Quadrature filters for maneuvering target tracking

In this paper, a maneuvering target tracking problem has been solved by using the Guss-Hermite filter (GHF) and sparse-grid Gauss-Hermite filter (SGHF). Univariate Gauss-Hermite quadrature rule is extended for multidimensional systems by using the product rule and the Smolyak's rule in GHF and SGHF respectively. The SGHF, which is an alternative of GHF reduces the computational burden considerably. The performance of the quadrature filters have been compared with the cubature Kalman filter (CKF), and the unscented Kalman filter (UKF) for the maneuvering target tracking problem. The simulation results exhibit the improvement of performance with the quadrature filters compared to the CKF and the UKF.

[1]  D.P. Atherton,et al.  Maneuvering target tracking using adaptive turn rate models in the interacting multiple model algorithm , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[2]  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..

[3]  D. S. Bayard,et al.  Extended horizon liftings for stable inversion of nonminimum-phase systems , 1994, IEEE Trans. Autom. Control..

[4]  Gene H. Golub,et al.  Calculation of Gauss quadrature rules , 1967, Milestones in Matrix Computation.

[5]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[6]  Shovan Bhaumik,et al.  Nonlinear estimation using transformed Gauss-Hermite quadrature points , 2013, 2013 IEEE International Conference on Signal Processing, Computing and Control (ISPCC).

[7]  Norikazu Ikoma,et al.  Maneuvering target tracking by using particle filter , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[8]  X. R. Li,et al.  Survey of maneuvering target tracking. Part I. Dynamic models , 2003 .

[9]  William H. Press,et al.  Numerical recipes in C , 2002 .

[10]  Kazufumi Ito,et al.  Gaussian filters for nonlinear filtering problems , 2000, IEEE Trans. Autom. Control..

[11]  S. Haykin,et al.  Cubature Kalman Filters , 2009, IEEE Transactions on Automatic Control.

[12]  Ming Xin,et al.  Sparse-grid quadrature nonlinear filtering , 2012, Autom..

[13]  Robert J. Elliott,et al.  Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature , 2007, Proceedings of the IEEE.

[14]  Sokratis K. Katsikas,et al.  Underwater tracking of a maneuvering target using time delay measurements , 1995, Signal Process..

[15]  Florian Heiss,et al.  Likelihood approximation by numerical integration on sparse grids , 2008 .

[16]  Ming Xin,et al.  High-degree cubature Kalman filter , 2013, Autom..