Hierarchical adaptive Kalman filtering for interplanetary orbit determination

A modular and flexible approach to adaptive Kalman filtering has recently been introduced using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters. The unknown or uncertain parameters can include elements of the state transition matrix, observation mapping matrix, process noise covariance matrix, and measurement noise covariance matrix. The gating network performs on-line adaptation of the weights given to individual filters based on performance. The mixture-of-experts approach is extended here to a hierarchical architecture which involves multiple levels of gating. The proposed architecture provides a multilevel hypothesis testing capability. The utility of the hierarchical architecture is illustrated via the problem of interplanetary navigation (Mars Pathfinder) using simulated radiometric data. It serves as a useful tool for assisting navigation teams in the process of selecting the parameters of the navigational filter over various operating regimes. It is shown that the scheme has the capability of detecting changes in the system parameters and switching filters appropriately for optimal performance. Furthermore, the expectation-maximization (EM) algorithm is shown to be applicable in the proposed framework.

[1]  X. R. Li,et al.  Performance Prediction of the Interacting Multiple Model Algorithm , 1992 .

[2]  R. Redner,et al.  Mixture densities, maximum likelihood, and the EM algorithm , 1984 .

[3]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[4]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[5]  C. Price.  An analysis of the divergence problem in the Kalman filter , 1968 .

[6]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[7]  Steve R. Waterhouse,et al.  Classification using hierarchical mixtures of experts , 1994, Proceedings of IEEE Workshop on Neural Networks for Signal Processing.

[8]  D. Magill.  Optimal adaptive estimation of sampled stochastic processes , 1965 .

[9]  R. Kalman,et al.  New results in linear prediction and filtering theory Trans. AMSE , 1961 .

[10]  Joydeep Ghosh,et al.  A mixture-of-experts framework for adaptive Kalman filtering , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[11]  Robert H. Bishop,et al.  Adaptive Orbit Determination for Interplanetary Spacecraft , 1996 .

[12]  Y. Bar-Shalom,et al.  An interacting multiple model approach for target tracking with glint noise , 1994, Proceedings of 1994 IEEE National Radar Conference.

[13]  H. P. Blom.  An efficient filter for abruptly changing systems , 1984, The 23rd IEEE Conference on Decision and Control.

[14]  Yaakov Bar-Shalom,et al.  Interacting multiple model tracking with target amplitude feature , 1993 .

[15]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[16]  Joydeep Ghosh,et al.  Structural adaptation in mixture of experts , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[17]  X. R. Li,et al.  Performance Prediction of the Interacting Multiple Model Algorithm , 1992, 1992 American Control Conference.

[18]  Y. Bar-Shalom,et al.  A recursive multiple model approach to noise identification , 1994 .

[19]  Robert A. Jacobs,et al.  Hierarchical Mixtures of Experts and the EM Algorithm , 1993, Neural Computation.

[20]  Michael I. Jordan,et al.  A Competitive Modular Connectionist Architecture , 1990, NIPS.

[21]  N. F. Toda,et al.  Divergence in the Kalman Filter , 1967 .

[22]  John S. Bridle,et al.  Training Stochastic Model Recognition Algorithms as Networks can Lead to Maximum Mutual Information Estimation of Parameters , 1989, NIPS.

[23]  Michael I. Jordan.  A statistical approach to decision tree modeling , 1994, COLT '94.

[24]  P. D. Burkhart,et al.  Sensitivity Analysis of the Enhanced Orbit Determination Filter--Error Budget Development , 1994 .

[25]  Sam W. Thurman,et al.  Precision X-band Doppler and ranging navigation for current and future Mars exploration missions , 1993 .

[26]  July , 1890, The Hospital.

[27]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .