Research And Applications Of Robust Kalman Filtering Algorithm Based On Cubature-rule

In actual production,all control systems are nonlinear and run in a variable environment.Consequently,system uncertainties commonly exist,such as the variations of model parameters,unknown parameters,sensor noises and external disturbances.In the presence of system uncertainties and nonlinearities,both the evaluation accuracy and robustness of system status using linear filtering technologies will be greatly affected,which may ultimately reduce system stability and disable it to maintain the desired performances.Therefore,the robust control technique to deal with system uncertainties has attracted more and more attention from scholars,as well as the development of nonlinear filtering technology.In the frames of the singular value decomposition aided Cubature Kalman filter and the singular value decomposition aided Cubature Quadrature Kalman filter,this paper studies the cubature-rule based robust Kalman filtering algorithms,aiming to eliminate or reduce the effect of system uncertainty on the performance of filter.The main works are as follows.Firstly,this paper puts forward an adaptive and robust singular value decomposition aided Cubature Kalman filter to solve the problem that state variation and gross error would lead to the decline or divergence of the performance of Kalman filter in the state estimation of a stochastic dynamic system.Since the covariance of innovation cannot keep orthogonal when state variation and gross error occur,the proposed adaptive and robust method uses Chi-square test to the judge state variation and gross error.To deal with these two kinds of uncertainties,the strong-tracking-filter-based adaptive algorithm is utilized for adjusting process noise covariance matrix,so as to eliminate the impact of state variation.Besides,the measurement-noise-inflating robust algorithm is applied for adjusting measurement noise,in order to eliminate the influence of gross error.The effectiveness of this algorithm is verified by the numerical simulation.The proposed algorithm is adaptive to state variation and robust under the condition of gross error.Especially,the switch of adaptive and robust algorithm based on Chi-square test result can keep adaptability and robustness when the two cases occur at the same time.Secondly,this paper presents a nonlinear unknown input observer based on singular value decomposition aided reduced dimension Cubature Kalman filter for a special class of nonlinear systems,the nonlinearity of which is only caused by part of its states.The theorem is derived to prove that the posterior means and covariance matrixes of all statuses can be represented by Gauss integrals using the state vector which causes the nonlinearity of the system.In this way,we can obtain the integral equivalent form by sampling all state vectors and their nonlinear part.The number of the sampling points of the resultant nonlinear unknown input observer will be greatly reduced,but the accuracy will still reach the third-order accuracy of Taylor's expansion.The simulation results show that the proposed algorithm can meet the requirements of the system,and it is a lot more important to increase the calculating efficiency.The effectiveness of this algorithm is verified in the target trajectory tracking simulation.Thirdly,a suggestion is made that the robust singular value decomposition aided Cubature Quadrature Kalman filter is to treat the uncertainties combining the H-? and Cubature Quadrature Kalman filter.The Cubature Quadrature Kalman filter adopts the hyper-sphere cubature rule and two-order Gauss-Laguerre quadrature rule to generate Cubature Quadrature points and calculate multiple moment integrals.Compared with Cubature Kalman filter,it has a better accuracy,and its number of sampling pints only increases linearly.At the same time,the introduction of H-? enhances the robustness of the system.In a word,the effectiveness of this algorithm is verified by both the numerical simulation and the simulation of the GPS/INS integrated navigation system.Finally,this paper advises the singular value decomposition aided Cubature Kalman filter with neural network.This method is based on the singular value decomposition aided Cubature Kalman filter with neural network.A three-layer BP neural network is utilized as a noise compensator which compensates process noise and measurement noise.The method is applied in a binocular stereo visual servoing system for estimating the image Jacobi matrix to verify its performance.The simulation results show the effectiveness of the proposed algorithm,and simplify the design of this system,as the model does not need to measure depth information.The effectiveness is also verified by the experiments of the binocular vision servo control system based on the MOTOMAN UP6 robot.