Study On Adaptive Estimation Algorithms For A Class Of Systems With Multiplicative Noise

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 adaptive estimation algorithms for systems with multiplicative noise and unknown transition matrix.The theory of Kalman filtering provides one set of recursive algorithm for computer to calculate. However, when Kalman filtering is used to solve practical problems, one rigorous limit is that all the model parameters and statistical properties should be known previously. Such as, the initial values of the system, the model parameter matrixes, and the statistical characteristics of noises etc. which are often unknown in practice, or approximately known, or partly of known: this often leads to large state estimation error, and even causes filter divergence. Hence, all the facts make it necessary to study the adaptive estimation theory. At present, adaptive filter algorithm theory and application have achieved fruitful results. On the basis of estimation theory for systems with multiplicative noise and adaptive estimation theory, state filtering, smoothing, and deconvolution estimation of stochastic input signals for stochastic systems with multiplicative noise and unknown transfer matrix have been studied in this dissertation. The main study of the dissertation is introduced as follows:1. For a class of systems with multiplicative noise and unknown transition matrix, a corresponding recursive algorithm is specifically developed in the sense of linear minimum-variance, according to the irrelevant status of w(k) and v(k). That is to say, estimations of parameters and states are obtained by the way of iteration, thus forming a case of adaptive filtering algorithms for systems with unknown transition matrix. At the same time, according to the relevant status of w(k) and v(k), a corresponding recursive algorithm of parameters (the unknown transition matrix) and states is obtained.2. On the basis of state filtering algorithms, under the condition of white noise and unknown transition matrix, a fixed-interval state suboptimal direct smoothing recursive algorithm is derived. With the introduction of the auxiliary variables, the fixed-interval state suboptimal indirect smoothing algorithm is obtained, which reduces the amount of computation for smoothers and makes the algorithm more practical.3. With the consequences of filtering and smoothing algorithms, a suboptimal algorithm of fixed-interval deconvolution for the system with multiplicative noise and unknown transition matrix is given.4. All the algorithms in the dissertation are validated by computer simulations. For comparison, the charts produced by computer simulation are all provided with the estimated value and the real value.