Multi-Sensor Adaptive Signal Processing for Landmines

Transcription

1 Multi-Sensor Adaptive Signal Processing for Landmines Leslie Collins, Mark Kolba, Peter Torrione, and Yongli Yu Electrical and Computer Engineering Duke University Work supported by DARPA/ARO MURI

2 Overview RDOF Feature Selection Adaptive Uncertainty Processing Tracking/Classification Sensor Management Simulations New developments Processing Georgia Tech data

3 Issues Sensor path through cell grid for unconstrained sensor 9 Suite of available sensors Performance and cost a function of sensor modality Grid to be searched. Adaptively determine where to go? what sensor to deploy? what sensor parameters to employ?

4 Previously: Adaptive Discrimination- Based Sensor Management Initial algorithm based on Kastella et al. S DPQ (, ) = Ps ( )ln( Ps ( )/ Qs ( )) s= Select a cell which maximizes D Can be calculated recursively Progress: Focus on considering assumptions that are inconsistent with the MURI application areas

5 Simulations x grid, Uniform prior Low SNR detection problem ( db) Number of targets present variable Initial simulations manage sensor threshold, cell sampling Constrained and unconstrained sensor motion Plot probability of error (finding the target at the right location in the grid) versus number of measurements

6 Preliminary Results.9.8 Error probability vs. number of measurements for sensor and target disc: db direct: db direct: 3 db direct: 6 db.7.6 Pe Measurements

7 Progress Extend to consider other priors on target locations Extend to multiple sensors, each with different performance, cost Sequential detection in each cell once selected Unknown number of targets Consider unknown Pd, Pf for each sensor Need to estimate ROCs (performance degrades quickly if unknown) Alternative (pure Bayesian) formulation Comparison to Theory of Optimal Experiments Application to Georgia Tech data

8 Multiple Sensors Performance of different sensor combinations Discrimination Search: S, S2, S3 Discrimination Search: S, S2 Discrimination Search: S Direct Search: S, S2, S3 Direct Search: S, S2 Direct Search: S Pe S: Pd =.9, Pfa =.4, Cost = S2: Pd =.9, Pfa =., Cost = S3: Pd =.99, Pfa =.2, Cost = Time

9 Same Parameters, Uncertainty in Performance Parameters Pe Performance of different sensor combinations Discrimination Search: S, S2, S3 Discrimination Search: S, S2 Discrimination Search: S Direct Search: S, S2, S3 Direct Search: S, S2 Direct Search: S Certain Performance of different sensor combinations Discrimination Search: S, S2, S3 Discrimination Search: S, S2 Discrimination Search: S Direct Search: S, S2, S3 Direct Search: S, S2 Direct Search: S Bayesian/ Integration Time.4 Uncertain Pe Time Pe Performance of different sensor combinations Discrimination Search: S, S2, S3 Discrimination Search: S, S2 Discrimination Search: S Direct Search: S, S2, S3 Direct Search: S, S2 Direct Search: S Time

10 Potential Solutions Bayesian integration over uncertainty is time consuming, provides little improvement in performance. Consider MLE estimation of parameters (GLRT) Need to estimate ROC easiest to estimate slope and threshold/bias in log-log space? Consider Bayesian and Theory of Optimal Experiments Approaches Needs to be adaptive location specific

11 Model Parameter Estimation Response model (ROC) defined by two parameters: slope and median/offset/bias Need to estimate the parameters adaptively Comparison of two methods for parameter estimation Bayesian adaptive estimation Theory of Optimal Experiments Dual adaptation: ROC parameter estimation and sensor parameters/sensor movement/sensor selection

12 Bayesian adaptive parameter estimation Use Bayes rule to calculate the probability of a set of model parameters λ given the response r (Pd) at a specific input intensity x (Pfa). prob( r λ, x) prob( λ) prob( λ r, x) = prob( r λ, x) prob( λ) Select next input to minimize the expected entropy λ ( λ ) E[ H ( x)] = H ( x) prob( r x) where H ( x) = prob( λ r, x)log prob( r, x) r r Update probability of model parameters using the outcome of the current trial r xt ( + ) = argmin( EH [ ( x)]) prob( λ) prob( r() t r, x() t x) x = t+ λ = = λ

13 Parameter estimation using the Theory of Optimal Experiments Find the parameter values that minimize the squared error between the collected data r and the model n(x,λ) ˆ arg min λ = (, ) λ x ( r n x λ ) 2 Select the next input to maximize the information gained, calculated using T xt ( + ) = arg max log + F B F x ˆλ nx (, λ) where column vector Fi () = and B is the Fisher information λi matrix in the form Bi (, j) = ( (), λ ) n( x(), t λ ) n x t λ λ t i j

14 Simulation Result: Estimating ROC Parameters Bias in median estimation Variance in median estimation Percentage of true parameter value % Bayesian adaptive Theory of Opt. Exp..%.%.%.% Trial Percentage of true parameter value % Bayesian adaptive Theory of Opt. Exp. %.%.% Trial Percentage of true parameter value % % Bias in slope estimation Bayesian adaptive Theory of Opt. Exp..% Trial Percentage of true parameter value Variance in slope estimation Bayesian adaptive % Theory of Opt. Exp. % Trial

15 Observations Relative performance depends on parameters of simulation some regions of slope/bias space better for one or the other. Overall, similar performance TOE 5 times faster to compute than optimal Bayesian approach

16 Simulation Results Grid Search with Adaptive Estimation of Sensor Performance.9.8 Known Pd/Pfa 2 iters iters 5 iters.7.6 Pe Time

17 Georgia Tech Multi-Sensor Data Subsampled collection grid in 9 x 9 grid Initial work with first 2 collections less complicated, fewer interactions Used previously developed decision statistics as sensor outputs in each grid 8 samples in each grid available Initially, each sensor has same cost, same detection performance

18 Collection, red=mines, blue=clutter

19 Results - Collection.9 Performance of discrimination-based and direct search techniques Discrimination Search Direct Search Pe Time

20 Results Collection Performance of discrimination-based and direct search techniques Pe Discrimination Search: S, S2, S3 Direct Search: S, S2, S3 Direct Search: S Direct Search: S2 Direct Search: S Time

21 Results - Collection Time = Time = Pd Time = 3 Time = Pd Pfa Pfa

22 Results - Collection 2 Performance of discrimination-based and direct search techniques Pe Discrimination Search: S, S2, S3 Direct Search: S, S2, S3 Direct Search: S Direct Search: S2 Direct Search: S Time

23 Results - Collection 2 Time = Time = Pd Time = 3 Time = Pd Pfa Pfa

24 Work In Progress Alternative decision metrics Incorporate TOE for GA Tech Data Overlapping targets More realistic (different performances, costs) for GA Tech data All cases of GA Tech data