Study On Optimal Estimation Algorithms For A Class Of2-D Systems With Multiplicative Noise

2-D system with multiplicative noise means there are both additive andmultiplicative noises existing in the measurement equation, the study of which hasprofound practical background and theoretical significance. With the development ofmodern control theory, people have come to pay more attention to the study of2-Dsystem. Compared with the1-D system, it is more difficult to study2-D system becauseof its structural complexity. The difficulties will increase a lot for the derivation of theestimation algorithm of2-D system with multiplicative noise. The2-D system hasmany applications in many engineering fields such as the multidimensional filteringnetwork, image analysis, the treatment of partial differential equations, digital signalprocessing and so on. The multiplicative noise can be used to describe thecharacteristics of the channel, such as the effect of signal distortion, energy loss andfading, which always exists in the practical systems. So it is essential to study the2-Dsystem with multiplicative noise. This dissertation puts forward the algorithms ofseveral models about2-D system with multiplicative noise. The main study of the paperis as follows:1. The derivation of the state filtering algorithm for2-D FM-Ⅱ system withmultiplicative noise is completed. The algorithm is derived based on the well-knowprojection theorem, and it is optimal in the linear minimum variance. The algorithm is adirect extension of the state filtering algorithm for1-D system with multiplicative noise.It is a recursive algorithm which is easy to implement on the computer. Theconvergence of the algorithm is also quick. At last, the simulation results prove theeffectiveness of the proposed algorithms.2. The derivation of the measurement noise estimation algorithm for2-D FM-Ⅱsystem with multiplicative noise is completed. Based on the state filtering algorithm,the filtering and smoothing algorithms of the measurement noise are developed inindependent noises by―projection theorem‖. The smoothing algorithms include twoparts—the fixed interval algorithm under single index changing and the fixed lengthalgorithm under double indexes changing. The algorithms mentioned above are optimalin the linear minimum variance. At last, simulation results validate the algorithm.3. In this paper, a set of state filtering algorithms are proposed for a class of2-Dsingular Roesser model (SRM) systems with multiplicative noise. First, two equivalentreduced order subsystems are obtained via the decomposition of Roesser modelsystems without jumping modes. One of the subsystems continues to be rewritten as theFM-Ⅱ model with correlated noise at the same coordinate point. In addition, the algorithm for2-D FM-Ⅱ is derived based on the well-know projection theorem, andthe filtering algorithm for2-D SRM is obtained accordingly. The algorithms areoptimal in the linear minimum variance. At last, the simulation results show theeffectiveness of the proposed algorithms. And the influence of signal to noise ratioabout the algorithm is also discussed.