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

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

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

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

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

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)

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

Measuring Doppler shift We use radio interferometry to measure Doppler frequency shifts with 0.21 Hz accuracy. 2 nodes T, A transmit sine waves @430 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.

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

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.

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

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

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

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

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

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.

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

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

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

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

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

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

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