A Study On Cubature Kalman Filter With Their Applications To State Estimation Of Inductor Motor

State estimation problem for nonlinear systems is focus of many engineering application domains including automatic control, moving target tracking, navigation etc. It leads to growing interest of researchers in the area of nonlinear filtering algorithms. In this regard, Cubature Kalman Filter (CKF) exhibits superior performance, portraying the qualities like rigorous analysis, simple structure, high filtering accuracy, good numerical stability. This method is suitable for nonlinear systems of high dimensionality and offers efficient procedure to deal with nonlinear filtering problems. With advancement of technology and increasing complexities of real-world applications, there is need for performance enhancement of existing algorithms to fit complex engineering applications, and primary objective of nonlinear filtering algorithms is to cope with such difficulties.On one side, CKF algorithm can overcome issues existing in other nonlinear filtering algorithms. On the other hand, it itself bears some limitations and hence requires in-depth research and improvement. In this thesis, focusing on two problems of normal CKF design requiring precise statistical characters of noise and the establishment of an accurate system model, an adaptive CKF and adaptive CKF strong tracking filter are proposed, respectively. In the filtering process of adaptive CKF, the statistical characters of noise can be estimated and corrected on-line by using Sage-Husa maximum a posterior (MAP) estimator, and filtering divergence is restrained. Therefore the estimation accuracy and stability of CKF is effectively improved. CKF strong tracking filter exhibits strong robustness to the mismatch of model parameters and rapid tracking ability to the abrupt state, meanwhile it is capable to overcome the problems of Strong tracking filter (STF). Generic STF algorithm has some theoretical limitations and the STF based on unscented transformation (UTSTF) declines in accuracy and further diverges when nonlinearity in filtering problem is severe. To further add novelty and contribution to our work, adaptive CKF strong tracking filter is proposed when the prior noise statistic is unknown and time-varying, exploiting Sage-Husa noise statistic estimator based on CKF strong tracking filter. Many simulations are performed, and results show that proposed algorithms are feasible and effective, and exhibit effective improvement over filtering effect of normal CKF algorithm.Considering nonlinear filtering problems in sensor-networks, performance of existing distributed filter based on Sigma point information filtering is easily affected by parameters, which limits its scope of application. A new distributed filter based on CKF is derived using information filter framework and average-consensus theory to design distributed program, in which each sensor node exchanges information with its neighbors so that local state estimate reaches a global consensus within the network. New algorithm not only bears the qualities of distributed filtering such as scalability and robustness to sensor failures, it also has high accuracy and strong stability of CKF. In order to compare the performance of the same type of existing filtering algorithms, distributed UKF (Unscented Kalman Filter) algorithm, for example, was made in simulation analysis also. Results show that the distributed CKF algorithm has higher filtering accuracy and numerical stability for target state estimation.The problem of distributed estimation for a class of discrete-time nonlinear systems with unknown inputs in a sensor network is investigated. Accordingly for nonlinear systems without or with direct feedthrough of unknown input to the measurement, a distributed DNRTSKF and distributed DNERTSIF are developed, respectively. For the case that the unknown inputs of system doesn’t have direct impact on outputs, a modification scheme to the derivative-free versions of nonlinear robust two-stage Kalman filter (DNRTSKF) is first introduced based on recently developed Spherical-Radial Cubature technique. Afterwards, a novel information filter is proposed by expressing recursion in terms of the information matrix based upon DNRTSKF. Distributed algorithm is developed by applying a new information consensus filter (ICF), in which each sensor node only fuses the local observation instead of the global information and updates the local information state and matrix from its neighbors’estimates using dynamic average-consensus strategy. As unknown inputs affect both the system state and outputs, a novel information filtering algorithm is derived by reconstructing the non-linear version of the extended recursive three-step filter (NERTSF) into the information filter architecture, and then information filter is extended to the ’derivative-free’ version with the help of Cubature transformation according to linear error propagation methodology. In the implementation procedure of distributed scheme, local statistics are diffused over the entire sensor network by the same way. The proposed distributed filters in two cases can achieve simultaneous input and state estimation of nonlinear systems with arbitrary unknown inputs over a sensor network. Specifically, state estimate is unbiased and the actual covariance matrix is close to that of the centralized fusion filter. The efficacy of the proposed distributed algorithms is demonstrated by simulation examples on target tracking and is compared with existing algorithms such as centralized fusion filter and distributed CKF, which lack in tracking the true dynamics of the unknown input.The problem of distributed estimation of nonlinear networked systems subject to measurement packet losses modeled as a Bernoulli process is also studied, in which measurement data loss from different sensors may experience different probabilities. A recursive information filtering structure (NEIF) is derived by reconstructing networked-EKF, and it’s derivative-free version is derived employing recently developed CKF, labeled as networked cubature information filter (NCIF). It offers better estimation accuracy and simple implementation since the evaluation of Jacobians during state estimation is not required unlike networked-EKF. Afterwards, a distributed NCIF is derived by introducing an average consensus scheme in the filter structure in order to diffuse local statistic to its neighbors. It is portrayed that proposed filtering structure is capable of handing the packet dropout for nonlinear systems in a networked environment.To highlight the application of proposed results to real-world problems, practical example of speed-sensorless vector-controlled induction motor (IM) drives is discussed. Speed and load torque are regarded as state variables, and full-order model of IM is derived by introducing the mechanism and torque equations. Then the state of IM can be estimated on-line by applying the proposed filters in this paper, such as adaptive CKF and adaptive CKF strong tracking filter. Adaptive CKF performs better than the conventional estimator, which can overcome the dependency of noise covariance matrix Q and R. Furthermore, adaptive CKF strong tracking filter can achieve rapid tracking to the abrupt state of IM, and then the speed-sensorless vector-controlled system has good static and dynamic control performance over full speed region. It still can achieve the effective tracking state in the case of motor parameters change, and estimate the change parameters accurately at the same time by a combined estimation method of parameters and states.