Kalman Estimator With Multiplicative Noise And Correlated Additive Noise

With the rapid development in the fields of aerospace,networked control systems,communication engineering,and speech processing,linear stochastic systems with multiplicative noise and colored noise have more extensive applications in the above-mentioned fields.Due to the variability of the environment or the limitation of economic conditions,problems such as related noise,various process disturbances,random uncertainties,and random nonlinearities are inevitable.This paper comprehensively considers the above characteristics of industrial systems and various stochastic phenomena,and solves the Kalman estimator of systems with multiplicative noise and related additive noise based on projective theory and the optimal estimation algorithm in the sense of linear unbiased minimum variance problem.The main research contents are as follows:1.The Kalman estimator is presented for the linear stochastic system with correlated and colored noises.By the augmented state method,the state equation with colored process noise can be transformed into the augmented state equation with white noises.In order to solve the colored measurement noise,based on the measurement difference approach,the new white measurement is rebuilded.The process noise and observation noise of this new system are one-step correlated.For this new system,the Kalman estimator is presented by applying the recursive projection formula and Kalman filtering theory,which includes the Kalman filter,one-step predictor and one-step smoother.Finally,two tracking system examples verify the effectiveness of the proposed algorithm.2.The optimal time-varying Kalman filtering is proposed for the linear stochastic descriptor systems with multiplicative noise and colored additive noises.By the singular value decomposition(SVD)method and fictitious noise approach,the descriptor system is transformed to two reduced-order non-descriptor systems without multiplicative noise.By the augmented state approach and difference transformation approach,the new augmented state space model with correlated white noise is presented.For the obtained non-descriptor standard system,the Kalman filter and predictor of reduced state and white process noise deconvolution filter and predictor are presented.Further,the optimal time-varying Kalman filter and predictor of original state for the descriptor system are obtained according to the relations of the new state and the original state.Finally,a power system simulation example verifies the effectiveness of the algorithm.3.For the multisensor system with multiplicative noise and correlated additive noise,the standard state space model with one-step correlated white noise is obtained by using augmented state method and measurement difference method,and the local optimal Kalman estimator are obtained by using Kalman filtering theory.Then the cross-covariance matrix of estimation error is calculated,and then the distributed weighted fusion estimator is given based on the matrix weighted,scalar weighted and diagonal matrix weighted fusion algorithm in the sense of linear unbiased minimum variance.At the same time,the three fusion estimation algorithms proposed are compared and analyzed in terms of accuracy.Finally,a simulation example verifies the effectiveness of the algorithm.