Recursive State Estimation Of Stochastic Jump Systems With Incomplete Information

Stochastic jump systems (SJSs) are special systems, which involve both continuous time-evolving and discrete event-driven mechanisms. Because of the special information structure, SJSs have been extensively used to model the systems with variable structures in many fields such as moving target tracking, process monitoring, signal processing, fault detection and petrol industry, et al. State estimation is to obtain the unmeasured state variable by analyzing a sequence of measurements sampled in a noisy environment. How-ever, the existing methods concerning on the state estimation of SJSs are mainly proposed with complete information (all the system parameter are assumed to be known perfectly), and fewer results consider the state estimation problem with incomplete information. In view of this, in this thesis, we focus on the state estimation of SJSs with some uncertain factors such as unknown time delay, uncertain model parameters, etc, and propose some different filtering algorithms suiting different situations. The major work of this thesis can be concluded as:(1) Consider the minimum mean square error estimation problem for a class of linear Markov jump systems (MJSs) with unknown mode-dependent state delays. To show the difficulties caused by the unknown delays, the online Bayesian equation of the investigated system is firstly developed by incorporating the time-delay estimation into the recursion of system states. However, computing such optimal estimation causes an exponential increase in the requirement of computation and storage load. Therefore, two different approximation techniques:interacting multiple-model ap-proximation and detection-estimation method are used to obtain two suboptimal but executable filtering algorithms, respectively. Simulation results of the proposed methods for a system are presented to illustrate the effectiveness.(2) A study of state estimation for nonlinear MJSs with uncertain transition probabil-ities (TPs) is investigated. The uncertainties of TPs are portrayed by intermediate stochastic variables depicted by truncated Gaussian probability density functions (TGPDFs). In order to incorporate the prior knowledge about uncertainties into the filtering process, a skew parameter is firstly inserted into TGPDF. Then, the state estimation method is derived based on multiple model mechanism together with particle filter using confidence TPs which are obtained by normalizing the expectations of STGPDFs. On the other hand, consider the state estimation for nonlinear SJSs with state-dependent TPs. In this method, a general approach is presented to model the state dependent transitions, the state and output spaces are discredited into cell space which handles the nonlinearities and computationally intensive problem.(3) An adaptive risk-sensitive filtering method which relaxes the restrictive assumption that risk-sensitive parameter is chosen as a prior is proposed for a class of discrete-time linear MJSs. Some analysis is presented to illustrate the essential effect of the risk sensitivity added into the filtering process and show the intrinsic reasons for the improvement of robustness. Then, a principle is developed to obtain the risk-sensitive parameter using the online measurements. To avoid overregulation under mismatched modes and mitigate the problem of smearing the feature of each model, a minimization mechanism is resorted to. Computer simulations are presented to reveal the effectiveness of our method.(4) The risk-sensitive filtering method is extended to nonlinear MJSs. In the method, the so-called reference probability technique together with particle approximation is used to derive the risk-sensitive filter in nonlinear non-Gaussian framework. The novelty of the proposed approach is that a "risky" interacting resampling step is performed to both moderate the modeling uncertainties and solve the problem of particle explosion. A designer-chosen parameter named risk-sensitive parameter allows us to make a trade-off between the filtering accuracy for the nominal model and the robustness to uncertainties. With a meaningful example, it shows that the developed method can outperform the widely used methods-PF and IMM-PF in nonlinear MJSs with uncertainties.(5) Consider the state estimation problem for a class of discrete-time non-homogeneous linear MJSs, where the transition probability matrix (TPM) is assumed to be time-variant and takes value in a finite set randomly at each time step. Two IMM-type approximation stages are employed to avoid the exponential computational require-ments. The resulting filter reduces to the IMM filter when the number of candidate TPMs is unity. A meaningful example is presented to illustrate the effectiveness of our method.