Study On Optimal Estimation Algorithm Of Measurement Noise In Singular System With Multiplicative Noise

Singular system with multiplicative noise means there are both additive and multiplicative noises existing in the measurement equation. Since the estimation algorithm for discrete stochastic systems with multiplicative noise is significantly important in signal processing, this dissertation mainly addresses the optimal estimation algorithms of measurement noise in singular system with multiplicative noise.Researches on the estimation of measurement noise are initiated by practical requirements. They are not only useful in distinguishing different noise sources, but also applicable in noise suppression. However, all the previous studies are not involved with singular systems. The singular systems are more capable in describing physical systems, due to the unique structure of state models. In addition, the multiplicative noise factor in estimation model is considerably practical in describing the characteristics of discrete stochastic systems. As a corollary, studies on estimation algorithms of measurement noise in singular system with multiplicative noise are of great value both in theoretical and practical researches. Hence, this dissertation is mainly focused on deducing the optimal filtering and smoothing algorithms of the measurement noise in the singular system with multiplicative noise. The deductions and results are approached by innovation and projection theorem in Hilbert space. As to the state estimation algorithm, which is essential in the deductive process, is thoroughly provided for further research. The main study of the dissertation is introduced as follows:1. According to the irrelevant status of w(k) and v(k), an optimal filtering algorithm of measurement noise and an optimal smoothing one are specifically developed in the sense of linear minimum-variance. Firstly, the system is transformed into two reduced-order subsystems by restricted equivalent transformation. Secondly, the state augmentation is used to restore the measurement noise which had been transformed. Based on the existed algorithms of the optimal state estimation of the singular system with multiplicative noise, the optimal filtering algorithm of measurement noise is given. An optimal fixed-interval smoothing algorithm is subsequently developed. Since the smoothing algorithm is not deduced by the conventional procedure, the ultimate formation is remarkably different from the previous result under similar case in ordinary system. Furthermore, this whole procedure can be referred in simplifying the previous algorithm.2. According to the relevant status of w(k) and v(k), an optimal estimation algorithm of the measurement noise and an optimal smoothing one are also developed in the sense of linear minimum-variance. Since the state filtering algorithm is essential in the estimation of the measurement noise, a brand-new state estimation algorithm is provided after the second restricted equivalent transformation. Then the discussion proceeded under two divided situations as impulse-free system and impulse system. The filtering algorithm of state in impulse-free system is optimal in the sense of linear minimum-variance, but the algorithm in impulse system is only sub-optimal. Nevertheless, due to the specific characteristic of the measurement noise, the filtering and smoothing algorithm are both optimal in the sense of linear minimum-variance.3. Regarding the irrelevant status of w(k) and v(k) as a special case in relevant status, which is tantamount to replacing zero into the correlate parameter. This is typically assuming the previous methods in measurement noise estimation. The results are compared with the former algorithm in their equivalences and differences.4. All the algorithms in the dissertation are proved effective by computer simulations. For comparison, the charts produced by computer simulation are all provided with the estimated value and the real value.