Unbiased Minimum-variance State Research Articles

STATE ESTIMATE SCHEMES FOR DESCRIPTOR SYSTEMS WITH MULTI-TIME DELAYED MEASUREMENTS

This paper deals with discrete-time stochastic descriptor (singular) systems with instantaneous and multi-time delayed measurements. The estimability condition of the descriptor systems involving delayed measurements is given. Using the measurements reorganization approach, the optimal Kalman filter and corresponding estimate error covariance are derived. Furthermore, an algorithm for the linear unbiased minimum variance state estimation is given. A numerical example is presented to illustrate the given algorithm.

CURRENT OUTPUT FILTER FOR STATE ESTIMATION OF SCALAR NONLINEAR SYSTEMS WITH APPLICATION TO CHAOTIC COMMUNICATION

A novel nonlinear state estimation technique called Current Output Filter is proposed in this paper. By taking two successive measurements into account and optimizing the coefficients of the proposed filter structure, an unbiased minimum variance state estimation algorithm with guaranteed estimation error performance is derived for scalar nonlinear systems. The performance of this filter is shown to be superior to the Extended Kalman Filter (EKF) in simulations. An application to a chaotic communication scheme is also presented in this work.

Rekursives Verfahren zur biasfreien Parameterschätzung mit minimaler Schätzfehlerkovarianz (RMV)

The Extended Kalman Filter (EKF) can be used to obtain unbiased minimum variance state estimates for nonlinear dynamic systems. The present paper discusses a modification of the EKF which allows additionally parameter identification of linear, discrete transfer functions. Besides this modification of the EKF algorithm, a rather pragmatic interpretation of the filter error covariances leads to the RMV algorithm (Recursive Minimum Variance), which is presented in this paper. When describing applications of this algorithm, we restrict ourselves to the estimation of parameters. In contrast to the RLS algorithm (Recursive Least Squares), which is the best-known recursive method for parameter identification of discrete transfer functions, the RMV algorithm delivers unbiased estimates at a comparable computational effort

A finite-time linear filter for discrete-time systems

The discrete-time linear filtering problem is considered where the system is constant and the noise is stationary. An optimal time-invariant linear filter is obtained in z-transfer function matrix form. The filter gives an unbiased minimum variance state estimate at the end of a given fixed filtering interval [ 0, T] This state estimate is the same as that which would be obtained using a time-varying Kalman filter, The estimate is therefore better than that which would be obtained from a Wiener filter at this time. The state estimates within the finite filtering interval can also be an improvement over those from a Wiener filter. The major advantage of this filter is that it may be easily implemented because it is time-invariant. The weighting sequence for the proposed filter is zero for times greater than the fixed filtering interval. The filter, at times t⩽ T, therefore uses the observations in a moving window of length T. The fixed memory length property of the filter has well known advantages in reduc...