| The classical continuous Lorenz system closely related to the weather forecast will produce chaotic phenomena when the parameters satisfy certain conditions.However,when the system is discretized or used as a signal carrier,it will inevitably add some random noise,which make chaotic systems more random and more difficult to track.Thus when we consider the Lorenz system with process noise or noise with parameters,the error will be magnified over time because of the initial sensitivity of chaos.Therefore,it is necessary to add some complete or incomplete observations.Then we use nonlinear filtering to obtain the optimal or suboptimal estimation of the state or parameters.In this paper,the unscented Kalman filter(UKF)with its error analysis,particle filter under the importance sampling and unscented Kalman particle filter(UPF)in nonlinear filtering are reviewed.They are used to estimate the state and parameters of the Lorenz system of Gaussian and non-Gaussian processes respectively.Finally we observe the effect of tracking and estimation.The estimation of the state can greatly reduce the error,and the estimation of the parameters is also accurate enough.We find that the interference caused by chaos is eliminated.At the end,we summarize and put forward relevant prospects. |
