Hierarchical Adaptive Kalman Filtering for Interplanetary Orbit Determination - Aerospace and Electronic Systems, IEEE Transactions on

0018-9251/98/$10.00 @) 1998 IEEE For a Kalman filter to operate in an optimal fashion, all filter parameters should be known exactly [ 1, 21. Incorrect selection of these parameters will result in large estimation errors or divergence [3, 41. This has motivated the design of a bank of Kalman filters with each filter using different parameters. An example is the classic Magill filter bank wherein the most suitable filter is selected through a sequential maximum a posteriori estimation procedure [5]. We have recently shown that the mixture-of-experts framework provides a more flexible and powerful alternative to traditional filter bank approaches [6]. The proposed solution was motivated by modular networks [7-91 whose general structure is shown in Fig. 1. In the suggested scheme, each module or expert is a particular Kalman filter realization. That is, each Kalman filter is modeled with a different realization of the unknown or uncertain parameter vector. Typically, the parameter vector contains the elements of the process noise and the measurement noise covariance matrices. The parameter vector can also contain various unknown or uncertain elements of the state transition and measurement mapping matrices. A gating network is used to regulate the Kalman filter bank by adaptively assigning weights to the individual filters based on their performance. It has been shown that the modular architecture regulated by a gating network has the ability to 1) select the best filter realization as measurements are processed, 2) rapidly change selection in case of a change in the operating regime, 3) adapt individual filters to better match incoming data, and 4) avoid numerical instabilities (usually encountered with Magill’s scheme, for example). A complete description of the suggested approach, mathematical derivations, adaptation of the parameter vectors, and a number of illustrative examples can be found in [6]. In this work, the adaptive Kalman filtering architecture in [6] is extended to a hierarchical structure which involves multiple levels of gating [8, 101. The proposed hierarchy has the ability to detect parameter changes and allows the examination of parameter changes on an individual basis and in combination with other parameters. Also, the expectation-maximization (EM) algorithm [ 1 1, 121 is shown to be applicable to the proposed hierarchy of adaptive Kalman filter banks, provided off-line solutions (i.e., batch) are acceptable. The mixture-of-experts hierarchical architecture provides a structured approach to conducting the necessary numerical experiments and to clarify the outcomes. The workings and power of the hierarchical adaptive Kalman filtering architecture are illustrated using the interplanetary orbit determination problem [ 131. The available measurements are simulated radiometric (Doppler) generated by Deep Space