Study Of Numerically Stable Estimation For Singular Systems With Multiplicative Noise

Studies on signal estimation method for stochastic systems with multiplicative noise are significant in signal processing theory. Numerical stability algorithm and outlier rejection algorithm for singular systems with multiplicative noise are discussed in this dissertation.In engineering practice, singular systems are more general because their mathematical models are more realistic as description of many practical systems. The previous research on singular systems is generally based on singular systems without multiplicative noise. In recent years, the optimal estimation algorithm in the linear minimum variance criterion has been extended to the estimation problem for singular systems with multiplicative noise by some scholars to enrich and develop the estimation theory for singular systems. However, numerical instability may occur during the application of these algorithms to practical systems, which will have negative impact on computational accuracy even will cause the algorithm divergent or completely ineffective. In addition, outlier data in the observation play an important role in computational accuracy of the algorithms, while the treatment of outlier data is not given in the conventional algorithms. Considering the above-mentioned two problems, this dissertation focuses on the numerical stability and the outlier rejection of the optimal estimation algorithms for singular systems with multiplicative noise. The specific work is as follows.Firstly, based on the first restricted equivalent transformation for singular systems and the existing optimal filtering algorithm, the numerically stable algorithm of the optimal filter in the linear minimum variance criterion for singular systems with multiplicative noise is proposed by using matrix singular value decomposition.Secondly, the direct method of the state optimal smoothing for the singular systems with multiplicative noise is derived in the sense of linear minimum variance. Based on this algorithm, the numerically stable algorithm of state optimal smoother is given based on the numerically stable algorithm of the optimal filter. Meanwhile, a numerically stable extraction method of the stochastic input signal is obtained in combination of the system's features in the deduction of the optimal filtering algorithm.Thirdly, based on the state space model, a weighted innovation method according to innovation sequence nature is adopted to develop an outlier rejection algorithm of the state filter for singular systems with multiplicative noise. Meanwhile, combining the numerically stable state filter algorithm, a numerically stable outlier rejection algorithm is given.The algorithms presented in this dissertation are not only deduced theoretically but also tested through the computer simulation. Satisfactory simulation results are given to validate the algorithms.