Study Of Optimal Estimation Algorithm For Singular Systems With Multiplicative Noise

In the field of signal processing, it is a significant matter to study the signalestimation for stochastic systems with multiplicative noise. The optimal estimationalgorithmsforsingularsystemswithmultiplicativenoisearemainlyresearchedinthisdissertation.In the past, the research productions with regard to the systems withmultiplicative noise are almost aimed at nonsingular systems. However, in theengineeringpractices, thesingularsystems have higher capabilitytodescribephysicalsystems and singular system models are morepractical than normal models in manycircumstances. At the same time, as far as the state estimation forsingular systems isconcerned,mostpreviousworksupposedthattheobservationequationsonlyinvolvedadditive noise, actually, many observation equations include not only additive noise,but also multiplicative noise. All the facts make it necessary to study the estimationtheory for singular systems with multiplicative noise. The signal estimation forsingular discrete stochastic systems with multiplicative noise is considered and threeoptimal estimation algorithms are proposed in this dissertation. The followings havebeenfinished:1. A state optimal estimation algorithm (direct way) for singular systems withmultiplicative noise in the sense of linear minimum-variance is developed. First, thesystem is transformed into two subsystems by restricted equivalent transformation.Then, based on the state estimation of the subsystems, the optimal filtering of theoriginal system is obtained. The dimension of the filter decreases due to thedecomposition,soitiseasytobecalculated.2. Because of the high computational complexity of the direct way, anaugmented optimal filtering algorithm is proposed for singular systems withmultiplicative noise. To begin with, the state estimation problem of the systems istransformed into the problem for reduced-order subsystems by restricted equivalenttransformation. It is noting that the measurement noise here becomes colored noise.To solve the problem, then, the method of state augmentation is used. The augmentedfiltering algorithm is optimal on the basis of the linear minimum-variance criterion.Furthermore, based on the filtering algorithm, the indirect algorithm of the optimalfixed-interval smoothing and the optimal deconvolution estimation algorithm aredeveloped. 3.However, forthe augmentedoptimalfilteringalgorithm,thedimension ofstatevector increases after the augmentation, so calculation load much increases. So, thethird method is considered. The singular systems are divided into two groups,impulse-freesingularsystems andimpulsesingularsystems.Forimpulse-freesingularsystems with multiplicative noise, the algorithm is optimal in the sense of linearminimum-variance, and the filtering algorithm for impulse singular systems withmultiplicativenoiseissuboptimal.4.Thealgorithmspresentedinthisdissertation arenotonlydeducedtheoreticallybut also tested through simulation. Satisfactorysimulation results are obtained, whichvalidatethealgorithms.