1. Tracking Mobile Nodes Using RF Doppler Shifts
Branislav Kusy
Computer Science Department
Stanford University
Akos Ledeczi, Xenofon Koutsoukos
Institute for Software Integrated Systems
Vanderbilt University
Published in Sensys 2007, Best paper Award
Presenter: ahey

2. Outline Problem Definition Mechanism Implementation
Doppler Effect
Tracking as optimization problem
Implementation
Experimental Evaluation
Simulation Evaluation
Conclusion

3. Tracking Mobile Objects
Problem definition: keep track of location and velocity of “cooperating” moving objects continuously over time.

4. Doppler Effect f’ = f + Δf Δf = - v / λf
Assume a mobile source transmits a signal with frequency f, and f’ is the frequency of received signal
f’ = f + Δf
Δf = - v / λf
v is relative speed of source and receiver
λf is wavelength of the transmitted signal
If an object transmits a signal and move relative to an observer, the frequency of the observed signal will be Doppler shifted and the magnitude of the shift depends on the frequency of the signal and the relative velocity of the transmitter and observer.
source
Jose Wudka, physics.ucr.edu

5. Utilizing Doppler Effect
Single receiver allows us to measure relative speed.
Given frequency(wavelength) of transmitted signal
f = c/λf we can compute the relative speed v by measuring the received frequency f’
If T is the traced node, Si is the anchor node, the above method can only determine to the relative speed v (projecting the velocity vector v on the TSi line), no bearings
Multiple receivers allow us to calculate location and velocity of the tracked node.
By measuring sufficiently many relative speeds
Mobile node T transmits a signal
Anchor nodes Si estimate relative speed of T from the received Doppler shifted signal

6. Can we Measure Doppler Shifts?
Typ. freq
Dopp. Shift 1 m/s)
Acoustic signals
1-5 kHz
3-15 Hz
Radio signals (mica2)
433 MHz
1.3 Hz
Radio signals (telos)
2.4 GHz
8 Hz
Problems with resource constrained hardware:
Not adequate for frequency domain analysis (takes 15 seconds to calculate 512-point FFT using 8MHz processor)

7. Can we Measure Doppler Shifts?
Time domain analysis requires relatively small signal frequency due to sampling rate limitations.
Doppler shift is proportional to frequency of measured signal. It cannot be too small for enough accuracy.
Solution: Radio Interferometry

8. Measuring Doppler shift
We use radio interferometry to measure Doppler frequency shifts with 0.21 Hz accuracy.
2 nodes T, A transmit sine MHz
fT, fA (let fT> fA)
Node Si receives interference signal (in stationary case)
Signal freq: fs = (fT + fA)/2
Envelope freq: fi = fT – fA
T is moving, fi is Doppler shifted
fi = fT – fA + Δfi,T
(one problem: we don’t know the value fT –fA accurately)
430MHz
430MHz+300Hz A
300Hz T Si
Two nodes transmit sine waves at different frequencies( for example fT and fA ) at the same time, so that the two signals interfere with each other and the resulting interference signal has a frequency of (fT + fA)/2 and a low frequency envelope of |fT - fA|
+ Δfi,T
Beat frequency is estimated using the RSSI signal.

9. Tracking
Unknowns:
Location(x,y) of moving object T
Velocity(vx,vy) of T
f^=fT -fA
define a parameter vector
x=(x,y,vx,vy,f^)T
Knowns (constraints):
Locations (xi,yi) of nodes Si
Doppler shifted frequencies fi
define an observation vector
c=(f1,…,fn) T
Function H(x)=c:
We want to calculate location and velocity of node T from the measured Doppler shifts.
H is a vector function consisting of n functions ( n anchor nodes) Hi: R5 -> R, each of them calculating the Doppler shifted interference frequency fi measured at Si.
Hard problem to solve - we model it as an optimization problem.
f4 = fT – fA + Δf4
= fT – fA + v4/λT

10. Tracking as Optimization Problem
Tracked node T with velocity v transmits a signal.
Sensor Si measures the Doppler shift of the signal which depends on vi, the relative speed of T and Si.
fi = Hi(x) = f^ – vi /λt
Non-linear system of equations!
sinα and cosα can be calculated using the coordinates (x,y) and (xi,yi)
Hard problem to solve - we model it as an optimization problem.

11. Tracking as Optimization Problem
Non-linear Least Squares (NLS)
Minimize objective function ||H(x) – c||
Start with initial approximation x0 and iteratively update this x until it converges to a local minimum of an objective function
Experiment:
1 mobile transmitter
8 nodes measure fi
Figure shows objective function for fixed (x,y) coordinates
We may not be able to find x, such that H(x) = c => objective function may not be zero
In other words, minimizing fi- (f^ - g(x,y, vx,vy,xi,yi,λt) ) for i =0 to n (n anchor nodes) , find x,y,vx,vy

12. Tracking as Optimization Problem
Constrained Non-linear Least Squares (CNLS)
In tracking, constrain the area where the tracked node located
Modify objective function by adding a barrier function, introduce positive penalty outside region of interest
Problems with NLS
Depending on starting point x0 and measurement errors that corrupts c, it may fail.
Multiple local minima exist, need Constrained NLS
Global minimum is still not accurate (as large as 5.6m location error)
We may not be able to find x, such that H(x) = c => objective function may not be zero
In other words, minimizing fi- (f^ - g(x,y, vx,vy,xi,yi,λt) ) for i =0 to n (n anchor nodes) , find x,y,vx,vy

13. State Estimation: Extended Kalman Filter
Noise corrupted observations degrade performance of CNLS
Assume measurement error is Gaussian
Model dynamics of the tracked node (constant speed)
Update state based on new observations
KF prediction phase:
EKF update phase:
Accuracy improves, but maneuvers are a problem
:predicted new state:
:previous state:
F models system dynamics
(state transition matrix)
Q : process noise covariance
P : error covariance matrix
Kk: kalman gain
R : measurement noise
P is error covariance matrix , a measure of the accuracy of estimated state x
Q is noise covariance

14. Improving Accuracy 6 5 4 3 Experiment:
tracked node moves on a line and then turns
KF requires 6 rounds to converge back. 2 1

15. Resolving EKF Problems
Combine Least Squares and Kalman Filter
Run standard KF algorithm
Detect maneuvers of the tracked node
Update KF state with CNLS solution
Too much trust: measurement error can introduce large tracking errors
Too little trust: errors in the system model introduces large errors
objective: improve EKF accuracy in the maneuvering case, while keeping the good performance in the non-maneuvering case

16. Extended Kalman filter Non-linear least squares
Tracking Algorithm
Infrastructure nodes record Doppler shifted beat frequency.
Doppler shifted frequencies
Extended Kalman filter
Location & Velocity
Calculate location and velocity using Kalman filter.
Maneuver detection
Yes
Run a simple maneuver detection algorithm. (Since velocity error is small, maneuver can be detected by speed estimate) No
Location & Velocity
Non-linear least squares
NLS Location & Velocity
Update EKF
Updated Location & Velocity
If maneuver is detected, calculate NLS solution and update EKF state.
Show location on the screen.

17. Implementation Platform Create Interference Signal
TinyOS
Mica2 mote (8MHz CPU, CC1000 Chipcon radio)
Create Interference Signal
f^=fT –fA is unknown due to 4kHz errors at 400MHz
Measuring Doppler Shiftsl
RSSI circuit applies a low pass filter, only beat frequency (envelope of interference signal) is visible in RSSI signal
Apply a moving average filter to smooth incoming signal
Find all peaks in the filtered signal 17

18. Experimental Evaluation
Vanderbilt football stadium
50 x 30 m area
9 infrastructure ExScal nodes
1 ExScal mote tracked
position fix in 1.5 seconds
ExScal:Mica2 compatible motes enclosed in a weather-proof packaging
Non-maneuvering case 18

19. Experimental Evaluation
Vanderbilt football stadium
50 x 30 m area
9 infrastructure ExScal nodes
1 ExScal mote tracked
position fix in 1.5 seconds
Only some of the tracks are shown for clarity.
Maneuvering case
Notice
that the velocity estimates have approximately the same errors
for both EKF and CNLS-EKF. Intuitively, this is because
our measurement model is based on estimating the relative
velocities of the tracked node which gives us more information
on its velocity than its location. Therefore, even if we
optimize our objective function at a wrong location, the velocity
estimates are still relatively accurate (see Fig. 6). 19

20. Experimental Evaluation
Notice
that the velocity estimates have approximately the same errors
for both EKF and CNLS-EKF. Intuitively, this is because
our measurement model is based on estimating the relative
velocities of the tracked node which gives us more information
on its velocity than its location. Therefore, even if we
optimize our objective function at a wrong location, the velocity
estimates are still relatively accurate (see Fig. 6).
Non-maneuver case : error is normally distributed around mean error
Maneuver case : frequent large errors due to Kalman filter diverging from the ground truth 20

21. Simulation Evaluation
Experimental evaluation is limited due to its complexity and is also time consuming
The parameters of the simulation engine are:
1. 2D coordinates of infrastructure nodes Si
2. the track of the mobile node (a set of time-stamped 2D points)
3. the wavelength λt of the transmitted signal
4. σm standard deviation of the measurement noise
5. σf standard deviation of the change of the interference frequency (f) for consecutive measurements
6. the measurement update time tm
For every measurement round, the location and the velocity of tracked node is recalculated based on track data, the relative speeds vi are calculated and converted to the frequencies fi.
Notice
that the velocity estimates have approximately the same errors
for both EKF and CNLS-EKF. Intuitively, this is because
our measurement model is based on estimating the relative
velocities of the tracked node which gives us more information
on its velocity than its location. Therefore, even if we
optimize our objective function at a wrong location, the velocity
estimates are still relatively accurate (see Fig. 6). 21

22. Simulation Evaluation
In general,
adding more receivers
limiting the maximum
speed of the tracked node
increasing the temporal resolution of the collected data
help to improve the accuracy. 22

23. Conclusions
Introduce a novel tracking algorithm that utilizes Doppler shift measurements only
Doppler shifts can be accurately measured using radio interferometry
Improve EKF performance in maneuvering case
Evaluate the algorithm both experimentally and in simulation