Tracking Mobile Nodes Using RF Doppler Shifts

Branislav KusyBranislav KusyComputer Science DepartmentComputer Science Department

Stanford UniversityStanford University

Akos Ledeczi, Xenofon KoutsoukosAkos Ledeczi, Xenofon KoutsoukosInstitute for Software Integrated SystemsInstitute for Software Integrated Systems

Vanderbilt UniversityVanderbilt University

Published in Sensys 2007, Best paper AwardPublished in Sensys 2007, Best paper Award

Presenter: aheyPresenter: ahey

Outline

• Problem Definition• Mechanism

• 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

• 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 signalsource

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

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?

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

• 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

Can we Measure Doppler Shifts?

430MHz

430MHz+300Hz

Measuring Doppler shiftWe use radio interferometry to measure Doppler frequency shifts with 0.21 Hz accuracy.

T

Si

A

•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)

300Hz+ Δfi,T

Beat frequency is estimated using the RSSI signal.

TrackingUnknowns:• Location(x,y) of moving object T• Velocity(vx,vy) of T• f^=fT -fA

define a parameter vectorx=(x,y,vx,vy,f^)T

Knowns (constraints):• Locations (xi,yi) of nodes Si

• Doppler shifted frequencies fi

define an observation vectorc=(f1,…,fn) T

Function H(x)=c:

f4 = fT – fA + Δf4

= fT – fA + v4/λT

We want to calculate location and velocity of node T from the measured Doppler shifts.

Tracking as Optimization Problem

Non-linear system of equations!

• 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

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

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)

State Estimation: Extended Kalman Filter

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 covarianceP : error covariance matrixKk: kalman gainR : measurement noise

Improving Accuracy

Experiment:• tracked node moves on

a line and then turns • KF requires 6 rounds to

converge back.

1 2

3

45 6

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

Tracking Algorithm

Doppler shifted frequencies

Infrastructure nodes record Doppler shifted beat frequency.

Extended Kalman

filterLocation & Velocity

Calculate location and velocity using Kalman filter.

Non-linear least

squaresNLS Location & Velocity

Update EKF

Updated Location & Velocity

If maneuver is detected, calculate NLS solution and update EKF state.

Show location on the screen.

Maneuver

detectionYes

Run a simple maneuver detection algorithm. (Since velocity error is small, maneuver can be detected by speed estimate)

No

Location & Velocity

Implementation

17

• Platform• 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

Experimental Evaluation

18

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

Experimental Evaluation

19

Vanderbilt football stadium

• 50 x 30 m area• 9 infrastructure ExScal

nodes• 1 ExScal mote tracked • position fix in 1.5

seconds

Maneuvering case

Only some of the tracks are shown for clarity.

Experimental Evaluation

20

• Non-maneuver case : error is normally distributed around mean error

• Maneuver case : frequent large errors due to Kalman filter diverging from the ground truth

Simulation Evaluation

21

• 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 signal4. σm standard deviation of the measurement noise5. σf standard deviation of the change of the interference frequency (f) for consecutive measurements6. 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.

Simulation Evaluation

22

In general,

1.adding more receivers2.limiting the maximumspeed of the tracked node3.increasing the temporal resolution of the collected data

help to improve the accuracy.

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