Hybrid State Estimation With Multiple Model Method

The hybrid system is a class of complex stochastic dynamical systems with interacting continuous and discrete dynamics.These systems typically contain variables or signals that take values from a Euclidean vector space and also variables that take values from a discrete finite state space.The propagation of the system state is driven by the continuous and discrete dynamics synchronously.With the widespread application of the hybrid system model in quantities of significant areas,for instance target tracking,air traffic control,embedded systems,signal processing,fault detection and so on,the hybrid state estimation as the core technology has received great attention.In this dissertation,four key problems of hybrid estimation,namely,model set adaptation,transition probability determination,hypothesis management and output combination,are studied given the consecution as the thread,and at last the problem of state estimation for Markov systems with measurement dropouts is considered.The detailed research content is as follows.1.The problem of active model set adaptation for hybrid systems is addressed.First the switching logic of active sub-set is designed using the information of the expectation value of system mode,model probability and likelihood function.Then the current minimal active sub-set is chosen from the total set based on the switching logic.The expected mode is calculated and augmented by to the current active sub-set,and the resultant set is utilized as the working set to execute the multiple model estimation.Based on this model set adaptation method,a novel variable structure multiple model hybrid estimator is obtained.Simulation results indicate that the proposed algorithm is of high estimation accuracy and efficiency in the complicated target tracking environments.2.The problem of state estimation for hybrid systems with known transition probability matrix(TPM)is studied.Firstly,under the assumption of a time-invariant but random TPM,an approximate recursion for the TPM's posterior probability density function within the Bayesian framework is derived.Based on this recursion,by adopting the idea of Quasi-Bayesian prior probability estimation of finite mixtures,an algorithm for online minimum mean-square error(MMSE)estimation of the TPM is proposed.The proposed TPM estimation is naturally incorporable into a typical online Bayesian estimation scheme for hybrid systems resulting in an adaptive version of hybrid estimators with unknown TPM.Simulation results illustrate that the TPM adaptation algorithm can significantly improve the estimation accuracy with high efficiency.3.The hypothesis management strategy is studied.Based on Gaussain mixture and moment matching equations,the number of mixture terms for each model-pair is maintained constant and thus the exponential growth of the hypotheses is avoided.To be specific,at the end of each mixing,the number of terms of the GM in each model-pair is reduced and kept constant by choosing for the GM the s most probable hypotheses.The remaining hypotheses are merged into a single one and will complete the GM which now contains s+1 terms for each model-pair.Based on this strategy,a novel hybrid estimator is proposed.The algorithm can inherit the statistic characteristics of the “likely” model sequences and reduce the“unlikely” ones at the same time with no information waste,thus is more precise and efficient.Simulation results indicate that the proposed approach is more superior in performance than the existing multiple model algorithms.4.The output combination process of the hybrid estimation is addressed.First,the cross-covariance of estimation errors instead of likelihood functions are calculated.On the basis of this,three types of model weights,that is,scalar weight,diagonal-matrix weight and matrix weight are derived based on the optimal fusion criteria.Therefore,the confusion of pdf and pmf in the existing algorithms is avoided.Furthermore,in order to handle the system and noise uncertainties,a H? filter with adaptive threshold is adopted as the sub-filters of the hybrid estimator.Based on the above,three novel robust interacting multiple model algorithms are obtained,and the detailed computational complexity analysis,theoretical analysis and simulation comparison are given.5.The state estimation problem for a class of jump Markov linear systems with packet dropouts is studied.The behavior of packet dropouts is described by a two-state(i.e.,packet-dropping and normal)Markov chain,which is independent of the system dynamics.Therefore,the obtained system can be modeled as a jump Markov linear system with two switching parameters.A product set is defined to combine the two mode sets and the corresponding relationship between models in the product set and models in the individual mode set is given.Based on the product set,the model is cast into the framework of the interacting multiple model(IMM)algorithm and the filtering steps are carried out in a layered manner.Furthermore,an optimal estimation algorithm is combined with the IMM to obtain the filtering results of the system.A maneuvering target tracking example is presented to prove the effectiveness of the proposed algorithm.