Researches On State Estimation Of Discrete-Time Markov Jump Linear Systems

Discrete-time Markov jump linear systems are discrete-time systems whose pa-rameters including the state matrix, observation matrix, and the noise covariance matrices evolve with discrete-time according to a finite-state Markov chain. As one of the most important hybrid systems, discrete-time Markov jump linear systems have been used in many fields such as target tracking, fault detection, telecommuni-cation, manufacturing and etc. In these fields, an important problem is to estimate the state of discrete-time Markov jump linear systems based on a sequence of the observation. Though the state estimation problem of discrete-time Markov jump linear systems has been extensively studied, there still exists many problems that have not been solved, such as how to effectively deal with Gaussian mixture and how to improve the performance and efficiency of the existing algorithms. Hence, using the theories of probability and stochastic processes, and applying the knowl-edge of expectation and covariance, the dissertation studies the state estimation problem of discrete-time Markov jump linear systems. The main contributions of this dissertation are as follows:1. State estimation problem for discrete-time Markov jump linear systems with mutually independent Gaussian noises is considered. By using orthogonal projective theorem at the first time, a novel suboptimal algorithm for state estimate of discrete-time Markov jump linear systems in the sense of minimum mean square error estimate is proposed. The proposed suboptimal algorithm is recursive and finite-dimensionally computable. Compared with the exiting algorithms, the novelty of the proposed suboptimal algorithm is that the pro-posed suboptimal algorithm uses orthogonal projective theorem to compute mode-conditional estimates. Simulation results indicate the effectiveness of the proposed suboptimal algorithm.2. A novel suboptimal algorithm in the sense of minimum mean-square error estimate is obtained where the computation and storage load of the subopti-mal algorithm is not ever-increasing with the length of the noise observation sequence. The proposed suboptimal algorithm and the SA algorithm are all based on a truncated approximation strategy. However, by using three original equalities, the proposed suboptimal algorithm largely reduces the approxima-tions of the SA algorithm. Simulation results indicate the effectiveness of the proposed suboptimal algorithm.3. State estimation problem for linear hybrid systems with mutually independent noises is considered. By using the properties of expectation, conditional ex-pectation, conditional covariance matrices and several original equalities, two algorithms in the sense of linear minimum mean-square error estimate are pro-posed at the first time. The first algorithm is an optimal algorithm which can exactly calculate the linear minimum mean-square error estimate of system state. The second algorithm is a suboptimal algorithm which is proposed to reduce the computation and storage load of the proposed optimal algorithm. The proposed suboptimal algorithm is recursive and finite-dimensionally com-putable. Compared with the existing minimum mean-square error estimate based algorithms, an advantage of the two algorithm is that they do not re-quire that system noise and observation noise must be Gaussian.4. State estimation problem for discrete-time Markov jump linear systems with arbitarily correlative Gaussian noises is considered. By using several original equalities, and the theories of probability and stochastic processes, two algo-rithms in the sense of minimum mean-square error estimate are proposed at the first time. The first algorithm is an optimal algorithm which can exactly cal-culate the minimum mean-square error estimate of system state. The second algorithm is a suboptimal algorithm which is proposed to reduce the compu-tation and storage load of the proposed optimal algorithm. An advantage of the proposed two algorithms in contrast to the existing minimum mean-square error estimate based algorithms is that the two algorithms do not require the independence of the noise affected the systems.5. State estimation problem for linear hybrid systems with arbitarily correlative noises is considered. By using several original equalities, and the theories of expectation, conditional expectation and stochastic processes, two algorithms in the sense of linear minimum mean-square error estimate are proposed at the first time. The first algorithm is an optimal algorithm which can exactly calculate the linear minimum mean-square error estimate of system state. The second algorithm is a suboptimal algorithm which is proposed to reduce the computation and storage load of the proposed optimal algorithm.