Research On State Estimation Based On Kalman Filter Algorithm Under Multiplicative Noise

The linear system with multiplicative noise is actually an extension of the classical linear Kalman filter system.With the continuous improvement of the accuracy of the system model in areas such as aquatic communications and satellite attitude estimation,the system of multiplicative noise is also getting more and more Concerned,its own advantages and characteristics also appear.With the continuous improvement of measurement technology,people have a clearer understanding of the system's own physical characteristics and movement characteristics,so that people get more prior information about the system and the filtering accuracy is also greatly improved.In this paper,the state additive noise of system under multiplicative noise interference is related to the measurement of additive noise.It is of great theoretical and practical value to study the state filter estimation of the system.The main research work of this paper is as follows:1.KF algorithm based on state filter estimation algorithm,including KF algorithm,EKF algorithm,UKF algorithm.The UKF algorithm is analyzed in detail.The advantages of the EKF algorithm and the UKF algorithm are verified by examples.2.The measurement equations of the system are affected by multiplicative noise,the multiplicative noise is white noise,and the measured additive noise of the system and the state additive noise satisfy a certain linear relationship.According to the orthogonal projection theorem,A new recursive optimal algorithm is obtained based on the minimum mean square error criterion.The effectiveness of the proposed optimal algorithm is verified by example simulation and is conducive to the further expansion of the noise.3.The equation of state and the measurement equation are both subject to multiplicative noise,and the system additive additive noise and state additive noise still meet certain linear relationship,and the optimal state estimation of the target is calculated.Based on the minimum mean square error estimation,the state estimation of discrete-time linear systems is obtained.The algorithm is recursive and optimal,and the simulation results show the effectiveness and accuracy of the proposed algorithm.4.Aiming at the target multi-model tracking problem under the multiplicative noise interference,the IMM algorithm which is affected by multiplicative noise is obtained through the joint use of Kalman filter and IMM algorithm with multiplicative noise.According to the actual law of target movement,two motion states of uniform velocity and uniform velocity are constructed.The proposed algorithm calculates the state estimation by using the IMM algorithm under the interference of multiplicative noise respectively.