Comparison of angle-only filtering algorithms in 3D using Cartesian and modified spherical coordinates

We compare the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF), and particle filter (PF) for the angle-only filtering problem in 3D using bearing and elevation measurements from a single maneuvering sensor. These nonlinear filtering algorithms use discrete-time dynamic and measurement models. Two types of coordinate systems are considered, Cartesian coordinates and modified spherical coordinates (MSC) for the relative state vector. The paper presents new algorithms using the UKF and PF with the MSC. We also present an improved filter initialization algorithm. Numerical results from Monte Carlo simulations show that the EKF-MSC and UKF-MSC have the best state estimation accuracy among all nonlinear filters considered and have comparable accuracy with modest computational cost.

[1]  David V. Stallard,et al.  Angle-only tracking filter in modified spherical coordinates , 1991 .

[2]  G. Peters,et al.  Monte Carlo Approximations for General State-Space Models , 1998 .

[3]  Samuel S. Blackman,et al.  Application of IMM filtering to passive ranging , 1999, Optics & Photonics.

[4]  Samuel S. Blackman,et al.  Implementation of an angle-only tracking filter , 1991, Defense, Security, and Sensing.

[5]  J. Davenport.  Editor , 1960 .

[6]  R. Singer.  Estimating Optimal Tracking Filter Performance for Manned Maneuvering Targets , 1970, IEEE Transactions on Aerospace and Electronic Systems.

[7]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[8]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[9]  A.H. Haddad,et al.  Applied optimal estimation , 1976, Proceedings of the IEEE.

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

[11]  Vikram Krishnamurthy,et al.  Integrated Tracking, Classification, and Sensor Management , 2013 .

[12]  Sherry Hammel,et al.  Observability Requirements for Three-Dimensional Tracking via Angle Measurements , 1985, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Sam Blackman,et al.  Integration of passive ranging with multiple hypothesis tracking (MHT) for application with angle-only measurements , 2010, Defense + Commercial Sensing.

[14]  S. S. Blackman,et al.  Angle-only tracking with a MSC filter , 1991, IEEE/AIAA 10th Digital Avionics Systems Conference.

[15]  C. Jauffret,et al.  Observability in passive target motion analysis , 1996 .

[16]  Qiang Li,et al.  Observability of Satellite to Satellite Passive Tracking from Angles Measurements , 2007, 2007 IEEE International Conference on Control and Automation.

[17]  N. Jeremy Kasdin,et al.  Two-step optimal estimator for three dimensional target tracking , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[18]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[19]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[20]  Branko Ristic,et al.  Comparison of the particle filter with range-parameterized and modified polar EKFs for angle-only tracking , 2000, SPIE Defense + Commercial Sensing.

[21]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[22]  Li,et al.  Utilization of Modified Spherical Coordinates for Satellite to Satellite Bearings-Only Tracking , 2009 .

[23]  Jean-Pierre Le Cadre,et al.  Closed-form Posterior Cramér-Rao Bound for a Manoeuvring Target in the Bearings-Only Tracking Context Using Best-Fitting Gaussian Distribution , 2006, 2006 9th International Conference on Information Fusion.

[24]  Jean-Pierre Le Cadre,et al.  Closed-form posterior Cramer-Rao bounds for bearings-only tracking , 2006, IEEE Transactions on Aerospace and Electronic Systems.

[25]  Lyudmila Mihaylova,et al.  Angle-only filtering in 3D using modified spherical and log spherical coordinates , 2011, 14th International Conference on Information Fusion.

[26]  Fredrik Gustafsson,et al.  Range estimation using angle-only target tracking with particle filters , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[27]  P. Robinson,et al.  Modified spherical coordinates for radar , 1994 .

[28]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[29]  Richard B. Vinter,et al.  Performance of the shifted Rayleigh filter in single-sensor bearings-only tracking , 2007, 2007 10th International Conference on Information Fusion.

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

[31]  M. Pitt,et al.  Filtering via Simulation: Auxiliary Particle Filters , 1999 .

[32]  Christian Musso,et al.  Improving Regularised Particle Filters , 2001, Sequential Monte Carlo Methods in Practice.

[33]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[34]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .