Estimation Algorithms For A Class Of Nonlinear Systems With Equality State Constraints And Multiplicative Noise

System with multiplicative noise is the promotion of the classic Kalman filtering linear system. With the increasing accuracy of modeling in the filed of underwater acoustic communication and satellite attitude estimation, the system with multiplicative noise shows the advantages and characteristics. With the development of measurement technology, people can know characteristics of the physical system and its movements. We can take advantage of these priori observed information to establish constraints, and it will improve the accuracy of the filering effectively. However, most systems are usually nonlinear in practice. It is full of theoretical and practical significance to study the state estimation of the systems with equality constraints and multiplicative noise.For the nonlinear system with equality state constraints and multiplicative noise, the thesis derives two filtering algorithms, with the use of the two representative nonlinear filtering algorithms:Extended Kalman filter and Unscented Kalman filter, combining with the equality constrained filtering. The thesis derives the smoothing algorhthm of EKF as well. This thesis presents a lot of simulation experiments to verify the effectiveness of the algorithms.The main contents of the paper are:1. The filtering algorithm is proposed for the nonlinear system with equality state constraints and multiplicative noise. By changing the state equation and observation equations based on Taylor formula, a new model of linear system with equation constraints and multiplicative noise can be obtained correspondingly. The dimension of the measurement equation is augmented by perfect measurements, and the filering algorithm is derived based on the projection throrem. At last, the simulation results show the effectiveness of the proposed algorithms. Finally, the smoothing algorithm is proposed.2. Based on the probability of fitting for linear filtering algorithms, the algorithm is proposed with the use of Unscented Kalman filter for the nonlinear system with equality state constraints and multiplicative noise. First, the Sigma points are obtained from the sampling strategies of center sampling. These Sigma points are through the linear transformation, we get the transformed Sigma points. With the weights from the sampling strategies, we get the state updates. By using the perfect measurements, the dimension of the measurement equation is augmented. Finally, we get the filtering algorithm of the nonlinear system with equality state constraints and multiplicative noise under the framework of Kalman filter.