The authors analyze the error behavior for the discrete-time extended Kalman filter for general nonlinear systems in a stochastic framework. In particular, it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough. This result is verified by numerical simulations for an example system.

Stochastic stability of the discrete-time extended Kalman filter

Performance evaluation of UKF-based nonlinear filtering

In this note, we consider a new filtering problem for linear uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design a linear filter such that, for all admissible parameter uncertainties and all possible incomplete observations, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prescribed upper bound. It is shown that, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like inequalities or linear matrix inequalities. The explicit expression of the desired robust filters is parameterized, and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.

/pdf/variance-constrained-filtering-for-uncertain-stochastic-4ktkeczl1e.pdf

Variance-constrained filtering for uncertain stochastic systems with missing measurements

This paper deals with a new filtering problem for linear uncertain discrete-time stochastic systems with randomly varying sensor delay. The norm-bounded parameter uncertainties enter into the system matrix of the state space model. The system measurements are subject to randomly varying sensor delays, which often occur in information transmissions through networks. The problem addressed is the design of a linear filter such that, for all admissible parameter uncertainties and all probabilistic sensor delays, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error for each state is not more than the individual prescribed upper bound. We show that the filtering problem under consideration can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities. We also characterize the set of desired robust filters in terms of some free parameters. An illustrative numerical example is used to demonstrate the usefulness and flexibility of the proposed design approach.

/pdf/robust-filtering-under-randomly-varying-sensor-delay-with-1dg7m4fze7.pdf

Robust filtering under randomly varying sensor delay with variance constraints

In this technical note, we analyze the error behavior of the discrete-time extended Kalman filter for nonlinear systems with intermittent observations. Modelling the arrival of the observations as a random process, we show that, given a certain regularity of the system, the estimation error remains bounded if the noise covariance and the initial estimation error are small enough. We also study the effect of different measurement models on the bounds for the error covariance matrices.

Stochastic Stability of the Extended Kalman Filter With Intermittent Observations

: The paper discusses the almost sure boundedness of linear and nonlinear randomly sampled systems. It is shown that if an autonomous linear randomly sampled system exhibits almost sure asymptotic stability, then the system is almost surely bounded input-bounded output. Moreover, for a bounded input, the second moment of the out-put remains bounded and this bound is easily computable. It is also found that linear or nonlinear systems which are almost surely asymptotically stable for a null input, remain almost surely bounded when the input consists of an uncorrelated noise with finite variance. (Author)

E. I. Jury

Papers

Almost sure boundedness of randomly sampled systems