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Joint Optimization of Detection and Tracking in Adaptive Radar Systems

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Advances in Heuristic Signal Processing and Applications

Abstract

A promising line of research attempts to bridge the gap between a detector and a tracker by means of considering jointly optimal parameter settings for both of these subsystems. Along this fruitful path, this chapter focuses on the problem of detection threshold optimization in a tracker-aware manner so that a feedback from the tracker to the detector is established to maximize the overall system performance. Special emphasis is given to the optimization schemes based on two non-simulation performance prediction techniques for the probabilistic data association filter, namely, the modified Riccati equation (MRE) and the hybrid conditional averaging algorithm. The possible improvements are presented in non-maneuvering target tracking where a number of algorithmic and experimental evaluation gaps are identified and newly proposed methods are compared with the existing ones in a unified theoretical and experimental framework. Furthermore, for the MRE-based dynamic threshold optimization problem, a closed-form solution is proposed. This solution brings a theoretical lower bound on the operating signal-to-noise ratio concerning when the tracking system should be switched to the track-before-detect mode.

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Notes

  1. 1.

    This includes the processing blocks prior to detection such as analog-to-digital (A/D) conversion, beamforming, pulse compression, clutter filtering, and Doppler processing [57].

  2. 2.

    This in turn determines the detector operating point (P FA,P D ) for a given SNR and hence the detection threshold.

  3. 3.

    In this chapter, we consider only the detection threshold as our optimization variable. A more general set including also the transmitting waveform as in the case of cognitive radar [25] is out of the scope of the present chapter.

  4. 4.

    See, e.g., [9, pp. 373].

  5. 5.

    This in essence results in a feedback from the tracker to the detector as illustrated in Fig. 6.1.

  6. 6.

    Examples of continuous uncertainties are the inaccuracy in the measurements and “small” perturbations in the target motion which are usually modeled as an additive measurement noise and process noise, respectively. These types of uncertainties are well-understood and solved in the literature over the past four decades under the title of classical state estimation [1, 9, 42]. However, major challenges of tracking arise from two discrete-valued uncertainties: measurement origin uncertainty, which is, in the words of Li and Bar-Shalom [46], the crux of tracking, and target maneuver which appears as an abrupt and “large” deviation in the target motion.

  7. 7.

    In this chapter, we consider this aspect, i.e., tracker-aware optimization of detection thresholds.

  8. 8.

    The common notation means that “the random variable x is normally (Gaussian) distributed with mean \(\bar{x}\) and covariance Σ.”

  9. 9.

    The gate probability (P G ) is defined as the probability that the target-originated measurement falls inside the validation gate given that the target is detected.

  10. 10.

    The measurement z(k) is said to be a validated measurement, if it is inside a validation gate defined in (6.3).

  11. 11.

    This covers homogeneous and Gaussian background detector noise, a Swerling-I target fluctuation and square-law detection scheme. In the radar detection theory, such assumptions are made frequently when obtaining the ROC curves for a specific detector [65]. We refer to this joint assumption shortly as \(\mathrm{HOG_{I}^{SQL}}\).

  12. 12.

    It can be argued that a decreasing value of N C , namely decreasing the number of resolution cells falling inside a validation gate, suggests that the gate volume (hence the Gaussian hyper-ellipse suggested by the filter covariance) is diminishing. This in turn suggests the convergence of the filter to its steady-state although this may not be guaranteed to be the correct state estimate. Conversely, by the same argument, a large value of N C suggests a large gate volume, which in turn suggests that the filter is comparatively in its transient phase.

  13. 13.

    Normally, a 2D radar provides polar measurements. A rectangular resolution cell is adopted to have a linear measurement model.

  14. 14.

    This is valid for a special case of a NP detector under \(\mathrm{HOG}_{\mathrm{I}}^{\mathrm{SQL}}\) assumption.

  15. 15.

    This is an important practical problem in the radar. Under excessive number of false detections, the radar may initiate lots of false tracks. This causes the radar to allocate its resources, e.g., dwell time, transmission power, unnecessarily and inefficiently.

  16. 16.

    Given an initial interval of uncertainty, [a,b] and the number of function evaluations, N, the Fibonacci Search algorithm reduces the length of the uncertainty interval to (b−a)/F N+1, where F N+1 is the (N+1)th number in the Fibonacci sequence {1,1,2,…}. Therefore, given the number N, the length of the final uncertainty interval, so the maximum error in finding the extremum point, is determined. Here, we do the other way around. That is, we specify the maximum error tolerance that we are required to have at the end of the algorithm which in turn determines the minimum required number of function evaluations, N.

  17. 17.

    We accept that the track is lost for the ith Monte Carlo run if \(\varepsilon_{\mathrm{POS}}^{i}>\rho\) where \(\rho\triangleq\sqrt{\mathrm{tr}\{R\}}\) is the measurement error level and \(\varepsilon_{\mathrm{POS}}^{i}\) is the average position estimation error for the ith run.

  18. 18.

    These measures can be seen also as transient vs. steady-state performance, respectively.

References

  1. Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Prentice-Hall, Englewood Cliffs (1979)

    MATH  Google Scholar 

  2. Aslan, M., Saranlı, A.: Threshold optimization for tracking a nonmaneuvering target. IEEE Trans. Aerosp. Electron. Syst. 47(4), 2844–2859 (2011)

    Article  Google Scholar 

  3. Aslan, M., Saranlı, A.: A tracker-aware detector threshold optimization formulation for tracking maneuvering targets in clutter. Signal Process. 91(9), 2213–2221 (2011)

    Article  MATH  Google Scholar 

  4. Aslan, M., Saranlı, A., Baykal, B.: Optimal tracker-aware radar detector threshold adaptation: a closed-form solution. In: International Conference on Information Fusion, pp. 470–477 (2008)

    Google Scholar 

  5. Aslan, M., Saranlı, A., Baykal, B.: Tracker-aware adaptive detection: an efficient closed-form solution for the Neyman–Pearson case. Digit. Signal Process. 20(5), 1468–1481 (2010)

    Article  Google Scholar 

  6. Bar-Shalom, Y., Li, X.R.: Multitarget–Multisensor Tracking: Principles and Techniques. YBS Publishing, Storrs (1995)

    Google Scholar 

  7. Bar-Shalom, Y., Tse, E.: Tracking in a cluttered environment with probabilistic data association. Automatica 11, 451–460 (1975)

    Article  MATH  Google Scholar 

  8. Bar-Shalom, Y., Campo, L.J., Luh, P.B.: From receiver operating characteristic to system operating characteristic: evaluation of a track formation system. IEEE Trans. Autom. Control 35(2), 172–179 (1990)

    Article  MATH  Google Scholar 

  9. Bar-Shalom, Y., Li, X.R., Kirubarajan, T.: Estimation with Applications to Tracking and Navigation. Willey, New York (2001)

    Book  Google Scholar 

  10. Bar-Shalom, Y., Willett, P.K., Tian, X.: Tracking and Data Fusion: A Handbook of Algorithms. YBS Publishing, Storrs (2011)

    Google Scholar 

  11. Bazaraa, M., Sherali, H., Shetty, C.: Nonlinear Programming Theory and Algorithms. Wiley, New York (2006)

    Book  MATH  Google Scholar 

  12. Blackman, S.S., Popoli, R.: Design and Analysis of Modern Tracking Systems. Artech House, Norwood (1999)

    MATH  Google Scholar 

  13. Boers, Y., Driessen, J.N.: Particle filter based detection for tracking. In: Proceedings of the American Control Conference, Arlington, VA, vol. 6, pp. 4393–4397 (2001)

    Google Scholar 

  14. Boers, Y., Driessen, H.: Modified Riccati equation and its application to target tracking. IEE Proc. Radar Sonar Navig. 153, 7–12 (2006)

    Article  Google Scholar 

  15. Boers, Y., Driessen, H.: Results on the modified Riccati equation: target tracking applications. IEEE Trans. Aerosp. Electron. Syst. 42, 379–384 (2006)

    Article  Google Scholar 

  16. Bréhard, T., Cadre, J.P.L.: Closed-form posterior Cramér–Rao bounds for bearings-only tracking. IEEE Trans. Aerosp. Electron. Syst. 42(4), 1198–1223 (2006)

    Article  Google Scholar 

  17. Chavali, P., Nehorai, A.: Scheduling and power allocation in a cognitive radar network for multiple-target tracking. IEEE Trans. Signal Process. 60(2), 715–729 (2012)

    Article  MathSciNet  Google Scholar 

  18. Daum, F.E.: Bounds on performance for multiple target tracking. IEEE Trans. Autom. Control 35(4), 443–446 (1990)

    Article  MATH  Google Scholar 

  19. Farina, A., Ristic, B., Timmoneri, L.: Cramér–Rao bound for nonlinear filtering with P d <1 and its application to target tracking. IEEE Trans. Signal Process. 50, 1916–1924 (2002)

    Article  MathSciNet  Google Scholar 

  20. Fortmann, T.E., Bar-Shalom, Y., Scheffe, M., Gelfand, S.: Detection thresholds for tracking in clutter—a connection between estimation and signal processing. IEEE Trans. Autom. Control AC-30(3), 221–229 (1985)

    Article  MathSciNet  Google Scholar 

  21. Frei, C.W.: A comparison of parallel and sequential implementations of a multisensor multitarget tracking algorithm. Master’s thesis, Northwestern University, Evanston, IL (1995)

    Google Scholar 

  22. Gelfand, S.B., Fortmann, T.E., Bar-Shalom, Y.: Adaptive detection threshold optimization for tracking in clutter. IEEE Trans. Aerosp. Electron. Syst. 32, 514–523 (1996)

    Article  Google Scholar 

  23. Goodman, N.A., Venkata, P.R., Neifeld, M.A.: Adaptive waveform design and sequential hypothesis testing for target recognition with active sensors. IEEE J. Sel. Top. Signal Process. 1, 105–113 (2007)

    Article  Google Scholar 

  24. Haykin, S.: Cognitive radar networks. In: 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pp. 1–3 (2005)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  26. Haykin, S.: Optimal waveform design for cognitive radar. In: 42nd Asilomar Conference on Signals, Systems and Computers, pp. 3–7 (2008)

    Chapter  Google Scholar 

  27. Haykin, S.: Cognitive tracking radar. In: IEEE Radar Conference, pp. 1467–1470 (2010)

    Google Scholar 

  28. Hernandez, M., Ristic, B., Farina, A., Timmoneri, L.: A comparison of two Cramér–Rao bounds for nonlinear filtering with P d <1. IEEE Trans. Signal Process. 52(9), 2361–2370 (2004)

    Article  MathSciNet  Google Scholar 

  29. Hernandez, M.L., Farina, A., Ristic, B.: PCRLB for tracking in cluttered environments: measurement sequence conditioning approach. IEEE Trans. Aerosp. Electron. Syst. 42(2), 680–704 (2006)

    Article  Google Scholar 

  30. Hernandez, M.L., Ristic, B., Farina, A., Sathyan, T., Kirubarajan, T.: Performance measure for Markovian switching systems using best-fitting Gaussian distributions. IEEE Trans. Aerosp. Electron. Syst. 44(2), 724–747 (2008)

    Article  Google Scholar 

  31. Hong, S.M., Shin, H.S.: An analytic approximation of information reduction factor for performance prediction of PDA tracking. In: Proceedings of the 41st SICE Annual Conference, vol. 3, pp. 1447–1449 (2002)

    Google Scholar 

  32. Hong, S.M., Evans, R.J., Shin, H.S.: Optimization of waveform and detection threshold for range and range-rate tracking in clutter. IEEE Trans. Aerosp. Electron. Syst. 41, 17–33 (2005)

    Article  Google Scholar 

  33. Hue, C., Cadre, J.P.L., Pérez, P.: Posterior Cramer–Rao bounds for multi-target tracking. IEEE Trans. Aerosp. Electron. Syst. 42(1), 37–49 (2006)

    Article  Google Scholar 

  34. Jauffret, C., Bar-Shalom, Y.: Track formation with bearing and frequency measurements in clutter. IEEE Trans. Aerosp. Electron. Syst. 26(6), 999–1010 (1990)

    Article  Google Scholar 

  35. Jung, Y.H., Hong, S.M.: Modeling and parameter optimization of agile beam radar tracking. IEEE Trans. Aerosp. Electron. Syst. 39(1), 13–33 (2003)

    Article  MathSciNet  Google Scholar 

  36. Kalandros, M., Pao, L.Y.: Multisensor covariance control strategies for reducing bias effects in interacting target scenarios. IEEE Trans. Aerosp. Electron. Syst. 41(1), 153–173 (2005)

    Article  Google Scholar 

  37. Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82, 34–45 (1960)

    Google Scholar 

  38. Kerr, T.H.: Status of CR-like lower bounds for nonlinear filtering. IEEE Trans. Aerosp. Electron. Syst. 25(5), 590–601 (1989)

    Article  MathSciNet  Google Scholar 

  39. Kershaw, D.J., Evans, R.J.: Optimal waveform selection for tracking systems. IEEE Trans. Inf. Theory 40(5), 1536–1550 (1994)

    Article  MATH  Google Scholar 

  40. Kershaw, D.J., Evans, R.J.: A contribution to performance prediction for probabilistic data association tracking filters. IEEE Trans. Aerosp. Electron. Syst. 32(3), 1143–1148 (1996)

    Article  Google Scholar 

  41. Kershaw, D.J., Evans, R.J.: Waveform selective probabilistic data association. IEEE Trans. Aerosp. Electron. Syst. 33, 1180–1188 (1997)

    Article  Google Scholar 

  42. Kumar, P.R., Varaiya, P.: Stochastic Systems: Estimation, Identification and Adaptive Control. Prentice-Hall, Inc., Englewood Cliffs (1986)

    MATH  Google Scholar 

  43. Leven, W.F.: Approximate Cramér–Rao bounds for multiple target tracking. Ph.D. thesis, Georgia Institute of Technology (2006)

    Google Scholar 

  44. Li, X.R.: Tracking in clutter with strongest neighbor measurements—Part I: theoretical analysis. IEEE Trans. Aerosp. Electron. Syst. 43(11), 1560–1578 (1998)

    MATH  Google Scholar 

  45. Li, X.R.: Multitarget–Multisensor Tracking: Applications and Advances, vol. III, pp. 499–567. Artech House, Inc., Norwood (2000). Chap. 10

    Google Scholar 

  46. Li, X.R., Bar-Shalom, Y.: Stability evaluation and track life of the PDAF for tracking in clutter. IEEE Trans. Autom. Control 36, 588–602 (1991)

    Article  Google Scholar 

  47. Li, X.R., Bar-Shalom, Y.: Performance prediction of the interacting multiple model algorithm. IEEE Trans. Aerosp. Electron. Syst. 29(3), 755–771 (1993)

    Article  Google Scholar 

  48. Li, X.R., Bar-Shalom, Y.: Detection threshold selection for tracking performance optimization. IEEE Trans. Aerosp. Electron. Syst. 30, 742–749 (1994)

    Article  Google Scholar 

  49. Li, X.R., Bar-Shalom, Y.: A hybrid conditional averaging technique for performance prediction of algorithms with continuous and discrete uncertainties. In: Proceedings of the American Control Conference, Maryland, pp. 1530–1534 (1994)

    Google Scholar 

  50. Li, X.R., Bar-Shalom, Y.: Tracking in clutter with nearest neighbor filters: analysis and performance. IEEE Trans. Aerosp. Electron. Syst. 32(3), 995–1010 (1996)

    Article  Google Scholar 

  51. Mori, S., Chang, K.C., Chong, C.Y., Dunn, K.P.: Prediction of track purity and track accuracy in dense target environments. IEEE Trans. Autom. Control 40(5), 953–959 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  52. Pao, L.Y., Trailović, L.: The optimal order of processing sensor information in sequential multisensor fusion algorithms. IEEE Trans. Autom. Control 45(8), 1532–1536 (2000)

    Article  MATH  Google Scholar 

  53. Rago, C., Willett, P., Bar-Shalom, Y.: Detection-tracking performance with combined waveforms. IEEE Trans. Aerosp. Electron. Syst. 34(2), 612–624 (1998)

    Article  Google Scholar 

  54. Ramdaras, U.D., Absill, F.G.J.: Sensor selection: the modified Riccati equation approach compared with other selection schemes. In: International Conference on Information Fusion, pp. 1–6 (2007)

    Google Scholar 

  55. Ramdaras, U.D., Absill, F.G.J.: Target tracking in sensor networks: criteria for sensor selection. In: IEEE Radar Conference, pp. 192–196 (2007)

    Google Scholar 

  56. Rapoport, I., Oshman, Y.: A Cramér–Rao-type estimation lower bound for systems with measurement faults. IEEE Trans. Autom. Control 50(50), 1234–1245 (2005)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  58. Ristic, B., Farina, A., Hernandez, M.: Cramér–Rao lower bound for tracking multiple targets. IEE Proc. Radar Sonar Navig. 151, 129–134 (2004)

    Article  Google Scholar 

  59. Rogers, S.R.: Diffusion analysis of track loss in clutter. IEEE Trans. Aerosp. Electron. Syst. 27(2), 380–387 (1991)

    Article  Google Scholar 

  60. Salmond, D.J., Birch, H.: A particle filter for track-before-detect. In: Proceedings of the American Control Conference, Arlington, VA, vol. 5, pp. 3755–3760 (2001)

    Google Scholar 

  61. Sinopoli, B., Schenato, L., Franceschetti, M., Poola, K., Jordan, M.I., Sastry, S.S.: Kalman filtering with intermittent observations. IEEE Trans. Autom. Control 49, 1453–1464 (2004)

    Article  Google Scholar 

  62. Sira, S.P., Papandreou-Suppappola, A., Morrell, D.: Dynamic configuration of time-varying waveforms for agile sensing and tracking in clutter. IEEE Trans. Signal Process. 55(7), 3207–3217 (2007)

    Article  MathSciNet  Google Scholar 

  63. Taylor, J.H.: The Cramér–Rao estimation error lower bound computation for deterministic nonlinear systems. IEEE Trans. Autom. Control AC-24(2), 343–344 (1979)

    Article  Google Scholar 

  64. Tichavský, P., Muravchik, C.H., Nehorai, A.: Posterior Cramér–Rao bounds for discrete-time nonlinear filtering. IEEE Trans. Signal Process. 46(5), 1386–1396 (1998)

    Article  Google Scholar 

  65. Varshney, P.K.: Distributed Detection and Data Fusion. Springer, New York (1997)

    Book  Google Scholar 

  66. Wang, J.T., Wang, H.Q., Qin, Y.L., Zhuang, Z.W.: Efficient adaptive detection threshold optimization for tracking maneuvering targets in clutter. Prog. Electromagn. Res. B 41, 357–375 (2012)

    Google Scholar 

  67. Willett, P., Niu, R., Bar-Shalom, Y.: Multitarget–Multisensor Tracking: Applications and Advances, vol. III, pp. 459–498. Artech House, Inc., Norwood (2000). Chap. 9

    Google Scholar 

  68. Willett, P., Niu, R., Bar-Shalom, Y.: Integration of Bayes detection with target tracking. IEEE Trans. Signal Process. 49(1), 17–29 (2001)

    Article  Google Scholar 

  69. Xu, B., Wu, Z., Wang, Z.: On the Cramér–Rao lower bound for biased bearings-only maneuvering target tracking. Signal Process. 87(12), 3175–3189 (2007)

    Article  MATH  Google Scholar 

  70. Zhang, X., Willet, P., Bar-Shalom, Y.: Dynamic Cramér–Rao bound for target tracking in clutter. IEEE Trans. Aerosp. Electron. Syst. 41(4), 1154–1167 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. İLTAREN, Advanced Technologies Research Institute, TÜBİTAK BİLGEM, Ümitköy, 06800, Ankara, Turkey

    Murat Şamil Aslan

  2. Dep. of Electrical and Electronics Engineering, Middle East Technical University, Ankara, Turkey

    Afşar Saranlı

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  1. Murat Şamil Aslan
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Correspondence to Murat Şamil Aslan .

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  1. Electrical Engineering Department, Jadavpur University, Kolkata, 700032, West Bengal, India

    Amitava Chatterjee

  2. Dept. of Aerospace Engineering, Sharif University of Technology, Azadi Street, Tehran, Iran

    Hadi Nobahari

  3. Laboratory LiSSi, University of Paris 12, av. du Général de Gaulle 61, Créteil, 94010, France

    Patrick Siarry

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Aslan, M.Ş., Saranlı, A. (2013). Joint Optimization of Detection and Tracking in Adaptive Radar Systems. In: Chatterjee, A., Nobahari, H., Siarry, P. (eds) Advances in Heuristic Signal Processing and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37880-5_6

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