Recursive filtering for a class of nonlinear systems with missing measurements

Abstract

This paper is concerned with the finite-horizon recursive filtering problem for a class of nonlinear time-varying systems with missing measurements. The missing measurements are modeled by a series of mutually independent random variables obeying Bernoulli distributions with possibly different occurrence probabilities. Attention is focused on the design of a recursive filter such that, for the missing measurements, an upper bound for the filtering error covariance is guaranteed and such an upper bound is subsequently minimized by properly designing the filter parameters at each sampling instant. The desired filter parameters are obtained by solving two Riccati-like difference equations that are of a recursive form suitable for online applications. A simulation example is exploited to demonstrate the effectiveness of the proposed filter design scheme.

Fusion Predictors for Multisensor Stochastic Uncertain Systems With Missing Measurements and Unknown Measurement Disturbances

“…Since no prior information about the measurement disturbance θ c (t) is available, we will produce a recursive state predictor decoupling with the disturbance θ c (t) for systems (5) and (9) in the Kalman-like form [23]:…”

“…However, it is optimal in the linear unbiased minimum variance sense under the given form (11) of Kalman-like recursive predictor. Due to its simple recursive form, similar estimators have been also designed in many systems such as [4], [5], [13], [14], and [17]. The globally optimal filter in linear unbiased minimum variance sense has been reported in [18].…”

“…Remark 2: From Theorem 1, it is readily known that the centralized fusion predictorx c (t + 1) in (11) and covariance matrix P c (t +1) in (18) for systems (5) and (9) with stochastic parameters are affected by the state second-order moment X (t) in (8), which is different from the standard Kalman predictor with deterministic parameters [23]. This is a common fact for systems with multiplicative noise [1], [8]- [10].…”

“…Caballero-Águila et al [3] design the centralized and distributed fusion filters and smoothers for multi-sensor linear discrete-time stochastic systems with missing measurements which are described by Bernoulli distributed variables assumed to be correlated at instants that differ m units of time. Wei et al [4] and Hu et al [5] study the gain-scheduled filter and optimal H ∞ filter for a class of nonlinear systems with missing measurements. Zhang et al [6] design an estimator based on the packet dropout compensation.…”