Dynamically Configured Waveform-Agile Sensor Systems

Transcription

1 Dynamically Configured Waveform-Agile Sensor Systems Antonia Papandreou-Suppappola in collaboration with D. Morrell, D. Cochran, S. Sira, A. Chhetri Arizona State University June 27, 2006 Supported by AFOSR MURI on Waveform Diversity for Full Spectral Dominance and DARPA ISP program

2 Sensing Activities at Arizona State University SenSIP: Sensing, Signal and Information Processing Center ( Research Topics Waveform-agile sensing Sensor scheduling for tracking applications Real-time sensing using Berkeley mote sensors (perimeter security) Adaptive tracking imager systems

3 Waveform-Agile Sensing Objective To dynamically select and configure time-varying waveforms in clutter environments for waveform-agile sensors Performance criterion: minimum mean square tracking error Nonlinear observation models preclude exact or closed form solutions Solution We use the unscented transform and a particle filter that employs probabilistic data association to deal with the uncertainty in the measurement origin due to clutter A greedy search is used to find the sensor configuration that minimizes the predicted tracking error

4 Target kinematics and observations models B (x B, y B ) [r B ṙ B ] y θ B Trajectory Target ẏ x ẋ [r A ṙ A ] θ A A (x A, y A ) Constant velocity kinematics model Sensors measure delay-doppler Narrowband received signal model X k = FX k 1 + W k, z k = h(x k ) + V k

5 Clutter Modeling Range Rate Target Observation Predicted Validation Gate Clutter Each sensor validates multiple observations Z k = [z 1 k, z 2 k,..., z m k k ] Number of false alarms assumed Poisson distributed due to clutter Range µ(m) = exp( ρv k)(ρv k ) m m! Clutter is assumed to be uniformly distributed in the observation space

6 Waveform Structure At every sampling instant, each sensor transmits a generalized FM chirp s(t) = a(t) exp (j2πbξ(t)), t < T/2 + t f Frequency (Hz) tf x a(t) 0 T PFM κ = 2.8 LFM tf t Trapezoidal envelope allows evaluation of the CRLB Each sensor is independently configured Waveform parameter vector is θ k = [ξ k (t) λ k b k ] T 4 EFM 2 HFM Time (s) x 10 4

7 Problem Statement At each sampling instant k, we seek the sensor configuration [ ] θ A θ k = k, that minimizes the predicted mean square tracking error Cost function for greedy optimization } J(θ k ) = E Xk, Z k Z 1:k 1 {(X k ˆX k ) T Λ(X k ˆX k ) The cost of using a waveform represents an average over future states, observations, and clutter realizations θ B k

8 Block Diagram p(x k Z 1:k, θ 1:k ) Target tracking Particle filter p(x k Z 1:k 1, θ 1:k 1 ) Candidate waveform f ξ(t/t r ) Unscented Transform Estimates of [r ṙ] T λ Grid Search MSE Prediction MSE Minimization Sensors Configuration that minimizes predicted MSE

9 Performance Criterion Due to the nonlinear observations model, the cost function J(θ k ) cannot be evaluated in closed form Stochastic optimization techniques may be used to find the best configuration θ k, but they are computationally expensive and difficult to control The unscented transform provides a suitable means of evaluating the cost function We use the covariance update of the unscented Kalman filter to approximate the cost

10 Predicted Cost Approximation Prediction of state covariance P k k 1 = FP k 1 k 1 F T + Q. Unscented transform is used to generate P i xz and P i zz corresponding to sensor i Covariance update if there were no clutter P c k k = ( Pi xz P i zz + N(θ i k )) 1 P i T xz Since measurements are of uncertain origin P i k k (θi k ) = P k k 1 q i 2 k P c k k Sequential updates for Sensor A and B yield P k k (θ k ) Cost function is approximated as J(θ k ) Trace{ΛP k k (θ k )}

11 Radar Simulation Averaged mean square error - LFM only 10 4 Averaged MSE (m 2 ) ρ = 1e 3 Configured 10 1 λ min λ max Configured ρ = 1e Time (s)

12 Radar Simulation Averaged mean square error - agile phase function 10 3 LFM PFM κ = 2.8 PFM κ = 3.0 EFM HFM Configured Averaged MSE (m 2 ) Configured Time (s)

13 Radar Simulation Typical waveform selection HFM Sensor A EFM PFM (3.0) PFM (2.8) LFM HFM Sensor B EFM PFM (3.0) PFM (2.8) LFM Time (s)

14 Waveform Characterization Correlation coefficient VG Volume Conditional Variance LFM PFM (2.8) PFM (3.0) EFM HFM LFM PFM (2.8) PFM (3.0) EFM HFM LFM PFM (2.8) PFM (3.0) EFM HFM Waveform type

15 Heavy Clutter Maritime Scenarios Returns from sea clutter are known to exhibit spatial and temporal correlation For detection of small-rcs targets using low grazing angle radars, clutter density is high and thus SCR low: if we assume similar clutter statistics in several range bins and high pulse repetition frequency (PRF), then estimation of the subspace occupied by the clutter returns is possible In low SCR scenarios, we can improve detection and tracking performance by subspace-based clutter suppression

16 Sea Clutter Modeling Following the work of Watts, Ward and Tough (2005) Sea surface presents the incident radar beam with a large number of scattering centers Independent contributions from the speckle give rise to locally Gaussian statistics, characterized by short correlation time (10 20 ms) and length scales Texture (large-scale swell structures) modulates the local mean power of this speckle-like return This texture can be modeled by a gamma distributed process which de-correlates much less rapidly (50-60 s) than the local speckle process Radar return is then represented as the product of this gamma process and a unit power Gaussian/Rayleigh process

17 Waveform Adaptive Detection and Tracking Clutter mapping, suppression and detection... Tracker update... interval k k + 1 k + 2 k + 3 dwell # Waveform adaptation Tracker update N N 1 PRI k k + 1 Two time frames - short PRI and long tracker update Radar scene is unchanged over two successive dwells

18 Clutter Suppression N Transmitted signal 0 r 0 r r j MF output in range bins range bins Scatterers assumed stationary across N snapshots in a dwell in jth range bin (due to high PRF) Due to high clutter, target contribution is minimal across range bins; estimate clutter space by estimating covariance matrix of clutter returns across neighboring range bins Measurements extract a waveform-independent estimate of clutter subspace; orthogonal projection of received signal on subspace can yield a clutter-suppressed signal

19 Clutter Suppression Form the estimate of the covariance matrix of clutter returns in the jth bin as ˆR j = 1 L L i=1 r i r H i where L is the number of bins surrounding the jth bin (training data) ˆQ j is the subspace corresponding to the M largest eigen values of ˆR j r j = (I ˆQ j )r j is the clutter suppressed signal SCR is defined as the ratio of target power over total clutter power in the range bin containing the target; better detection is achieved with higher scatterer density

20 Simulation Example Pulse length: 100 ns PRF: 2 khz Bandwidth: 15 MHz SCR: 20 db LFM chirp waveform N = 20 snapshots L = 40 range-bins for covariance estimation about 750 scatterers in the observation space SCR 20 db, ρ = 0.0 SCR 20 db, ρ = 0.0 Magnitude of MF signal Tracker update Range bin Magnitude of clutter suppressed signal Tracker update Range bin Original signal, r j 2 Clutter suppressed signal, r j 2

21 Performance of Clutter-suppression Algorithm P d P fa Clutter map generated during the first dwell of each pair will be used to design the waveform for the second dwell Waveform design will aim at improving range estimation of the target, and eventually minimizing tracking error

22 Conclusions: Waveform Design A greedy optimization algorithm for waveform scheduling to minimize the predicted mean square tracking error was presented Nonlinear observations models significantly complicate the waveform selection problem In more recent work, we incorporate the affect of the sidelobes of the ambiguity function on the estimation errors We exploit the temporal correlation of clutter in a subspace-based approach to the suppression of clutter returns (Asilomar 2006)

23 Binary Programming for Sensor Scheduling Problem Statement Track a moving target through a field of motes. Measurements are acoustic energy from target; tracking done at a base station Motes are either active or in very low power standby mode. Goal is to activate selected sensors to minimize energy consumed while maintaining a desired track accuracy Constrained discrete optimization problem: find set of sensor configurations to satisfy constraint Computational intractable as number of motes increases

24 Combined Tracking and Scheduling

25 Sensor Scheduling Approach Pose constrained discrete optimization problem as a constrained binary programming Approximate computation of predicted tracker error Linearize measurement model about predicted state (e.g. Extended Kalman Filter) Inverse of error covariance matrix (constraint function) is linear in binary control variables (1 if mote is used, 0 is mote is not used) Error is polynomial function of control variables Binary programming for sensor scheduling Natural framework for on/off scheduling problems Linear programming relaxation combined with Branch & Bound algorithm (existing software) Typically avoids significant enumeration of solution space

26 Sensor Costs: Energy Model Packet Transmit Energy Packet Receive Energy Sensor Circuitry Energy Processing Energy

27 Simulations and Results Sensor field 100 m x 100 m 400 randomly placed acoustic sensors Maximum sensors scheduled: 70 Energy use adopted from MICA2 datasheet Target velocity: (3, -3) m/s Target travels for 35 time steps of 1 s each 4,000 particles used in particle filter Error threshold: 0.1 m 2 to 0.6 m 2

28 Tracking Performance MC = true SE averaged over MC simulations Pred = SE predicted by scheduler PF = SE approximated by particle filter Error threshold is 0.3 m 2

29 Tracking Performance Average number of sensors activated versus error threshold

30 Tracking Performance Average energy consumption versus error threshold

31 Tracking Performance Average run time versus error threshold

32 Conclusions: Sensor Scheduling Sensor scheduling: Integral part of sensor signal processing: Intelligent allocation of sensing resources Reduce cost consumption of sensors Sensor scheduling effective when: Scheduling formulation is amenable to optimization Need to exploit structure of the problem Binary programming for sensor scheduling is a natural framework for on/off scheduling problems that avoids significant enumeration of solution space