Estimation For Discrete-time Linear Systems Research Articles

Back-and-forth nudging moving horizon estimation for discrete-time linear systems

In this paper, we propose a novel moving horizon estimation algorithm for discrete-time linear systems with a limited number of measurements. Motivated by the idea of the back-and-forth nudging algorithm, we design the back-and-forth nudging in time moving-horizon estimation method by deploying two moving horizon estimators that move backward and forward iteratively. Based on a finite number of measurements, the proposed algorithm can be used for moving-horizon state estimation with guaranteed convergence. By using the proposed method, we show that the norm of the state estimation error is upper bounded by a sequence that converges to its steady-state in finite-time (i.e., using a finite number of measurements), provided that suitable parameters are selected. The unbiasedness properties and comparison results with the conventional (forward-in-time) moving horizon estimation are discussed. The effectiveness of the proposed approach is validated through a numerical example.

Set membership state estimation for discrete-time linear systems with binary sensor measurements

This paper addresses the problem of state estimation for discrete-time linear systems, based on measurements provided by an output binary sensor. The problem is formulated and solved in a set theoretic framework. Two algorithms are devised for recursively computing outer approximations of the set of state vectors compatible with the information provided by the binary sensor. This allows one to obtain a nominal state estimate and to characterize the associated uncertainty. The procedures can be tuned to suitably trade off the quality of set approximations and the required computational load. An input design technique based on the computed feasible state sets, which is aimed at promoting uncertainty reduction, is provided. The case of time-varying sensor threshold is also considered and a strategy for selecting online the value of the threshold is formulated. All the proposed methods are validated in simulations on two numerical examples.

Distributed Exponential State Estimation for Discrete-Time Linear Systems Over Jointly Connected Switching Networks

The existing results on distributed state estimation problems for discrete-time linear systems were obtained over connected static networks, or every-time connected switching networks by a two-time-scale design. This paper further studies the same problem over jointly connected switching networks which can be disconnected at every time instant by a single-time-scale distributed design. Since the existing distributed designs critically rely on the connectedness assumption on the networks and thus may not apply to jointly connected switching networks, we have to modify the local observers and develop a novel approach which makes use of the uniform complete observability property for a discrete-time time-varying system. Additionally, we establish two exponential stability results for two classes of discrete-time switched systems, which may be of independent interest.

Tighter Interval Estimation for Discrete-Time Linear Systems With a New Dynamic Triggering Approach

Tighter Interval Estimation for Discrete-Time Linear Systems With a New Dynamic Triggering Approach

Two-step zonotopic estimation method for discrete-time linear delayed systems

This paper deals with interval state estimation for discrete-time linear systems with known time-varying delay. The considered systems are subject to unknown but bounded disturbances and measurement noise in predefined zonotopes. The main contribution lies in the development of a two-step interval estimation method which integrates a robust observer design providing more degrees of design freedom with a zonotopic analysis technique. By introducing the H∞ formalism in the observer design, the proposed method is effective in reducing the effects of unknown uncertainties and improving the estimation accuracy. Based on the designed observer, the interval estimation is guaranteed by a novel zonotopic analysis taking into account the effects of the time-delay on the system dynamics. By using zonotopes, the proposed approach is intuitive and is able to overcome the wrapping effects, which refers to the significant growth of the constructed set dimension in the propagation process. Numerical simulations of a two-stage chemical reactor with delayed streams are given to show the effectiveness and superiority of the proposed method.

Minimum variance constrained estimator

This paper is concerned with the problem of state estimation for discrete-time linear systems in the presence of additional (equality or inequality) constraints on the state (or estimate). By use of the minimum variance duality, the estimation problem is converted into an optimal control problem. Two algorithmic solutions are described: the full information estimator (FIE) and the moving horizon estimator (MHE). The main result is to show that the proposed estimator is stable in the sense of an observer. The proposed algorithm is distinct from the standard algorithm for constrained state estimation based upon the use of the minimum energy duality. The two are compared numerically on the benchmark batch reactor process model.

Fast interval estimation for discrete-time linear systems: An [formula omitted] optimization method

This paper studies interval estimation for discrete-time linear systems with unknown but bounded disturbances. Inspired by the parity space approach, we propose a point estimator with fixed-time convergence property. The estimator is combined with the zonotope-based interval analysis to achieve fast interval estimation. The parameter matrix in the estimator is optimized by minimizing the length of the edges of the outer box of the error zonotope. It is formulated as L1 optimization problem and can be efficiently solved by linear programming. Comparison studies illustrate the superiority of the proposed method over existing techniques.

Reduced-order observer-based interval estimation for discrete-time linear systems

This paper proposes an interval estimation method for discrete-time linear systems by designing robust reduced-order observer with reachability analysis. First, the discrete-time linear system is transformed into a reduced-order system via a special equivalent transformation, which depends on the orthogonal procedure on the output matrix. Then, a kind of robust reduced-order observer is developed such that the states of the original discrete-time system can be indirectly estimated, where the technique is used to attenuate the effects of disturbances. Based on the estimated states provided by the reduced-order observer, the interval estimation can be obtained by reachability analysis. A simulation example is given to illustrate that the proposed method of interval estimation has better performance than the full-order observer-based interval estimation.

Fast interval estimation for discrete-time systems based on fixed-time convergence

This paper studies interval estimation for discrete-time linear systems with unknown but bounded disturbance and measurement noise. Inspired by the well-known parity space approach in the field of fault diagnosis, we propose a fast interval estimation method with fixed-time convergence property. A singular value decomposition-based parameter optimization algorithm is used to attenuate the effect of uncertainties on the estimation error. Comparison study illustrates the superiority of the proposed method over existing technique.

Interval estimation for discrete-time linear systems: A two-step method

This paper proposes a two-step interval estimation method for discrete-time linear systems by integrating robust observer design with reachability analysis. The proposed method is designed based on a new observer structure which can provide more degrees of design freedom. For improving estimation accuracy, H∞ technique is used in observer design to attenuate the effects of disturbances and noise. Based on the obtained observer, interval estimation can be achieved via reachability analysis. The proposed method provides an intuitive design paradigm for interval estimation and is effective in controlling the wrapping effect, which refers to the additional growth of the constructed sets resulting from the propagations of overestimations at each step. Simulation results are given to demonstrate the performance of the proposed method.

Adaptive Kalman Filtering for Systems Subject to Randomly Delayed and Lost Measurements

This paper investigates the problem of state estimation for discrete-time linear systems where the observation data are transmitted from the sensor to the filter subject to random delay and dropout. The loss and latency of the measurements are modeled by a group of Bernoulli distributed random variables with uncertain probabilities, which appear in the Kalman filter parameters. An adaptation factor, which is defined by comparing the theoretical and practical values of the innovation covariance, is employed to adjust the filter gains during estimation. Simulation results are presented to verify the improved performance of the proposed adaptive filter.

Moving horizon estimation for discrete-time linear systems with binary sensors: Algorithms and stability results

The paper addresses state estimation for linear discrete-time systems with binary (threshold) measurements. A Moving Horizon Estimation (MHE) approach is followed and different estimators, characterized by two different choices of the cost function to be minimized and/or by the possible inclusion of constraints, are proposed. Specifically, the cost function is either quadratic, when only the information pertaining to the threshold-crossing instants is exploited, or piece-wise quadratic, when all the available binary measurements are taken into account. Stability results are provided for the proposed MHE algorithms in the presence of unknown but bounded disturbances and measurement noise. Performance of the proposed techniques is also assessed by means of simulation examples.

Linear Minimum Mean Square Filters for Markov Jump Linear Systems

This paper studies optimal mean square error estimation for discrete-time linear systems with observed Markov jump parameters. New linear estimators are introduced by considering a cluster information structure in the filter design. The set of filters constructed in this way can be ordered in a lattice according to the refines of clusters of the Markov chain, including the linear Markovian estimator at one end (with only one cluster) and the Kalman filter at the other end (with as many clusters as Markov states). The higher is the number of clusters, the heavier are precomputations and smaller is the estimation error for embedded sequences of partitions so that the cardinality and choice of the clusters allows for a tradeoff between performance and computational requirements. In this paper, we propose the estimator, give the formulas for precomputation of gains, present some properties, and give an illustrative numerical example.

Optimal Estimation for Discrete-Time Linear Systems in the Presence of Multiplicative and Time-Correlated Additive Measurement Noises

In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise. An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix. The proposed estimator has a recursive structure, and has time-independent computation and storage load. Computer simulations are carried out to demonstrate the performance of the proposed estimator. The simulation results show the superiority of the proposed estimator.

Robust receding-horizon state estimation for uncertain discrete-time linear systems

An approach to robust receding-horizon state estimation for discrete-time linear systems is presented. Estimates of the state variables can be obtained by minimizing a worst-case quadratic cost function according to a sliding-window strategy. This leads to state the estimation problem in the form of a regularized least-squares one with uncertain data. The optimal solution (involving on-line scalar minimization) together with a suitable closed-form approximation are given. The stability properties of the estimation error for both the optimal filter and the approximate one have been studied and conditions to select the design parameters are proposed. Simulation results are reported to show the effectiveness of the proposed approach.

DESIGN OF RECEDING-HORIZON FILTERS FOR DISCRETE-TIME LINEAR SYSTEMS USING QUADRATIC BOUNDEDNESS

State estimation for discrete-time linear systems is addressed by developing a filter that provides an estimate of the state depending only on a batch of recent measurement and input vectors. This problem has been solved by introducing a receding-horizon objective function that includes also a weighted penalty term related to the prediction of the state. Convergence results and unbiasedness properties have been proved for this estimator in a previous work. In this paper, the focus is on the problem of designing such a filter using results related to quadratic boundedness of the estimation error. Upper bounds on the norm of the estimation error have been found by constructing a suitable positively invariant set. Moreover, these bounds may be expressed in terms of Linear Matrix Inequalities (LMIs), and are well-suited to being minimized for the purpose of design.

A state-set estimation algorithm for linear systems in the presence of bounded disturbances

This paper concerns the problem of state-set estimation for discrete-time linear systems. The linear system is given in state-space form and the system's uncertainty is described by bounded scalar variations. We present a recursive algorithmic procedure of computing guaranteed estimated state sets. In particular, a polyhedron variation algorithm is presented. The new algorithm is based on linear-programming and sensitivity analysis techniques for improved computational efficiency and practicability.