Study on conditionally optimal filtering methods

Abstract

The problem of determining the state of a system from noisy measurements is called estimation or filtering. The use of the system naturally tries to minimize the inaccuracies caused by the presence of this noise by filtering. In order to have any sort of filtering problem in the first place, there must be a system of which measurements are available. But optimal filters require exact knowledge of the process noise and the measurement noise, and exact descriptions of system dynamics. Thus optimal filters are generally demanding on computational burden, and optimality is unachievable if the required computational capabilities are not available. Because an unlimited computer capability is not usually available, the designer of a filter or smoother purposely ignores or simplifies certain effects when he represents them in his design equations; this results in a suboptimal data processor[6]. We suggest suboptimal discrete filters for stochastic systems with different types of observations. Linear Kalman filter and extended Kalman filter are replaced by unconnected each other local filters which allow parallel processing of observations and reduce off-line and on-line computational requirements. This has been achieved via the use of a decomposition of multidimensional observation vector into a set of subvectors of lower dimension. The obtained filtering equations have a parallel structure and are very suitable for parallel programming. The numerical example demonstrates the efficiency and high-accuracy of the proposed suboptimal filters. And the practical application of approximate methods of optimal filtering is restricted by the high order of filters, especially in problems of high dimension. Even the application of the simplest method of normal approximation or other methods necessitates the integration of the set of high order equations in such problems. Therefore, the only way of designing practically realizable filters in high dimension problems is the decrease...