Target Detection via Cognitive Radars Using Change-Point Detection, Learning, and Adaptation

Abstract

Many radar detection algorithms that assume a stationary environment (clutter) have been proposed and analyzed over the years. However, in practice, changes in the nonstationary environment can perturb the parameters of the clutter distribution, or even alter the clutter distribution family, which can greatly deteriorate the target detection capability. To avoid such potential performance degradation, cognitive radar systems are envisioned which are required to rapidly realize the nonstationarity, accurately learn the new characteristics of the environments, and adaptively update the detector. In this paper, aiming to develop a fully cognitive radar for target detection in nonstationary environments, we propose a unifying framework that integrates (i) change-point detection of clutter distributions by using a data-driven cumulative sum (CUSUM) algorithm and its extended version, (ii) learning/identification of clutter distribution by applying sparse theory and kernel density estimation methods, and (iii) adaptive target detection by automatically modifying the likelihood-ratio test and corresponding detection threshold. Further, with extensive numerical examples, we demonstrate the achieved improvements in detection performance due to the proposed framework in comparison with a nonadaptive case, an adaptive matched filter method, and the clairvoyant case. We also use Wilcoxon rank-sum tests to evaluate the statistical significance of the performance improvements.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

References

  1. 1.

    M. Akcakaya, S. Sen, A. Nehorai, A novel data-driven learning method for radar target detection in nonstationary environments. IEEE Signal Process. Lett. 23(5), 762–766 (2016)

    Article  Google Scholar 

  2. 2.

    M. Basseville, I.V. Nikiforov et al., Detection of Abrupt Changes: Theory and Application, vol. 104 (Prentice Hall, Englewood Cliffs, 1993)

    Google Scholar 

  3. 3.

    K.L. Bell, C.J. Baker, G.E. Smith, J.T. Johnson, M. Rangaswamy, Cognitive radar framework for target detection and tracking. IEEE J. Sel. Top. Signal Process. 9(8), 1427–1439 (2015)

    Article  Google Scholar 

  4. 4.

    P. Chen, W.L. Melvin, M. Wicks, Screening among multivariate normal data. J. Multivariate Anal. 69(1), 10–29 (1999)

    MathSciNet  Article  Google Scholar 

  5. 5.

    E. Conte, A. De Maio, C. Galdi, Statistical analysis of real clutter at different range resolutions. IEEE Trans. Aerospace Electron. Syst. 40(3), 903–918 (2004)

    Article  Google Scholar 

  6. 6.

    G. Cui, L. Kong, X. Yang, GLRT-based detection algorithm for polarimetric MIMO radar against sirv clutter. Circuits Syst. Signal Process. 31(3), 1033–1048 (2012)

    MathSciNet  Article  Google Scholar 

  7. 7.

    J. DiFranco, W. Rubin, Radar Detection (SciTech Publishing Inc, Raleigh, 2004)

    Google Scholar 

  8. 8.

    A. Farina, A. Russo, F. Studer, Coherent radar detection in log-normal clutter, in IEE Proceedings F-Communications, Radar and Signal Processing, vol. 133, pp. 39–53. IET (1986)

  9. 9.

    J.D. Gibbons, S. Chakraborti, Nonparametric Statistical Inference (Chapman and Hall/CRC, Cambridge, 2011)

    Google Scholar 

  10. 10.

    F. Gini, M. Greco, M. Diani, L. Verrazzani, Performance analysis of two adaptive radar detectors against non-Gaussian real sea clutter data. IEEE Trans. Aerosp. Electron. Syst. 36(4), 1429–1439 (2000)

    Article  Google Scholar 

  11. 11.

    J.R. Guerci, E.J. Baranoski, Knowledge-aided adaptive radar at DARPA: an overview. IEEE Signal Process. Mag. 23(1), 41–50 (2006)

    Article  Google Scholar 

  12. 12.

    J.R. Guerci, R.M. Guerci, M. Rangaswamy, J. Bergin, M. Wicks, CoFAR: cognitive fully adaptive radar, in IEEE Radar Conference, pp. 0984–0989 (2014)

  13. 13.

    S. Haykin, Cognitive radar: a way of the future. IEEE Signal Process. Mag. 23(1), 30–40 (2006)

    Article  Google Scholar 

  14. 14.

    S. Haykin, D.J. Thomson, Signal detection in a nonstationary environment reformulated as an adaptive pattern classification problem. Proc. IEEE 86(11), 2325–2344 (1998). https://doi.org/10.1109/5.726792

    Article  Google Scholar 

  15. 15.

    S.M. Kay, Fundamentals of Statistical Signal Processing, Vol: II Detection Theory (Prentice Hall, Englewood Cliffs, 1998)

    Google Scholar 

  16. 16.

    M. Kelsey, S. Sen, Y. Xiang, A. Nehorai, M. Akcakaya, Sparse recovery for clutter identification in radar measurements. Proc. SPIE 1021106, 1–10 (2017)

    Google Scholar 

  17. 17.

    K. Krishnamoorthy, Handbook of Statistical Distributions with Applications (Chapman and Hall/CRC, Cambridge, 2006)

    Google Scholar 

  18. 18.

    G. Lorden et al., Procedures for reacting to a change in distribution. Ann. Math. Stat. 42(6), 1897–1908 (1971)

    MathSciNet  Article  Google Scholar 

  19. 19.

    H.B. Mann, D.R. Whitney, On a test of whether one of two random variables is stochastically larger than the other. Ann. Math. Stat. 18, 50–60 (1947)

    MathSciNet  Article  Google Scholar 

  20. 20.

    W. Melvin, J. Guerci, Knowledge-aided signal processing: a new paradigm for radar and other advanced sensors. IEEE Trans. Aerosp. Electron. Syst. 42(3), 983–996 (2006)

    Article  Google Scholar 

  21. 21.

    J. Metcalf.: Signal processing for non-Gaussian statistics: clutter distribution identification and adaptive threshold estimation. Ph.D. thesis, University of Kansas (2015)

  22. 22.

    J. Metcalf, S. Blunt, B. Himed, A machine learning approach to distribution identification in non-Gaussian clutter, in IEEE Radar Conference, pp. 0739–0744 (2014)

  23. 23.

    G.V. Moustakides et al., Optimal stopping times for detecting changes in distributions. Ann. Stat. 14(4), 1379–1387 (1986)

    MathSciNet  Article  Google Scholar 

  24. 24.

    A. Ozturk, An application of a distribution identification algorithm to signal detection problems, in Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, vol. 1, pp. 248–252 (1993). https://doi.org/10.1109/ACSSC.1993.342510

  25. 25.

    M. Pollak, Optimal detection of a change in distribution. Ann. Stat. 13, 206–227 (1985)

    MathSciNet  Article  Google Scholar 

  26. 26.

    M. Rangaswamy, D.D. Weiner, A. Ozturk, Non-Gaussian random vector identification using spherically invariant random processes. IEEE Trans. Aerosp. Electron. Syst. 29(1), 111–124 (1993)

    Article  Google Scholar 

  27. 27.

    M.A. Richards, Fundamentals of Radar Signal Processing (Tata McGraw-Hill Education, New York, 2005)

    Google Scholar 

  28. 28.

    M. Sekine, T. Musha, Y. Tomita, T. Hagisawa, T. Irabu, E. Kiuchi, On Weibull-distributed weather clutter. IEEE Trans. Aerosp. Electron. Syst. 15, 824–830 (1979)

    Article  Google Scholar 

  29. 29.

    G. Sun, Z. He, Y. Zhang, Distributed airborne MIMO radar detection in compound-Gaussian clutter without training data. Circuits Syst. Signal Process. 37(10), 4617–4636 (2018)

    Article  Google Scholar 

  30. 30.

    V.V. Veeravalli, T. Banerjee, in Academic Press Library in Signal Processing, ed. by A.M. Zoubir, M. Viberg, R. Chellappa, S. Theodoridis. Quickest change detection, vol 3 (Elsevier, Oxford, UK and Waltham, MA, USA, 2014), pp. 209–255

  31. 31.

    H. Wang, Y. Xiang, E. Dagois, M. Kelsey, S. Sen, A. Nehorai, M. Akcakaya, Clutter identification based on kernel density estimation and sparse recovery. Proc. SPIE 10658, 1–10 (2018)

    Google Scholar 

  32. 32.

    J. Wang, A. Dogandzic, A. Nehorai, Maximum likelihood estimation of compound-Gaussian clutter and target parameters. IEEE Trans. Signal Process. 54(10), 3884–3898 (2006)

    Article  Google Scholar 

  33. 33.

    P. Wang, H. Li, B. Himed, Bayesian parametric GLRT for knowledge-aided space-time adaptive processing, in IEEE Radar Conference, pp. 329–332 (2011)

  34. 34.

    P. Wang, H. Li, B. Himed, Knowledge-aided parametric tests for multichannel adaptive signal detection. IEEE Trans. Signal Process. 59(12), 5970–5982 (2011)

    MathSciNet  Article  Google Scholar 

  35. 35.

    P. Wang, H. Li, Z. Wang, B. Himed, Knowledge-aided parametric adaptive matched filter with automatic combining for covariance estimation, in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 6067–6071 (2014)

  36. 36.

    P. Wang, Z. Sahinoglu, M.O. Pun, H. Li, B. Himed, Knowledge-aided adaptive coherence estimator in stochastic partially homogeneous environments. IEEE Signal Process. Lett. 18(3), 193–196 (2011)

    Article  Google Scholar 

  37. 37.

    S. Watts, Radar detection prediction in K-distributed sea clutter and thermal noise. IEEE Trans. Aerosp. Electron. Syst. AES–23(1), 40–45 (1987)

    Article  Google Scholar 

  38. 38.

    Y. Xiang, M. Kelsey, H. Wang, S. Sen, M. Akcakaya, A. Nehorai, A comparison of cognitive approaches for clutter-distribution identification in nonstationary environments, in IEEE Radar Conference, pp. 0467–0472 (2018)

Download references

Acknowledgements

The work was supported by AFOSR under Grant No. FA9550-16-1-0386. The work of Sen was performed at the Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy, under Contract DE-AC05-00OR22725. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Arye Nehorai.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendices

Proof of \(\hat{t}_{\text {AMF}}\sim F(2, 2LN)\) under the null hypothesis

First, under the null hypothesis,

$$\begin{aligned} LN\frac{\hat{\sigma }^2}{\sigma ^2/2}\sim \chi ^2_{2LN}. \end{aligned}$$
(32)

Further, because \(\varvec{y}_0^{(k)H}\varvec{1}\sim \mathcal {CN}(0, N\sigma ^2)\), we have

$$\begin{aligned} \frac{|\varvec{y}_0^{(k)H}\varvec{1}|^2}{N\sigma ^2/2}\sim \chi ^2_2. \end{aligned}$$
(33)

Note that \(\varvec{1}^H\varvec{1}=N\), thus, we have

$$\begin{aligned} \hat{t}_{\text {AMF}}\sim \frac{\chi ^2_2/2}{\chi ^2_{2LN}/2LN}, \end{aligned}$$
(34)

where the right-hand side coincides with definition of an F-distribution, because these two \(\chi ^2\)-distributions are independent due to the independence of the data in the CUT and the secondary data.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xiang, Y., Akcakaya, M., Sen, S. et al. Target Detection via Cognitive Radars Using Change-Point Detection, Learning, and Adaptation. Circuits Syst Signal Process (2020). https://doi.org/10.1007/s00034-020-01465-z

Download citation

Keywords

  • Nonstationary environments
  • Cognitive radar
  • Adaptive target detection
  • Change-point detection
  • Clutter distribution identification