The problem of state estimation for discrete systems with parameters which may be switching within a finite set of values is considered. In the general case it is shown that the optimal estimator requires a bank of elemental estimators with its number growing exponentially with time. For the Markov parameter case, it is found that the optimal estimator requires only N2 elemental estimators where N is the number of possible parameter values.

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The purpose of this report is to examine several Kalman filter algorithms that can be used for state estimation with a multiple sensor system. In a synchronous data collection system, the statistically independent data blocks can be processed in parallel or sequentially, or similar data can be compressed before processing; in the linear case these three filter types are optimum and their results are identical. In multilateration radar tracktng applications, the data compression method is shown to be computationally most efficient, followed by the sequential processing, the parallel processing is least efficient. These algorithms are described in detail and their results are compared with a suboptimum tracking algorithw which processes only multiple range measurements. A state estimate compression algorithm is also described. Various radar measurement transformation formulas are listed. Algorithms for a nonsynchronous data collection system are not examined in detail but possible approaches are suggested. fil ..