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Vehicle sensing in optically and thermally
obscured environments
Ee Kent Lew, Benjamin Shih
Electrical and Computer Engineering, Carnegie Mellon University
Abstract— This report presents a magnetometer designed to
detect vehicles in optically and thermally obscured environments.
Due to the ferromagnetic properties of materials used in the
construction of vehicles, vehicles perturb the Earth’s magnetic
field. The magnetometer senses these perturbations through
electromagnetic induction. Signal processing techniques are
employed to harness and amplify actual signal from
environmental noise. The design, layout, physics, principles of
operation, performance characteristics and limitations are
theoretically and experimentally discussed in this paper. It is
found that the transfer characteristics are extremely non-linear
and the device is limited by Johnson noise.
Earth’s magnetic field. These fluctuations are not susceptible
to environmental conditions.
Applications of the sensor system include commercial
applications for vehicle detection in highways and parking
systems, and vehicle safety in collision detection systems.
Military applications include the detection of military vehicles
and equipment for defensive force protection; early warning
and remote sensing capabilities; and vehicle detection for
pyrotechnics such as mines, intelligent and guided munitions.
Index Terms— magnetism, magnetic field perturbation,
magnetic flux, vehicle detection, non-line-of-sight sensing, remote
sensing, electro-magnetic induction.
Current vehicle sensors today are heavily limited by sensing
range. Most vehicle sensors employ the induction loop method
for detecting vehicles, and are primarily used in highway and
parking systems. These induction loop sensors are buried
underground and positioned 1-2 feet away from the vehicle
base. Their sensing range and direction are heavily limited due
to their magnetic energy and physical size constraints.
Increasing their range would lead to significantly impractical
increases in power consumption, radiated magnetic energy and
physical size.
Longer range vehicle sensors employed by commercial and
military users include radar, Light Detection and Ranging
(LIDAR), infra-red, ultrasound, EM-signal triangulation such
as GPS and radio-tower triangulation. The effectiveness of
these techniques is reduced in optically and thermally
obscured environments.
This paper presents a magnetometer that is designed and
calibrated for remote sensing of vehicles with a range that
exceeds current inductive loop sensors in the market; physical
dimensions that are significantly smaller than existing sensors;
higher mobility and the potential to scale up towards 3dimensional sensing. The sensor system proposed is capable
of sensing vehicles in optically and thermally obscured
environments such as sandstorms by detecting changes in the
Fig. 1. Visualization of the Earth's magnetic field
The magnetic field strength on the Earth’s surface varies from
0.25 to 0.65 Gauss, or 25000 to 65000 nT (National
Geophysical Data Center). For the purpose of our sensor
system to be used in North America, we can accurately
estimate that the Earth’s magnetic field strength on the surface
of North America is 0.55 Gauss (U.S. Geological Survey). To
operate the sensor in other areas, the sensor can be calibrated
against a different environment’s magnetic field strength.
Fig. 2 shows a matlab visualization of how a standard size
vehicle perturbs the Earth’s surface magnetic field. The red
centered sphere represents a standard vehicle. Earth’s
magnetic field travels from top to bottom. We can see that the
field converges into the car and diverges out of the car,
leaving a region of magnetic vacuum surrounding the car
perpendicular to the field direction.
model our magnetometer will be based upon. The region of
operation for the sensor is when H-field is between x and y.
Fig. 4 shows the system-level setup of our sensor system with
the various circuit components.
User Interface
Filter &
Fig. 2. Matlab visualization of a vehicle's distortion of the Earth's
magnetic field
In the diagram above, the Earth’s magnetic field travels from
the right to left. Through modelling, it is found that
perturbations of the Earth’s magnetic field by the vehicle
(black sphere centered in the picture) as a function of distance
can be characterised by the following relationship:
 Ur  1  R 
H  2  43.69  cos()  
   ^3  
Ur  2  r 
Fig. 4. Flow chart for sensor system.
The proposed Function Generating Circuit (FGC) has the
following circuit schematic as shown in Fig. 5:
R is defined to be the radius of sphere centered onto Fig.2 and
simulates an ordinary standard-sized passenger vehicle. ‘r’ is
defined as the separating distance between the vehicle and the
magnetometer sensor. µr is the relative permeability of the
material in the vehicle. For the purposes of our simulation, we
chose a value of 100 as an accurate approximation with metals
used for the construction of vehicles. The angle phi is defined
to be the angle of deviation of the sensor with respect to the
vehicle with the reference point at parallel to the Earth’s
background magnetic field direction.
Our choice of material for our magnetometer is the N30 ferrite
core consisting of base material MnZn. This material gives us
the following B-H curve shown in Fig. 3. An approximation of
the curve using power series was obtained and illustrated by
the black curve with its equation.
Fig. 3. Approximation of B-H curve.
From Fig. 3 above, the core saturates when the H field exceeds
100 amperes per meter (A/m). The desired region of operation
for the sensor is non-saturation, where the H-field will never
exceed 100A/m. For this region of operation, the power series
expansion is:
y  3E - 05x 3 - 0.0226x 2  5.2491x
The model is accurate for characterizing the B-H characteristic
of our choice of material. Equation 2 will be the quantitative
Fig. 5. Function generating circuit used to produce sine wave.
The function generating circuit is modeled after a quadrature
oscillator, and produces 1kHz sine and cosine waves, both
with a 5V DC offset. The circuit consists of two primary Opamps (OA1, OA2), which are integrators. Each individual
output is fed into the input of the other Op-amp, and the only
pair of functions which can be integrated repeatedly and retain
the same oscillation is sine and cosine. The second stage
consists of an inverting amplification stage with gain 10, as
well as a unity gain inverting amplifier that acts as a buffer for
the sign of the signal in order to obtain a more easily
detectable driving function. A switch is used at V-impulse to
initialize the feedback oscillations necessary to produce the
sine and cosine outputs waveforms. This gives the option of
mobility to the sensor system for field tests in different
environments. For the purposes of our project, testing was
conducted in the laboratory using the Agilent Function
Generator in place of the function generating circuit.
The function generator produces a sine wave signal with
amplitude of 10 volt at a frequency of 1KHz with 5 voltage
offset. This signal will be fed into the Driving Excitation Coil
(DEC) on the left of the magnetometer shown in Fig. 6:
Fig. 6. Magnetometer core compared to a dollar coin.
The dimensions of the magnetometer core (blue) are: outer
diameter = 58.3 mm, inner diameter = 40.8 mm, height = 17.6
mm, impedance of the driving coil = 843 ohms. The DEC has
150 turns wound tightly in two layers. The magnetic field (H)
produced by the excitation coil can be characterized by the
following equation:
Ho 
Idec* Ndec
On the left of the magnetometer core are two Sensing
Detector Coils (SDC): SDC 1 (top coil) and SDC 2 (bottom
coil). SDC 1 and 2 are wound tightly in layers around the core
and in opposite directions, such that the electromotive force
(EMF) induced in one coil cancels out that of the other coil.
The magnetometer sensor measures changes in the
background magnetic field strength through variations in the
induced EMF at the sense coils.
Figure 7: B-H Curve operating points for sensing coil 1 (Left)
and 2 (Right) without voltage offset.
Given an arbitrary input function from the driving coil with a
total peak-to-peak spanning the black markers in Fig. 7 and
Fig. 8, the location on the B-H curve of the core with an
unperturbed magnetic field varies with and without an offset
applied to the driving function. Assuming sense coil 1 is
parallel and sense coil 2 is perpendicular to the Earth’s
magnetic field. Without applying an offset to the B-H curve of
the ferromagnetic core, the operating point of the core is
depicted in Fig. 7. Assuming no magnetic field detection in
coil 2, and given some input, the resulting output peak-to-peak
spans some range on the B-H curve. Now, given the same
input, but in coil 1, the output span on the B-H curve will
simply be shifted while remaining in a linear region. In this
regime, the output will shift the same amount as the input
whether or not the sensing coils are affected by a background
magnetic field strength. Thus, in terms of differences in the BH curve magnitude, no change in magnetic flux, and thus no
object, can be detected. Since both sensing coils are wound
oppositely, the change in magnetic flux in both coils is exactly
the same due to its linear operating point, despite the operating
point being shifted. On the other hand, Fig. 8 denotes the
desired operating point on the B-H curve that will enter the
magnetic saturation region when the driving function has a
voltage DC offset. In this situation, given some input, the
offset combined with coil 1 will result in a non-linear
relationship between the input and output, whereas the region
of coil 2 will remain in a linear operating regime. The
saturation of the ferromagnetic core’s B-H curve causes the
resulting difference in the output signal of the device. By
operating on the B-H curve with an offset, the device can be
used to detect disturbances in the Earth’s magnetic field.
Each SDC will have an end probe, and they will be
connected to the Signal Amplifying Circuit in Fig. 9 to boost
the amplitude of our signal.
Fig. 9. Signal Amplifying Circuit.
For our laboratory demonstration we build an envelope
detector circuit for analysis. The envelope detector in Fig. 10
is connected after the amplifier circuit to trace the peak values
of the alternating signal.
Figure 8: B-H Curve operating points for sensing coil 2 (Left)
and B (Right) with voltage offset.
Figure 10: Envelope Detector Circuit
Alternatively, for future work we propose using an Analog-toDigital converter with a sampling frequency (2.1KHz), just
over twice that of the input signal (1 KHz) in accordance to
the Shannon-Nyquist sampling theorem. The output voltage
from the Signal Amplifier Circuit will be fed into a 16-bit
Analog-to-Digital converter. The ADC has an operating
temperature range of 0 to 70 degrees Celsius with a Signal-toNoise Ratio (SNR) of 90 dB at 1 KHz. Its input ranges from 12 to 12 volts and has an input impedance of 7.9 Ohms. Its
acquisition time is 1.82 microseconds, which is more than
sufficient for our sampling frequency. The output from the 16
bit ADC will enable recording and further analysis currently
outside the scope of this sensor project. The output from the
ADC will also be channeled into a RMS-to-DC converter
AD637 which will compute the true RMS value of the Vout
sinusoidal waveform. The AD637 has an operating
temperature of 0 to 70 degrees Celsius and a bandwidth of
9MHz for the input its voltages.
For the purposes of testing and characterizing our sensor
system, we used an air-core solenoid with a radius of 17mm
and 565 turns of magnetic wire. The current through the wire
coil is 0.55 amperes at 3.12 volts. This creates a turn density
of 194 turns/cm. The device produces a field of:
We used this solenoid to simulate the vehicle of interest, and
characterized our sensor system with this test solenoid device.
Out final data of interest is the output voltage obtained from
the envelope detector. We obtained the transfer function of:
V(Out) = 0.0108r 4 - 0.33r3 + 3.7244r2 - 18.868r + 40.334
‘r’ is the distance between the sensor and solenoid.
Fig. 12. Plot of sensitivity vs. distance from perturbation.
We note that sensitivity is non-linear and decreases as distance
ranges from 2.5cm to 6cm, and stays fairly constant from 6cm
to 10cm. It increases from 10cm thereafter which is caused by
the non-ideal approximation of our transfer function with a
fourth order polynomial estimate.
B. Linearity:
Although the transfer function is inherently non-linear, other
sources also contribute to the non-linearity of the sensor
system. These external sources include:
1. Wire diameter variations in the driving and sensing
2. Non-uniformity of wire windings.
3. Changing of resistance in wires with variations of
C. Dynamic range
The maximum sensing distance (r) of our sensor is
determined by the sensitivity of our sensor. At further
experimentation, our maximum reasonable sensing range
is 11cm at 1.81 volts. The nearest distance our sensor can
operate is at the surface of the vehicle is 2.5cm at 12.4
volts. This is because our amplifier goes into saturation of
12.5 volts for distances nearer than 2.5 cm.
Dynamic Range
The dynamic range is calculated as the log of the ratio of
the range. The minimum incremental resolution of our
sensor is 0.05V.
20*log10((12.4-1.81)/0.05V) = 46.5 dB
The resolution of the sensor is given by:
Re s 
Figure 11: Transfer function
A. Calculated Sensitivity
Voltage _ SpanDis tan ce _ Re s   (12.4  1.81)0.25cm   0.311V
Dis tan ce _ Span
Resolution is limited by potential sources of interference
and the Signal-to-Noise Ratio (SNR) of the electrical
components used in the sensor system.
D. Hysteresis
Magnetic hysteresis is an issue if the toroid core is
brought to saturation levels. Fig.13 below shows the
graphical representation of hysteresis:
Using data provided from the Op-Amp data specification
sheet, the summarized key values for the noise in the Op-Amp
Fig. 13. Graphical representation of hysteresis.
E. Deadband
The sensor has a Deadband when angle phi is + 90 degrees
and -90 degrees. This is because as shown in equation 1, the
change in H-field becomes zero with these phi angles due to
the inherent limitations of the boundary value problem in the
mathematical model. Hence, the Deadband exist when angle
phi is +90 and -90 degrees.
F. Output Range
The input is valid from r to infinity. It is valid at r due to
boundary value conditions, and invalid within the Lorentz
sphere due to the solutions obtained from the Laplacian.
The output ranges from Vref = 1.80V to Vmax = 12.4V. Vref
is defined as the value when r = infinity. Vmax is defined as
the value when r = R (boundary value condition).
G. Saturation
Using the values for our parameters from the output range
section, Vref = 1.80V to Vmax = 12.4V.
H. Noise analysis
The noise of the whole sensor system originates
predominantly from two sources: First, the noise from the
magnetometer sensor from the background fluctuations in
magnetic field strengths caused by electrical components and
devices and the resistor thermal noise from the resistance in
wires in the coils. Secondly, the noise from the interface
circuit, such as thermal noise from the resistors, capacitors and
the noise from the operational amplifier. Other sources of
noise besides Johnson noise such as Shot noise and Flicker
Noise are less significant.
All the thermal noise from resistors and capacitors can be
given as:
Johnson noise calculations:
vR _ DEC  G
4k TR f  41.38  10
vR _ SDC  G
4k TR f  41.38  10
vR _ Amp1  G
4k TR f  41.38  10
vR _ Amp 2  G
4k TR f  41.38  10
 23
 23
 23
 total 
 3.1nV   4.57V 
J /  K 300 K 82 1000 Hz  36.3nV
J /  K 300 K 20000 1000 Hz  560nV
J /  K 300 K 0.6 1000 Hz  3.1V
J /  K 300 K 1.3 1000 Hz  4.57V
 23
  36.3V    560nV   0.56 V
Calculated resistance of wires in DEC = 0.6 Ohms. Calculated
resistance of wires in SDC = 1.3 Ohms.
Voltage Noise From Op-Amp RTI: env = 3560nV
Current Noise From Op-Amp RTI (as a voltage): eni = 1.67nV
Resistor Noise RTI:enr = 4020nV
Total Noise RTI: en in = √((3560nV)2 + ((1.67nV)2 +
((4020nV)2) = 5369nV
Total Noise RTO: en out = en in * gain = (5369nV)(1) = 5369nV
Then, the total noise of the system and the Signal to Noise
Ratio can be calculated as:
SystemNois e   system   total   other 
 0.56V 
 total 2   other 2
  5369nV   5.40 V
 OutputSpan 
 12.4  1.81 
  20 log
dB  125dB
SNR  20 log
 5.40V 
The magnetometer and accompanying circuits have much
potential for detecting perturbations in the Earth’s magnetic
field located up to 14cm for this proof of concept. The input
and output ranges are reasonably measurable values with high
enough resolution to handle the noise we considered in our
analysis. The primary limitation of performance is the medium
range of the magnetic field detection. Our measurement of
interest falls off proportional to 1/r3, and thus it is would
additional specialized and sensitive instruments to accurately
distinguish objects farther than 14cm away.
Future work for the sensor includes consideration of other
noise sources in order to further improve its response to noise.
In addition, sharper filters could be designed to better isolate
the harmonics we are interested in analyzing. In order to
improve on location mapping, a multi-sensor system would be
necessary to triangulate the position of the perturbing source.
This proof of concept shows that it is possible to construct
vehicle sensors using magnetometers. Future research and
developments into this area would provide methods of vehicle
detection with work based on this current concept.
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