Bias compensation for the bearings-only pseudolinear target track estimator

The bearings-only pseudolinear target track estimator is known to suffer from severe bias problems. This paper presents a bias analysis for the pseudolinear estimator and develops a method of bias compensation, resulting in a closed-form reduced-bias pseudolinear estimator. The reduced-bias estimator is then incorporated into an instrumental variable estimator to produce asymptotically unbiased target motion parameter estimates. Unlike batch iterative estimators, the proposed instrumental variable estimator has a closed-from solution and therefore avoids the convergence problems associated with iterative estimators. The performance of the proposed instrumental variable estimator is illustrated by way of simulation examples and is shown to be almost identical to that of the computationally more demanding iterative maximum likelihood estimator.

[1]  K. Gong,et al.  Position and Velocity Estimation Via Bearing Observations , 1978, IEEE Transactions on Aerospace and Electronic Systems.

[2]  Dinh-Tuan Pham,et al.  Some quick and efficient methods for bearing-only target motion analysis , 1993, IEEE Trans. Signal Process..

[3]  J. Cadre,et al.  On the convergence of iterative methods for bearings-only tracking , 1999 .

[4]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[5]  R. Streit,et al.  A linear least squares algorithm for bearings-only target motion analysis , 1999, 1999 IEEE Aerospace Conference. Proceedings (Cat. No.99TH8403).

[6]  V. Aidala,et al.  Biased Estimation Properties of the Pseudolinear Tracking Filter , 1982, IEEE Transactions on Aerospace and Electronic Systems.

[7]  K. Gong,et al.  Fundamental properties and performance of conventional bearings-only target motion analysis , 1984 .

[8]  T. Ferguson.  A Course in Large Sample Theory , 1996 .

[9]  V. Aidala.  Kalman Filter Behavior in Bearings-Only Tracking Applications , 1979, IEEE Transactions on Aerospace and Electronic Systems.

[10]  Yiu-Tong Chan,et al.  Bearings-only and Doppler-bearing tracking using instrumental variables , 1992 .

[11]  K. Dogancay.  Least squares algorithms for constant acceleration target tracking , 2003, 2003 Proceedings of the International Conference on Radar (IEEE Cat. No.03EX695).

[12]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[13]  J. Passerieux,et al.  Optimal observer maneuver for bearings-only tracking , 1998 .

[14]  Yaakov Bar-Shalom,et al.  Multitarget-Multisensor Tracking: Applications and Advances , 1992 .

[15]  S. Nardone,et al.  A closed-form solution to bearings-only target motion analysis , 1997 .

[16]  V. Aidala,et al.  Observability Criteria for Bearings-Only Target Motion Analysis , 1981, IEEE Transactions on Aerospace and Electronic Systems.

[17]  Kwan Wong,et al.  Identification of linear discrete time systems using the instrumental variable method , 1967, IEEE Transactions on Automatic Control.

[18]  Kutluyil Dogançay,et al.  On the bias of linear least squares algorithms for passive target localization , 2004, Signal Process..

[19]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[20]  R. Fisher.  The Advanced Theory of Statistics , 1943, Nature.

[21]  J. Holst,et al.  A nearly unbiased inherently stable bearings-only tracker , 1993 .

[22]  Kutluyil Dogançay.  Passive emitter localization using weighted instrumental variables , 2004, Signal Process..

[23]  D. Lerro,et al.  Bias compensation for improved recursive bearings-only target state estimation , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[24]  V. Aidala,et al.  Utilization of modified polar coordinates for bearings-only tracking , 1983 .

[25]  J. Mendel.  Lessons in Estimation Theory for Signal Processing, Communications, and Control , 1995 .

[26]  S. K. Rao,et al.  Pseudo-linear estimator for bearings-only passive target tracking , 2001 .

[27]  Alfonso Farina,et al.  Target tracking with bearings - Only measurements , 1999, Signal Process..

[28]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[29]  Don Koks.  Passive Geolocation for Multiple Receivers With No Initial State Estimate , 2001 .

[30]  P. Kumar,et al.  Theory and practice of recursive identification , 1985, IEEE Transactions on Automatic Control.