State estimation via limited capacity noisy communication channels

The paper addresses a state estimation problem involving communication errors and capacity constraints. Discrete-time partially observed linear systems perturbed by stochastic unbounded additive disturbances are studied. Unlike the classic theory, the sensor signals are communicated to the estimator over a limited capacity noisy digital link modeled as a stochastic discrete memoryless channel. It is shown that the capability of the noisy channel to ensure state estimation with a bounded in probability error is identical to its capability to transmit information with as small probability of error as desired. In other words, the classic Shannon capacity of the channel constitutes the boundary of the observability domain. It is shown that whenever the Shannon capacity bound is met, a reliable observation can be ensured by means of a state estimator consuming a bounded (as time progresses) computational complexity and memory per unit time. The corresponding state estimator is constructed explicitly and is based on the classic block coding approach, so that traditional block encoding–decoding procedures can be employed for its implementation. This work was supported by the Australian Research Council and the Russian Foundation for Basic Research grant 06-08-01386.     

Design and analysis of discrete-time robust Kalman filters

In this paper, the problem of finite and infinite horizon robust Kalman filtering for uncertain discrete-time systems is studied. The system under consideration is subject to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of linear filters having an error variance with an optimized guaranteed upper bound for any allowed uncertainty. A novel technique is developed for robust filter design. This technique gives necessary and sufficient conditions to the design of robust quadratic filters over finite and infinite horizon in terms of a pair of parameterized Riccati equations. Feasibility and convergence properties of the robust quadratic filters are also analyzed.     

The problem of LQG optimal control via a limited capacity communication channel

The paper addresses a LQG optimal control problem involving bit-rate communication capacity constraints. A discrete-time partially observed system perturbed by white noises is studied. Unlike the classic LQG control theory, the control signal must be first encoded, then transmitted to the actuators over a digital communication channel with a given bandwidth, and finally decoded. Both the control law and the algorithms of encoding and decoding should be designed to archive the best performance. The optimal control strategy is obtained. It is shown that where the estimator-coder separation principle holds, the controller-coder one fails to be true.     

Precision missile guidance using radar/multiple-video sensor fusion via communication channels with bit-rate constraints

We consider a precision missile guidance problem in which the objective is twofold: to come as close as possible to hitting the target, and also to do so from a particular direction. The effectiveness of a guidance law is strongly dependent on the quality of information available to it. In this work we construct a precision guidance law that combines information from an on-board video camera with data transmitted from ground-based radars and video cameras mounted on unmanned aerial vehicles. The communication channels are bit-rate limited, and recent results in control and estimation over finite-data-rate channels are used to construct a nonlinear state estimator. Simulations show the performance improvements which are possible compared to the use of the on-board sensor alone.     

Robust state estimation for a class of uncertain time-delay systems

This paper considers a robust state estimation problem for a class of uncertain time-delay systems. In this problem, the noise and uncertainty are modelled deterministically via an integral quadratic constraint. The robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint. This set is found to be an ellipsoid which is constructed via a linear state estimator.     

Robust stabilization of linear uncertain discrete-time systems via a limited capacity communication channel

The paper considers the problem of robust stabilization of linear uncertain discrete-time systems via limited capacity communication channels. We consider the case when the control input is to be transmitted via communication channel with a bit-rate constraint. A constructive method to design a robustly stabilizing controller is proposed.     

The problem of optimal robust sensor scheduling

This paper considers the sensor scheduling problem which consists of estimating the state of an uncertain process based on measurements obtained by switching a given set of noisy sensors. The noise and uncertainty models considered in this paper are assumed to be unknown deterministic functions which satisfy an energy type constraint known as an integral quadratic constraint. The problem of optimal robust sensor scheduling is formulated and solution to this problem is given in terms of the existence of suitable solutions to a Riccati differential equation of the game type and a dynamic programming equation. Furthermore, a real time implementable method for sensor scheduling is also presented.     

Sensor data scheduling for optimal state estimation with communication energy constraint

In this paper, we consider sensor data scheduling with communication energy constraint. A sensor has to decide whether to send its data to a remote estimator or not due to the limited available communication energy. We construct effective sensor data scheduling schemes that minimize the estimation error and satisfy the energy constraint. Two scenarios are studied: the sensor has sufficient computation capability and the sensor has limited computation capability. For the first scenario, we are able to construct the optimal scheduling scheme. For the second scenario, we are able to provide lower and upper bounds of the minimum error and construct a scheduling scheme whose estimation error falls within the bounds.     

Probabilistic performance of state estimation across a lossy network

We consider a discrete time state estimation problem over a packet-based network. In each discrete time step, a measurement packet is sent across a lossy network to an estimator unit consisting of a modified Kalman filter. Using the designed estimator algorithm, the importance of placing a measurement buffer at the sensor that allows transmission of the current and several previous measurements is shown. Previous pioneering work on Kalman filtering with intermittent observation losses is concerned with the asymptotic behavior of the expected value of the error covariance, i.e. as k→∞. We consider a different performance metric, namely a probabilistic statement of the error covariance , meaning that with high probability the error covariance is bounded above at any instant in time. Provided the estimator error covariance has an upper bound whenever a measurement packet arrives, we show that for any finite M this statement will hold so long as the probability of receiving a measurement packet is nonzero. We also give an explicit relationship between M and and provide examples to illustrate the theory.     

Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with Petersen—Hollot bounds

A state-estimation design problem involving parametric plant uncertainties is considered. An error bound suggested by recent work of Petersen and Hollot is utilized for guaranteeing robust estimation. Necessary conditions which generalize the optimal projection equations for reduced-order state estimation are used to characterize the estimator which minimizes the error bound. The design equations thus effectively serve as sufficient conditions for synthesizing robust estimators. An additional feature is the presence of a static estimation gain in conjunction with the dynamic (Kalman) estimator, i. e., a nonstrictly proper estimator.