Design, Analysis And Application Of The Filter Algorithm Based On UKF

The data processing and information fusion technology are the main reasons that affect the navigation performance, accuracy, reliability and automation degree in modern navigation systems. Most traditional navigation filter adopts the extended Kalman filter (EKF) algorithm. In the recent years, because of the characteristics of high precision, small computing burden and well practicability, the unscented Kalman filter (UKF) becomes an effective method of nonlinear filtering and the research focus of data processing and information fusion technology in navigation systems.Based on this background, this dissertation deals with the design, application and stability analysis problems of the unscented Kalman filter by using the control theory. The related unscented Kalman filter algorithms are proposed and analyzed for the uncertainties in navigation systems, such as the signal propagation delay, the disturbance of external environment, the unknown random bias, correlated noises and the unknown random parameters, etc. Also, the filtering estimates of navigation systems can be solved. The main works and innovations are as follows:The briefs of the development and main research contributions of the Kalman filter are reviewed. The unscented transformation technique and sampling strategy of the unscented Kalman filtering are summarized.The stability performance of the unscented Kalman filter (UKF) for general nonlinear stochastic discrete-time systems is investigated. At the same time, the relationship between the observability of the nonlinear system and the stability of the algorithm is analyzed. Motivated by the encouraging results of stability for the usual Kalman filter and stochastic stability analysis for general nonlinear estimation problems, the error behavior of the UKF is analyzed. In order to improve stability, slight modifications of the standard UKF are performed by introducing an extra positive definite matrix in the noise covariance matrix. It is shown that the design of the matrix can be considered as a tradeoff between stability and accuracy.The performance of the unscented Kalman-Bucy filter (UKBF) for general nonlinear stochastic continuous-time system is investigated. At the same time, the relationship between the observability of the nonlinear system and the stability of the algorithm is analyzed. Motivated by the stability of the usual Kalman-Bucy filter for linear systems and by the successful application of the stochastic stability theory to solve nonlinear-estimation problems, the error behavior of the UKBF is analyzed. The general nonlinear stochastic continuous-time system consists of two types of systems: the nonlinear continuous-time system with linear measurement equation and the nonlinear continuous-time system with nonlinear measurement equation. The stabilities of the algorithms for the two types of systems are analyzed, respactively.Based on the UKF, the filter processing is presented for nonlinear stochastic systems with correlated noises, which consists of the modified UKF (MUKF) algorithm and the adaptive UKF (AUKF) algorithm. In MUKF and AUKF, the related prediction and measurement equations hold the sigma points chosen by unscented transformation (UT) technique as the parameter sampling in the normal UKF. In order to improve stability of MUKF, an extra positive definite matrix is introduced in the noise covariance matrix to enlarge the prediction covariance matrix. In AUKF, the design of the adaptive covariance matrix plays an important role in improving the stability and robustness of the algorithm. Through the analysis of stability, it is shown that the estimation error of MUKF remains bounded even if the initial error is large. Through the analysis of the adaptive prediction covariance in AUKF, it is shown that the estimation error of AUKF remains bounded on the effect of the initial error and the unknown disturbances. The high performances of algorithms and the stability sufficient conditions are verified by using Matlab simulations on numerical systems.The two-stage unscented Kalman filter (TUKF) is proposed to consider the nonlinear system in the presence of unknown random bias. The adaptive fading UKF is designed by using the forgetting factor to compensate the effects of incomplete information. The TUKF to estimate unknown random bias is designed by using the adaptive fading UKF. In order to analyze the stability of the TUKF, an augmented-state TUKF can be obtained. It is shown that the augmented-state UKF is uniformly asymptotically stable and the stability of the augmented-state TUKF means the stability of the TUKF. The performance of the TUKF is verified by using simulation on the high-update rate wheel mobile robot.Based on the UKF, the nonlinear filter is presented for parameter estimation in the linear system with correlated noise. The state consists only of the parameters to be estimated, while the corresponding inputs, outputs, and computed residuals are collected in the observation matrix of the state equations. This results again in a nonlinear system, and the UKF state estimator directly gives the parameter estimates only. Convergence properties of the proposed algorithm are analyzed and ensured based on the associated differential equation. The algorithm is verified by using simulations on the vehicle navigation systems with aided GPS.Based on the UKF, the nonlinear filter is presented for the input-output estimation of nonlinear systems with extended noise environments. A special case of symmetrical environments is proposed for both UKF and EIV filtering. The filtering problem is solved, including two sub-cases:the errors-in-variables filtering is the optimal estimate of inputs and outputs from noisy observations, and the unscented Kalman filtering is the optimal estimate of state and output in presence of state and output noise. The evaluation of the expected performance of the filter is then considered. The algorithm is verified by using a Monte Carlo simulation.Based on the UKF, the filtering problems in the INS/GPS integrated navigation system is dealt with. Firstly, the UKF is introduced to the nonlinear model of the integrated navigation system. And the adaptive UKF which have strong tracking capability is proposed. The STUKF algorithm has high convergence speed and its precision is similar to that of normal UKF. The effectiveness of the proposed algorithm in the convergence rate and estimation precision is verified by simulations.Based on the UKF, the problem of parameter estimation of an underwater target in real time is addressed. The filter models including the processed longitude and latitude errors are designed. And based on the models, the UKF is used to obtain joint estimates of both the original system state and the system unknown parameters through appending the unknown parameters into the original state variables for an enlarged system. Finally, simulation results illustrate the performance of the UKF for the underwater positioning systems.Based on the UKF and the NID control law, the suitable estimator structure for the aircraft flight control in wind shear is proposed. The aircraft nonlinear dynamics in wind shear are partitioned into slow-and fast-time-scale subsystems. Then the NID control law is applied to the subsystems, respectively. The UKF is designed to provide accurate estimates for the controler. The simulation results are organized to facilitate a comparison of the UKF/NID flight trajectory with that obtained using optimal trajectory analysis and the EKF/NID flight trajectory, as well as to illustrate the estimation performance of the UKF.Finally, the conclusions of the dissertation are drawn and further research directions are put forward.