A novel truncated approximation based algorithm for state estimation of discrete-time Markov jump linear systems

In this paper, state estimation problem for discrete-time Markov jump linear systems is considered. First, three equalities are proposed. Next, they are applied to the state estimation problem of considered systems so that a novel suboptimal algorithm in the sense of minimum mean-square error estimate is obtained where the computation and storage load of the suboptimal algorithm is not ever-increasing with the length of the noise observation sequence. The proposed algorithm and the suboptimal adaptive algorithm proposed in [1] are all based on a truncated approximation strategy. However, compared with the algorithm of [1], the proposed algorithm requires much less approximations. Computer simulations are carried out to evaluate the performance of the proposed algorithm.     

Extensions of the SMC-PHD filters for jump Markov systems

The probability hypothesis density (PHD) filter is a promising algorithm for multitarget tracking, which can be extended for jump Markov systems (JMS). Since the existing multiple model sequential Monte Carlo PHD (MM SMC-PHD) filter is not interacting, two extensions of the SMC-PHD filters are developed in this paper. The interacting multiple-model (IMM) SMC-PHD filter approximates the model conditional PHD of target states by particles, and performs the interaction by resampling without any a priori assumption of the noise. The IMM Rao-Blackwellized particle (RBP) PHD filter uses the idea of Rao-Blackwellized to further enhance the performance of target state estimation for JMS with mixed linear/nonlinear state space models. The simulation results show that the proposed algorithms have better performances than the existing MM SMC-PHD filter in terms of state filtering and target number estimation.     

Iterative algorithms for state estimation of jump Markov linearsystems

Jump Markov linear systems (JMLSs) are linear systems whose parameters evolve with time according to a finite state Markov chain. Given a set of observations, our aim is to estimate the states of the finite state Markov chain and the continuous (in space) states of the linear system. In this paper, we present original deterministic and stochastic iterative algorithms for optimal state estimation of JMLSs. The first stochastic algorithm yields minimum mean square error (MMSE) estimates of the finite state space Markov chain and of the continuous state of the JMLS. A deterministic and a stochastic algorithm are given to obtain the marginal maximum a posteriori (MMAP) sequence estimate of the finite state Markov chain. Finally, a deterministic and a stochastic algorithm are derived to obtain the MMAP sequence estimate of the continuous state of the JMLS. Computer simulations are carried out to evaluate the performance of the proposed algorithms. The problem of deconvolution of Bernoulli-Gaussian (BG) processes and the problem of tracking a maneuvering target are addressed     

Novel extended Viterbi-based multiple-model algorithms for state estimation of discrete-time systems with Markov jump parameters

This paper considers a state estimation problem for discrete-time systems with Markov switching parameters. For this, the generalized pseudo-Bayesian second-order-extended Viterbi (GPB2-EV) and the interacting multiple-model-extended Viterbi (IMM-EV) algorithms are presented. The derivations of these new algorithms rely on a nontrival incorporation of some functional mechanisms of a new extended Viterbi algorithm into the GPB2 and the IMM methods for hypothesis reductions in order to improve computational efficiency and/or estimation performance. The IMM-EV (and the GPB2-EV) algorithm and the IMM (and the GPB2) algorithm have some common components, but their schemes for the calculation of weights and for the combination of the inputs and outputs are different. Indeed, the IMM-EV (and the GPB2-EV) algorithm spans the continuum from hard-decision methods with merged-hypothesis-tree style to the IMM (and the GPB2) algorithm inclusive. The proposed algorithms are well suited to state estimation problems in maneuvering target tracking. Simulations demonstrate that an IMM-EV algorithm can be an improvement to the IMM, the GPB2, and the variable-structure multiple model with likely-model set methods for tracking a target undergoing various types of maneuvers at some unknown times.     

Robust peak-to-peak filtering for Markov jump systems

The peak-to-peak filtering problem is studied for a class of Markov jump systems with uncertain parameters. By re-constructing the system, the dynamic filtering error system is obtained. The objective is to design a peak-to-peak filter such that the induced L_∞ gain from the unknown inputs to the estimated errors is minimized or guaranteed to be less or equal to a prescribed value. By using appropriate stochastic Lyapunov–Krasovskii functional, sufficient conditions are initially established on the existence of mode-dependent peak-to-peak filter which also guarantees the stochastic stability of the filtering error dynamic systems. The design criterions are presented in the form of linear matrix inequalities and then described as an optimization problem. Simulation results demonstrate the validity of the proposed approaches.     

Recursive state estimation for linear dynamic systems under algebraic constraints

A minimum variance recursive linear estimator is discussed for linear dynamic systems where the state vector is also subject to linear algebraic equality constraints.<>     

Joint state filtering and parameter estimation for linear stochastic time-delay systems

This paper presents the joint state filtering and parameter estimation problem for linear stochastic time-delay systems with unknown parameters. The original problem is reduced to the mean-square filtering problem for incompletely measured bilinear time-delay system states over linear observations. The unknown parameters are considered standard Wiener processes and incorporated as additional states in the extended state vector. To deal with the new filtering problem, the paper designs the mean-square finite-dimensional filter for incompletely measured bilinear time-delay system states over linear observations. A closed system of the filtering equations is then derived for a bilinear time-delay state over linear observations. Finally, the paper solves the original joint estimation problem. The obtained solution is based on the designed mean-square filter for incompletely measured bilinear time-delay states over linear observations, taking into account that the filter for the extended state vector also serves as the identifier for the unknown parameters. In the example, performance of the designed state filter and parameter identifier is verified for a linear time-delay system with an unknown multiplicative parameter over linear observations.     

Recursive short-data-record estimation of AV and MMSE/MVDR linear filters for DS-CDMA antenna array systems

The presence of the desired signal during estimation of the minimum mean-square error (MMSE)/minimum-variance distortionless-response (MVDR) and auxiliary-vector (AV) filters under limited data support leads to significant signal-to-interference-plus-noise ratio (SINR) performance degradation. We quantify this observation in the context of direct-sequence code-division multiple-access (DS-CDMA) communications by deriving close approximations for the mean-square filter estimation error, the probability density function of the output SINR, and the probability density function of the symbol-error rate (SER) of the sample matrix inversion (SMI) receiver evaluated using both a desired-signal-"present" and desired-signal-"absent" input covariance matrix. To avoid such performance degradation, we propose a DS-CDMA receiver that utilizes a simple pilot-assisted algorithm that estimates and then subtracts the desired signal component from the received signal prior to filter estimation. Then, to accommodate decision-directed operation, we develop two recursive algorithms for the on-line estimation of the AV and MMSE/MVDR filter and we study their convergence properties. Finally, simulation studies illustrate the SER performance of the overall receiver structures.     

Online Bayesian estimation of transition probabilities for Markovian jump systems

Markovian jump systems (MJSs) evolve in a jump-wise manner by switching among simpler models, according to a finite Markov chain, whose parameters are commonly assumed known. This paper addresses the problem of state estimation of MJS with unknown transition probability matrix (TPM) of the embedded Markov chain governing the jumps. Under the assumption of a time-invariant but random TPM, an approximate recursion for the TPMs posterior probability density function (PDF) within the Bayesian framework is obtained. Based on this recursion, four algorithms for online minimum mean-square error (MMSE) estimation of the TPM are derived. The first algorithm (for the case of a two-state Markov chain) computes the MMSE estimate exactly, if the likelihood of the TPM is linear in the transition probabilities. Its computational load is, however, increasing with the data length. To limit the computational cost, three alternative algorithms are further developed based on different approximation techniques-truncation of high order moments, quasi-Bayesian approximation, and numerical integration, respectively. The proposed TPM estimation is naturally incorporable into a typical online Bayesian estimation scheme for MJS [e.g., generalized pseudo-Bayesian (GPB) or interacting multiple model (IMM)]. Thus, adaptive versions of MJS state estimators with unknown TPM are provided. Simulation results of TPM-adaptive IMM algorithms for a system with failures and maneuvering target tracking are presented.     

Silhouette-based human pose estimation using reversible jump Markov chain Monte Carlo

A novel approach for recovering the human body configuration based on the silhouette is presented. By considering pose inference as traversing the difference subspaces and using a data-driven mechanism, reversible jump Markov chain Monte Carlo (RJMCMC) can explore such solution space very efficiently. Experimental results are provided to demonstrate the efficiency and effectiveness of the proposed approach.     

Efficient particle filtering for jump Markov systems. Application to time-varying autoregressions

We present an efficient particle filtering method to perform optimal estimation in jump Markov (nonlinear) systems (JMSs). Such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure. We take advantage of these specificities in order to develop a generic filtering methodology for these models. The method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature, namely, the auxiliary particle filter and the unscented transform. This algorithm is applied to the complex problem of time-varying autoregressive estimation with an unknown time-varying model order. More precisely, we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations. We show that this problem can be formulated as a JMS and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper. Simulations demonstrate the performance of our method compared to standard particle filtering techniques.     

部分转移概率离散奇异Markov跳变系统的镇定

针对具有更广泛意义的部分转移概率未知情况下的离散时间奇异 Markov跳变线性系统,给出了使开环系统正则、因果、随机稳定的充分条件,并表示为严格线性矩阵不等式形式,且消除了等式约束条件。部分转移概率未知的条件包括了完全开关系统和随机跳变转移概率完全未知的情况,适用范围更广泛;在此基础上,通过求解严格线性矩阵不等式的可行解,设计了模式依赖状态反馈控制器,使闭环系统正则、因果、随机稳定,实现了系统的镇定;最后,给出一个仿真算例验证了所提方法的有效性。     

Hidden Markov model state estimation with randomly delayedobservations

This paper considers state estimation for a discrete-time hidden Markov model (HMM) when the observations are delayed by a random time. The delay process is itself modeled as a finite state Markov chain that allows an augmented state HMM to model the overall system. State estimation algorithms for the resulting HMM are then presented, and their performance is studied in simulations. The motivation for the model stems from the situation when distributed sensors transmit measurements over a connectionless packet switched communications network     

Robust Kalman filters for linear time-varying systems withstochastic parametric uncertainties

We present a robust recursive Kalman filtering algorithm that addresses estimation problems that arise in linear time-varying systems with stochastic parametric uncertainties. The filter has a one-step predictor-corrector structure and minimizes an upper bound of the mean square estimation error at each step, with the minimization reduced to a convex optimization problem based on linear matrix inequalities. The algorithm is shown to converge when the system is mean square stable and the state space matrices are time invariant. A numerical example consisting of equalizer design for a communication channel demonstrates that our algorithm offers considerable improvement in performance when compared with conventional Kalman filtering techniques     

THE REALIZATION OF LINEAR SHIFT-VARIANT FILTERS THROUGH STATE FEEDBACK

In this paper a new method to realize rational generalized transfer functions of linearshift-variant digital filters through state feedback is presented In some practical applications therequired characteristics of the filter change slowly.Under these circumstances,the proposedmethod is very effective and the resulting filter structure is simple.A numerical example isprovided to show the performance of the method.     

Resonant frequency estimation for adaptive notch filters in industrial servo systems

This paper proposes a new algorithm for estimating the resonant frequency of adaptive notch filters used in servo systems. Notch filters and adaptive notch filters are widely used in commercial servo systems for suppressing a resonance which is a major obstacle in improving their performance. However, the conventional frequency estimation algorithm gives a dynamic behavior that is proportional to the difference between the square of the estimated frequency and the square of the actual frequency. This can cause the estimation dynamics to be too slow for low-frequency resonances, if both low- and high-frequency resonances are present and if the estimator gain is designed for a high frequency. This paper develops a new algorithm to give a dynamic behavior that is proportional to the difference in the estimated frequency and actual frequency. This allows selecting the estimation parameters independent from the value of resonant frequencies. The developed algorithm is implemented to a production servo controller and applied to a production printed-circuit-board inspection system. The experimental results show that the developed algorithm is much more effective in suppressing the resonances of both low- and high-frequencies, compared to the pervious algorithm. Furthermore, the ability to suppress vibration allows increasing the feedback gain, which in turn allows improving the tack time performance from 190 ms to 100 ms. All experiments reported in this paper were performed in an actual industrial environment using a production system, and the developed algorithms are applied to the production system.     

Two-stage adaptive estimation of irrational linear systems

In the present paper, an adaptive parameter estimation algorithm applicable to linear systems with transfer functions of arbitrary structure is proposed. The approach can be applied to a wide class of linear processes, including non-linearly parameterized ones. The proposed method is applicable to fractional-order systems, distributed-parameter and delayed systems, and other classes of systems described by irrational transfer functions. In the first stage of the proposed procedure, values of the transfer function at specific frequencies are pinpointed by means of the Recursive Least Square algorithm with forgetting factor. In the second stage, the unknown parameters are found by numerically inverting complex non-linear relations linking them to the quantities estimated in the first stage. The inversion is performed by means of an iterative, gradient-based scheme. The method is illustrated by several detailedly explained numerical examples.     

Expectation maximization algorithms for MAP estimation of jumpMarkov linear systems

In a jump Markov linear system, the state matrix, observation matrix, and the noise covariance matrices evolve according to the realization of a finite state Markov chain. Given a realization of the observation process, the aim is to estimate the state of the Markov chain assuming known model parameters. Computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations. We present three expectation maximization (EM) algorithms for state estimation to compute maximum a posteriori (MAP) state sequence estimates [which are also known as Bayesian maximum likelihood state sequence estimates (MLSEs)]. The first EM algorithm yields the MAP estimate for the entire sequence of the finite state Markov chain. The second EM algorithm yields the MAP estimate of the (continuous) state of the jump linear system. The third EM algorithm computes the joint MAP estimate of the finite and continuous states. The three EM algorithms optimally combine a hidden Markov model (HMM) estimator and a Kalman smoother (KS) in three different ways to compute the desired MAP state sequence estimates. Unlike the conditional mean state estimates, which require computational cost exponential in the data length, the proposed iterative schemes are linear in the data length     

Nonlinear state estimation for uncertain systems with an integralconstraint

This paper considers a problem of robust filtering for a class of uncertain nonlinear systems. The solution involves a set-valued state estimate that is obtained by solving a Hamilton-Jacobi-Bellman equation. In addition, a less computationally intensive approximate solution to the problem is obtained for filtering problems defined over a large time interval. The paper also presents an approximate solution to the robust filtering problem, which leads to a robust version of the extended Kalman filter     

Some new algorithms for recursive estimation in constant linear systems

Recursive least-squares estimates for processes that can be generated from finite-dimensional linear systems are usually obtained via ann times nmatrix Riccati differential equation, wherenis the dimension of the state space. In general, this requires the solution ofn(n + 1)/2simultaneous nonlinear differential equations. For constant parameter systems, we present some new algorithms that in several cases require only the solution of less than2nporn(m + p)simultaneous nonlinear differential equations, wheremandpare the dimensions of the input and observation processes, respectively. These differential equations are said to be of Chandrasekhar type, because they are similar to certain equations introduced in 1948 by the astrophysicist S. Chandrasekhar, to solve finite-interval Wiener-Hopf equations arising in radiative transfer. Our algorithms yield the gain matrix for the Kalman filter directly without having to solve separately for the error-covariance matrix and potentially have other computational benefits. The simple method used to derive them also suggests various extensions, for example, to the solution of nonsymmetric Riccati equations.