Tracking Mobile Nodes Using RF Doppler Shifts

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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
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Outline

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

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Tracking Mobile Objects
Problem definition keep track of location and
velocity of cooperating moving objects
continuously over time.
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Doppler Effect

• Assume a mobile source transmits a signal with
  frequency f, and f is the frequency of received
  signal

source Jose Wudka, physics.ucr.edu
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Utilizing Doppler Effect

• Single receiver allows us to measure relative
  speed.
• Given frequency(wavelength) of transmitted
  signal
• f c/?f 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

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Can we Measure Doppler Shifts?

• Problems with resource constrained hardware
• Not adequate for frequency domain analysis (takes
  15 seconds to calculate 512-point FFT using 8MHz
  processor)

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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

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

• 2 nodes T, A transmit sine waves _at_430 MHz
• fT, fA (let fTgt 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 ?fi,T
• (one problem we dont know the value fT fA
  accurately)

T
Si
?fi,T
Beat frequency is estimated using the RSSI signal.
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Tracking

• Unknowns
• Location(x,y) of moving object T
• Velocity(vx,vy) of T
• ffT -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.
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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 /?t
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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

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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)

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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
covariance P error covariance matrix Kk kalman
gain R measurement noise
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Improving Accuracy
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• Experiment
• tracked node moves on a line and then turns
• KF requires 6 rounds to converge back.

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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

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Tracking Algorithm
Infrastructure nodes record Doppler shifted beat
frequency.
Doppler shifted frequencies
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Implementation

• Platform
• TinyOS
• Mica2 mote (8MHz CPU, CC1000 Chipcon radio)
• Create Interference Signal
• ffT 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

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Experimental Evaluation

• Vanderbilt football stadium
• 50 x 30 m area
• 9 infrastructure ExScal nodes
• 1 ExScal mote tracked
• position fix in 1.5 seconds
• ExScalMica2 compatible motes enclosed in a
  weather-proof packaging

Non-maneuvering case
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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
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Experimental Evaluation

• Non-maneuver case error is normally distributed
  around mean error
• Maneuver case frequent large errors due to
  Kalman filter diverging from the ground truth

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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 ?t of the transmitted signal
• 4. sm standard deviation of the measurement noise
• 5. sf 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.

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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.

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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