A Step Towards the Cognitive Radar: Target Detection under Nonstationary Clutter

Transcription

1 A Step Towards the Cognitive Radar: Target Detection under Nonstationary Clutter Murat Akcakaya Department of Electrical and Computer Engineering University of Pittsburgh Satyabrata Sen *, Yijian Xiang, and Arye Nehorai Oak Ridge National Laboratory * Washington University in St. Louis International Conference on InfoSymbiotics/DDDAS August 7-9,

2 Acknowledgement This material is based upon the work supported by the Air Force Office of Scientific Research (AFOSR), the DDDAS Program, under Grant No. FA We thank AFOSR/DDDAS for supporting this project. 2

3 Outline Introduction Challenges Motivations Our approach Relevance to DDDAS Target Detection Method Change point detection CUSUM Extended CUSUM Numerical Results Conclusions and Future Work 3

4 Introduction 4

5 Problem Description Goal: Improve target detection capability in the presence of nonstationary clutter. Challenges: Characteristics of the clutter can vary enormously depending on radar-operational scenarios (e.g., weather change, dynamic target, and changes in the environment). However, most existing radar algorithms assume stationary, parametric distributions for the clutter and noise processes, consider the availability of a dictionary of possible probability density functions (pdfs), do not address the problem of estimating the time instant when the characteristics of the clutter changes. Therefore, the radar performance can severely deteriorate when the inherent nonstationary characteristics are not accounted for. 5

6 Problem Description (cont.) radar Sea Sea clutter Land clutter Land Characteristics of sea-clutter is starkly different than land-clutter An illustrative example of target detection in nonstationary environment 6

7 Motivation Cognitive radar framework conceptualizes an advanced radar system that senses its scenario effectively, learns from its experience, adapts to the changes. Thus, in a nonstationary environment, a cognitive radar provides a unifying approach by autonomously learning and estimating the change-point in the statistical characteristics of the scenario, incorporating the newly learned environment statistics into the target detection algorithm. 7

8 Our Approach Employ a data-driven active drift detection algorithm to detect changes of statistical characteristics of the environment. Environment with targets Apply incremental learning (i.e., learning under concept drift) algorithms to learn the new statistical characteristics of the environment. Transmitter Transmitted signal Receiver Detection Algorithms Measurements Integrate the newly learned environment characteristics in the detection algorithm to adapt to the changes in the environment. Model Parameters Update Environment / Target Learning Module 8

9 Relevance to DDDAS Our proposed technique with adaptive learning and cognitive augmentation is of high relevance to remotely piloted radar systems for substantially better intelligence, surveillance, and reconnaissance (ISR) capability It is also germane to the key science and technology frontiers of DDDAS: Applications modeling Developing data-driven learning algorithms to detect any significant change in the underlying distribution of the model Jointly combining newly measured data with the previously-stored calibration data to learn the environment model Advances in Mathematical and Statistical Algorithms Incorporating learned model parameters into radar algorithms to provide robust and improved detection performance Application Measurement Systems and Methods [on-going work, not part of this presentation] Synthesizing the next transmit waveforms based on the updated model parameters Using the designed waveforms as control-agents to dynamically steer the next received measurements Software Infrastructures and other systems software [future work, not part of this presentation] Addressing the near real-time implementation issues of the proposed signal processing algorithms. 9

10 Target Detection Method 10

11 Data-Driven Active Drift Detection A typical change point detection problem: At current time NN, decide from two hypotheses: DD 0 : DD 1 : yy 1, yy 2,, yy NN ~ pp θθ0 yy 1, yy 2,, yy kk0 ~ pp θθ0, yy kk0 +1,, yy NN ~ pp θθ1 where yy nn : observed data at time nn; kk 0 : change point; pp θθ0, pp θθ1 : two different distributions before and after the change point. pp θθ0 pp θθ1 Stopping time (ττ) Change point Estimation delay 11

12 Data-Driven Active Drift Detection (cont.) Change point detection formulation for radar detection problem: where ττ = argmin ττ sup nn 1 ess sup EE nn such that EE ττ αα ττ nn + YY cc cc 0,, YY nn 1 CC cc, cc 0,1 : two classes representing the absence and presence of the target; YY 0 = yy 0,tt, rr 0,tt, tt = 1,, TT 0 : calibration data set for two classes, yy 0,tt : tt th radar measurement rr 0,tt = 0 if yy 0,tt CC 0 and rr 0,tt = 1 if yy 0,tt CC 1 TT 0 : number of measurements in the calibration data; YY nn c : radar data observed at measurement time nn from class cc; ττ : stopping time; xx + = max 0, xx ; EE nn [ ] : expectation with respect to pp nn cc, pp nn cc : probability distribution when the change occurs at nn; EE [ττ] : mean time between false alarms, assuming that change never happens; ess sup : essential supremum of a set of random variables XX; it is a random variable ZZ such that (i) PP ZZ XX = 1 XX XX; and (ii) PP YY XX = 1, XX XX PP YY ZZ = 1, XX XX. (1) 12

13 Data-Driven Active Drift Detection (cont.) CUmulative SUM (CUSUM) algorithm: provides the optimum stopping time ττ for the problem in (1) ττ = inf nn 1: gg YY 0 cc,, YY nn cc where RR kk = kk ii=1 nn : batch index ln pp cc θθ cc YY 1 ii cc pp θθ0 cc YY ii bb : a predefined threshold Parameter training procedure: = RR nn min 1 kk nn RR kk bb i. Find an estimate of θθ 0 cc using ii. iii. iv. a) calibration data YY cc 0, cc 0, 1 b) knowledge of the parametric distribution underlying the data Compute the confidence intervals for θθ 0 cc Assign the confidence interval extremas to θθ 1 cc Assign bb = max 1 tt TT 0 gg YY 0 cc, where YY 0 cc = yy 0,tt rr 0,tt = cc, tt = 1,, TT 0 13

14 Data-Driven Active Drift Detection (cont.) Extended CUSUM algorithm: when no prior knowledge is available about the distribution of YY nn cc, cc 0, 1 Convert measurements into new samples (take YY 0 cc as an example): zz 0,tt,ii = 1 MM iiii yy 0,tt,vv Convert ZZ 0 cc zz 0,tt NN MM Convert vv= ii 1 MM+1 zz 0,tt = zz 0,tt,1,, zz 0,tt,NN/MM TT MM YY 0 cc = yy 0,tt rr tt = cc ZZ 0 cc = zz 0,tt rr tt = cc NN where yy 0,tt,vv and zz 0,tt,ii are vv th and ii th entries of vectors yy 0,tt and zz 0,tt, respectively. YY 0 cc yy 0,tt 14

15 Data-Driven Active Drift Detection (cont.) Extended CUSUM algorithm (cont.): Use new samples to employ CUSUM algorithm: where ττ = inf nn 1: gg ZZ 0 cc,, ZZ nn cc kk RR kk = ii=1 ln pp cc θθ cc ZZ 1 ii cc pp θθ0 cc ZZ ii nn is the batch index = RR nn min 1 kk nn RR kk bb bb is a predefined threshold Parameter training procedure: i. Find an estimate of θθ 0 cc using the calibration data ZZ 0 cc, cc 0, 1 ii. iii. iv. Compute the confidence intervals for θθ 0 cc Assign the confidence interval extremas to θθ 1 cc Assign bb = max 1 tt TT 0 gg ZZ 0 cc, where ZZ 0 cc = zz 0,tt rr 0,tt = cc, tt = 1,, TT 0 15

16 Numerical Results 16

17 Simulation Setup Assumptions: Radar collects measurements from multiple range cells (indexed by jj) over a sequence of coherent processing intervals (CPIs) (indexed by kk) Radar receives and processes NN temporal samples in each CPI Target is assumed to be present in the jj = 1 range cell Target remains in a cell during the entire processing of kk = 1, 2,, KK CPIs Target response is considered to be known and constant (denoted as aa) Detection problem (of jj th range cell at kk th CPI): H 0: yy kk jj = nn kk jj H 1 : yy kk jj = aa11 + nn kk jj, for kk = 1,2,, KK, jj = 0,1,2, where each vector is of dimension NN 1. Nonstationary modeling: For kk = 1, 2,, kk 0, we have nn jj kk ~pp nn,θθ0, i.e., yy jj kk ~pp θθ0 cc For kk = kk 0 + 1,, KK, we have nn jj kk ~pp nn,θθ1, i.e., yy jj kk ~pp θθ1 cc 17

18 Simulation Setup (cont.) Parameter training procedure: Suppose we have TT cc 0 training data for class cc, i.e., YY cc cc 0 = yy 0,tt for tt = 1,, TT cc 0. If the noise before change point is known as nn kk jj ~NN 0, σσ 2 II, then 1. θθ 1 0 = aa, σσ 2, θθ 0 0 = 0, σσ 2 2. Compute sample mean μμ cc and sample variance TT 0 cc μμ cc = 1 TT cc 0 NN tt=1 11 TT cc yy 0,tt ss 2cc = 1 TT 0 cc TT 0 cc NN 1 tt=1 ss 2cc cc yy 0,tt μμ cc 11 TT cc yy 0,tt μμ cc Take the lower/upper limits on the 95% confidence intervals of mean and variance aa cc llll = μμ cc 1.96 σσ llll 2cc = TT 0 cc NN 1 2 XX TT0 cc NN 1 σσ TT 0 cc NN ss 2cc αα/2 aa cc uuuu σσ llll 2cc = = μμ cc 1.96 TT 0 cc NN 1 2 XX TT0 cc NN 1 4. Evaluate gg nn = RR nn min RR kk, with RR kk = kk tt=1 1 kk nn σσ TT 0 cc NN ss 2cc 1 αα/2 ln pp cc θθ cc yy 0,tt 1 pp θθ0 cc yycc 0,tt where αα = 0.05 having parameters from θθ cc 0 to either θθ cc 1 = aa cc llll, σσ 2cc llll, θθ cc 1 = aa cc llll, σσ 2cc uull, θθ cc 1 = aa cc uull, σσ 2cc llll, or θθ cc 1 = aa cc 2cc uull, σσ uull 5. Let bb = max 1 nn TT 0 cc gg nn 18

19 Simulation Setup (cont.) Parameter training procedure (cont.): If the noise nn kk jj distribution is unknown, then the conversion for the extended CUSUM algorithm is used: θθ cc 0 = μμ cc zz, ss 2cc zz, where μμ cc zz and ss zz 2cc are sample mean and variance of ZZ cc 0 = zz 0,tt (training data after the conversion) under H cc θθ cc 1 and bb can be trained similar to the above. Change Point Detection: Once θθ 0 cc, θθ 1 cc, and bb are obtained, then CUSUM (or extended CUSUM) algorithm is used to detect the change point. Adaptive Target Detection: Once a change in the clutter distribution is detected, the proposed radar accordingly modifies the log-likelihood ratio ln pp θθ 0 cc jj yy kk H1 pp θθ0 cc yy kk jj H0 ln pp θθ 1 cc yy kk jj H1 pp θθ1 cc yy kk jj H0 cc before change point after change point 19

20 Simulation Setup (cont.) We consider four clutter distributions: Gaussian distribution Student-t distribution K distribution Weibull distribution Based on the proposed framework, 12 cases are included in the simulation results for target detection under nonstationary clutter as follows: TABLE I: Distributions of Clutter in Target Detection Before Change Point After Change Point Gaussian Student-t K Weibull Student-t Gaussian K Weibull K Gaussian Student-t Weibull Weibull Gaussian Student-t K CUSUM Extended CUSUM We present the results in terms of the (i) change point estimation delay and (ii) adaptive detection performance. 20

21 Numerical Results Gaussian Student-t Change point detection (CUSUM) Observation: Change in clutter distribution is detected within one processing interval for more than 96.5% of the time ROC curves (10dB and 20dB) Observation: Detection performance improves substantially (PD increased by 0.4) due to the incorporation of the modified clutter characteristics 21

22 Numerical Results (cont.) Gaussian K Change point detection (CUSUM) Observation: Change in clutter distribution is detected within one processing interval for more than 95.5% of the time ROC curves (10dB and 20dB) Observation: Detection performance improves substantially (PD increased by > 0.5) due to the incorporation of the modified clutter characteristics 22

23 Numerical Results (cont.) Weibull K Change point detection (extended CUSUM) Observation: Change in clutter distribution is detected within one processing interval for more than 99.6% of the time ROC curves (-10dB and -20dB) Observation: Detection performance improves substantially (PD increased by 0.4) due to the incorporation of the modified clutter characteristics 23

24 Numerical Results (cont.) Change Point Detection Performance Summary: Clutter before change point Gaussian (G) Student-t (T) K Weibull (W) Clutter after change point Probability of change detection in one step delay Estimation delay when probability of change detection 99% T 96.85% 7 K 95.85% 10 W 97.10% 6 G 91.80% 2 K 99.40% 1 W 98.90% 2 G 98.90% 3 T 98.60% 2 W 93.05% 2 G 97.20% 14 T 97.00% 2 K 99.75% 1 24

25 Numerical Results (cont.) Improved Detection Performance Summary: Clutter before change point Gaussian (G) Student-t (T) K Weibull (W) Clutter after change point Improved PP D when PP FA = 0.01 SNR= 10dB SNR= 20dB T 40.9% 42.1% K 0.8% 34.4% W 1.6% 48.7% SNR= -10dB SNR= -20dB G 4.0% 24.8% K 56.0% 11.7% W 64.4% 2.5% G * * T * * W 86.3% 27.4% G * * T * * K 13.4% 1.6% 25 * No comparable data exist since the case likelihood ratio=0/0 arise too often in conventional radar.

26 Conclusions and Future Work 26

27 Conclusions and Future Work Conclusions: We developed a data-driven algorithm to detect a target in the presence of nonstationary environment (clutter). Applied an active drift learning technique to detect and estimate any change-point (if present) in the clutter distribution. Employed the incremental learning and drift detection algorithms to incrementally learn the environment and update the system parameters on the fly. Demonstrated with numerical examples that the proposed algorithm quickly detects a change in the underlying clutter distribution, significantly improves the target detection performance. Future Work: Extend the model to include a Bayesian formulation of the change point parameter. Explore the active drift learning under noisy labels and passive drift leaning methodologies. Validate the performance of our proposed technique with real data. Incorporate waveform design and other adaptive techniques to further improve the detection and tracking performance under nonstationary environment. 27

28 Thank you! 28

29 Appendix 29

30 More Numerical Results Gaussian->Weibull Change point detection (CUSUM) ROC curve (10dB and 20dB) 30

31 More Numerical Results Student-t->Gaussian Change point detection (extended CUSUM) ROC curve (-10dB and -20dB) 31

32 More Numerical Results Student-t->K Change point detection (extended CUSUM) ROC curve (-10dB and -20dB) 32

33 More Numerical Results Student-t->Weibull Change point detection (extended CUSUM) ROC curve (-10dB and -20dB) 33

34 More Numerical Results Weibull->Gaussian Change point detection (extended CUSUM) ROC curve (-10dB and -20dB) 34

35 More Numerical Results Weibull->Student-t Change point detection (extended CUSUM) ROC curve (-10dB and -20dB) 35

36 More Numerical Results K->Gaussian Change point detection (extended CUSUM) ROC curve (-10dB and -20dB) 36

37 More Numerical Results K->Student-t Change point detection (extended CUSUM) ROC curve (-10dB and -20dB) 37

38 More Numerical Results K->Weibull Change point detection (extended CUSUM) ROC curve (-10dB and -20dB) 38

39 Numerical Results (cont.) Improved Detection Performance Summary: Clutter before change point Gaussian (G) Student-t (T) K Weibull (W) Clutter after change point Improved PP D when PP FA = 0.01 Improved PP D when PP FA = SNR=10dB SNR=20dB SNR=10dB SNR=20dB T 40.9% 42.1% 20.8% 43.0% K 0.8% 34.4% 0.3% 3.2% W 1.6% 48.7% 0% 48% SNR=-10dB SNR=-20dB SNR=-10dB SNR=-20dB G 4.0% 24.8% 4.8% 10.6% K 56.0% 11.7% 56.5% 2.2% W 64.4% 2.5% 25.0% 0.5% G * * * * T * * * * W 86.3% 27.4% 64.5% 10.1% G * * * * T * * * * K 13.4% 1.6% 3.4% 0.4% 39 * No comparable data exist since the case likelihood ratio=0/0 arise too often in conventional radar.