A mixture-of-experts approach to adaptive estimation

The mathematical model and model parameters we use to describe a physical system generally do not match reality. The models are a mathematical approximation of the real world. The Kalman filter assumes that the model and model parameters perfectly describe the physical system. Also, when the model parameters are time-varying, the variation is assumed to be known exactly. In real-world problems uncertainties always exist. To address the problem of filtering in the presence of uncertainty, a new approach to adaptive filtering is developed and investigated for application to interplanetary spacecraft navigation.; A modular and flexible approach to adaptive Kalman filtering using the framework of a mixture-of-experts regulated by a gating network is proposed. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters. The gating network performs on-line adaptation based on filter performance. The proposed scheme compares very favorably with the classical Magill filter bank (which is based on a Bayesian technique) in terms of (i) estimation accuracy, (ii) response to changing external environments, and (iii) numerical stability and computational demands. The on-line weight assignment performed by the gating network is accomplished utilizing an instantaneous gradient ascent learning algorithm. The expectation-maximization algorithm is also shown to be an applicable learning strategy in the proposed framework.; The proposed filter bank is further enhanced by periodically using a search algorithm in a feedback loop. Two search algorithms are considered. The first algorithm uses a recursive quadratic programming approach which extremizes a modified maximum likelihood function to update the parameters of the best performing filter in the bank. The second algorithm uses a genetic algorithm to search for the parameter vector.; The proposed adaptive Kalman filtering framework is also extended to a hierarchical architecture which involves multiple levels of gating. This particular architecture provides a multi-level hypothesis testing capability by allowing the examination of parameter variations in isolation, as well as in combination with other parameters.; The workings and power of the filtering architectures are illustrated using a simulated Mars Pathfinder mission. The obtained results demonstrate the effectiveness of the adaptive Kalman filtering schemes.