of pedestal spherical coordinates from the
ADC interface circuits.
5) Converts the elevation, azimuth and range into Xa, Ya, Za
coordinates.
6) Add the total differentials dXm, dYm and dZm to the position
Xa, Ya, Za.
7) Filter the resulting coordinates Xm, Ym and Zm.
8) Convert the smoothed velocity, which is received from the
Alpha-Beta filter, into spherical deviations and send the results
to the pedestal’s azimuth and elevation encoders.
9) Convert the X, Y, and Z filtered coordinates and send the
results (El, Az, and R) to the Radar Manager.
}
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Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
All of these functions are represented in Figure 5.
Figure 5. Tracking Algorithm Block Diagram
D
E
V
I
A
T
I
O
N
dLat
dR
dZm
P
E
D
E
S
T
A
L
Az
Xa
Az
dXm
POLAR TO CARTESIAN
( T O T A L D I F F E R E N C E)
CONVERTER
dEl
POLAR TO CARTESIAN
(POSITION)
CONVERTER
El
dYm
Ya
Za
R
+
+
+
Xm
Ym
Zm
Hardware Specifications
Pedestal
The pedestal serves as a low cost stand for the antenna. The
pedestal can rotate 360° in azimuth and in elevation. Pedestal
angles are available at each period of the PRI. Double
potentiometers provide a voltage that is proportional to the angle,
for example 1 V/degree. Using double potentiometers eliminated
(see Figure 6) a discontinuity, when the angle passes from 360° to
0°, that was encountered with a single potentiometer. This
ambiguity was suppressed by adding the second potentiometer
(see Figure 7), which is calibrated to 0° when the first
potentiometer passed 360°. Thus, suppressing the shift forward.
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
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SPRA301
Figure 6. One Potentiometer Device
V / deg
360°
0°
Shift Effect
Figure 7. Two Potentiometer Device
V / deg
0°
24
360°
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
SPRA301
DMA Memories
The DMA 0 was used for transferring data from project 1 to project
2. The DMA0 constant word can also be defined.
DMA0: 0010 00A0 Hex
Data transfer between project 2 and project will be made with the
TRANSFER MODE 00. Thus, the ICRDY signal is used to
synchronize DMA channel transfers. When DSP 2 sends data, the
ICRDY interrupt allows DSP 3 to write from the DMA to internal
memory. For using this mode, several bits of the DMA Channel
Control must be configured. The two bits of DMA SYNC MODE
must be set to 01 value. So, a read will not be performed until the
ICRDY interrupt will occur.
The DMA Channel Control variable can also be fixed as:
CONTROL : 00C0 0040 Hex
The communication port 0 will be used as the source address.
The constant used to address this port will be:
SOURCE :
0010 0040 Hex
Because only one word will be transferred at each interrupt, the
source index register will be set to 0. The destination index will be
set to 1 for incrementing the destination address after each
transfer.
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
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SPRA301
Conclusion
The accomplishment of such as device requires the use if a fast
processor because the calculus of the three deviations and all the
tracking algorithms including the Alpha-Beta filters must be
brought up up to date during a period lower than the Pulse
Repetition Impulsion.
The DSP toolkit pack allows to compile, link, optimize, and to test
the whole C code implemented for these algorithms. The AXIR
program contains a simulation of all the parts of the radar.
This TI DSP Solutions Challenge allows to the three
undergraduate students to find out a concrete aspect of their
digital processing course. All the DSP facilities such as the direct
memory access concept and pipe line programation can
accelerate the process and also increment the resolution of the
radar.
The main advantages of the AXIR radar are:
‰
‰
‰
26
Its very high Doppler quality.
Its auto-adaptive digital pulse compression.
Its intelligent automatic trajectory smoothing.
Implementing a Digital Tracker for Monopulse Radar Using the TMS320C40 DSP
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