The recursive estimation problem is studied for a class of uncertain dynamical systems with different delay rates sensor network and autocorrelated process noises. The process noises are assumed to be autocorrelated across time and the autocorrelation property is described by the covariances between different time instants. The system model under consideration is subject to multiplicative noises or stochastic uncertainties. The sensor delay phenomenon occurs in a random way and each sensor in the sensor network has an individual delay rate which is characterized by a binary switching sequence obeying a conditional probability distribution. By using the orthogonal projection theorem and an innovation analysis approach, the desired recursive robust estimators including recursive robust filter, predictor, and smoother are obtained. Simulation results are provided to demonstrate the effectiveness of the proposed approaches.

The Kalman filter is very popular for estimating the system states of a class of linear systems which are characterized by state-space models. Since its inception in the early 1960s, it has played an important role in the research fields of target tracking, communication, control engineering, and signal processing. An implied assumption of traditional Kalman filter is that the system model and measurement model are exactly known. Unfortunately, this assumption does not always hold due to the constrained knowledge and the variation of the system and environment. When the system model and measurement model under consideration are not exactly known, the performance of traditional Kalman filter can deteriorate appreciably [

In traditional state estimation theory, the process noises are usually assumed to be Gaussian and uncorrelated with each other. However, this assumption is not always realistic, correlated noises are commonly encountered in practical applications. For example, in a target tracking system, the system state is usually consecutive (i.e., the system state at time

On another research frontier, with the development of network technologies, the sensor network has attracted increasing attention from many researchers in different fields due to their wide scope applications in surveillance, environment monitoring, information collection, wireless networks, robotics, and so on. In the sensor network, the network-induced time-delay or/and packet dropouts cannot be avoided due to limited single-sensor energy and communication capability and these have brought us new challenges in the design of the desired state estimators. The binary switching sequence is a popular way to describe the network-induced time-delay or/and packet dropouts since the time-delay or/and packet dropouts in the sensor network are inherently random [

Motivated by the above analysis, in this paper, we aim to investigate the recursive robust estimation problem for uncertain systems with different delay rates sensor network and autocorrelated noises. The system model and measurement model under consideration are both subject to stochastic uncertainties or multiplicative noises. Different sensors in the sensor network have different delay rates and different delay rates are described by different binary switching sequences. The process noises are assumed to be one-step autocorrelated across time and the autocorrelation property is described by the covariances between different time instants. Based on an innovation analysis approach (IAA) and the orthogonal projection theorem (OPT), recursive robust estimators including filter, predictor, and smoother are obtained. This paper extends the results in [

The remainder of the paper is organized as follows. In Section

Consider the following system model and measurement model:

The measurement model (

The noise signals

By defining

It can be seen from (

Observe that the system model and measurement model of system (

A seemingly natural way of handling the autocorrelated noises is the augmentation of the system states. However, such a state augmentation approach gives rise to significant increase in the system dimension, which would inevitably lead to computational burden. In addition, in the state augmentation method, the noises are treated as components of the auxiliary system state, generally, it is difficult for an estimator to track noise signals, and this will affect the estimation of other components of the auxiliary system state. Without resorting to state augmentation, in our current work, we treat system (

For convenience of later development, let us introduce the following lemmas, which are very useful in establishing our main results.

For stochastic matrices

Lemma

For system state

Lemma

The state covariance matrix

Lemma

Furthermore, defining

If

For the addressed system (

Please see Appendix

In the traditional recursive estimation problem, the innovation is calculated as

Next, we will derive the recursive robust predictor and recursive robust smoother based on Theorem

For the addressed system (

Please see Appendix

For the addressed system (

Please see Appendix

Consider the following uncertain system with different delay rates sensor network and autocorrelated process noises:

In the simulation, the initial value

From Figures

MSE1 filter, predictor, and smoother.

MSE2 filter, predictor, and smoother.

From Figures

MSE1 filter of this work and Zeng et al. [

MSE2 filter of this work and Zeng et al. [

In this paper, we have studied the recursive robust estimation problem for a class of uncertain systems with autocorrelated process noises and different delay rates sensor network. The system model and measurement model are both subject to stochastic uncertainties. The process noises are one-step autocorrelated across time. Each sensor in the sensor network has a different delay rate and the delay rate has been described by an individual binary switching sequence obeying a conditional probability distributed. Based on an IAA and the OPT, recursive robust estimators including filter, predictor, and smoother have been obtained. Simulation results have indicated that the smoother has the best performance and the predictor has the worst performance, and the filter obtained in this work has better performance than the filter of Zeng et al. [

Using the OPT, the one-step measurement prediction

Again, according to the OPT, the state prediction

Noting the fact that

It implies from (

Again, by using the OPT, the state estimation

Taking into account the fact that the process noise

According to the OPT, the

The author declares that there is no conflict of interests regarding the publication of this paper.

This work was supported by the National 973 Program of China (Grant no. 973-61334).