Eduardo Rohr

Kalman Filtering With Intermittent Observations: On the Boundedness of the Expected Error Covariance

This paper addresses the stability of a Kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator. We give a necessary condition and a sufficient condition, with a trivial gap between them, for the boundedness of the expected value of the estimation error covariance. These conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order Markov process. Hence, we extend the class of systems for which these conditions are known in two directions, namely, by including degenerate systems, and by considering network models more general than i.i.d. and Gilbert-Elliott. We show that these conditions recover known results from the literature when evaluated for non-degenerate systems under the assumption of i.i.d. or Gilbert-Elliott packet loss models.

Statistical properties of the error covariance in a Kalman filter with random measurement losses

In this paper we study statistical properties of the error covariance matrix of a Kalman filter, when it is subject to random measurement losses. We introduce a sequence of tighter upper bounds for the asymptotic expected error covariance (EEC). This sequence starts with a given upper bound in the literature and converges to the actual asymptotic EEC. Although we have not yet shown the monotonic convergence of this whole sequence, monotonic convergent subsequences are identified. The feature of these subsequences is that a tighter upper bound is guaranteed if more computation is allowed. An iterative algorithm is provided for computing each of these upper bounds. A byproduct of this paper is a more compact proof for a known necessary condition on the measurement arrival probability for the asymptotic EEC to be finite. A similar analysis leads to a necessary condition on the measurement arrival probability for the error covariance to have a finite asymptotic variance.

Kalman filtering with intermittent observations: Bounds on the error covariance distribution

When measurements are subject to random losses, the covariance of the estimation error of a state estimator becomes a random variable. In this paper we present bounds on the cumulative distribution function of the covariance of the estimation error for a discrete time linear system. We also show that the bounds can be arbitrarily tight if sufficient computational power is available. Numerical simulations show that the proposed method provides tighter bounds than the ones available in the literature.

Kalman filtering for a class of degenerate systems with intermittent observations

This paper addresses the performance of a Kalman filter when measurements are intermittently available, i.e., network transmission problems. More specifically, we present a method to determine whether the expected value of the estimation error covariance is bounded for a given stochastic network model. The method applies to very general network models and for a class of degenerate systems. It can be easily adapted to non-degenerate systems, recovering known results on the critical value. The main result follows from the convergence conditions on a series that describes the bounds on the expected error covariance.

Robustness analysis of nonlinear systems subject to state feedback linearization

This paper presents a methodology to the robust stability analysis of a class of single-input/single-output nonlinear systems subject to state feedback linearization. The proposed approach allows the analysis of systems whose nonlinearities can be represented in the rational (and polynomial) form. Through a suitable system representation, the stability conditions are described in terms of linear matrix inequalities, which is known to have a convex (numerical) solution. The method is illustrated via a numerical example.

A unified framework for mean square stability of Kalman filters with intermittent observations

This paper presents a unified framework for analysis of the stability of the expected error covariance (EEC) of Kalman filters subject to intermittent observations. A brief literature review summarizing some of the most important results in the area is provided. We state a method in the most general form, making no assumptions on the network model and only minor assumptions on the system. Then, as we adopt particular network models and assume some particular system structures, we recover most of the known results in the literature, which can be seen as a special case of our approach. Tight necessary and sufficient conditions for the EEC to be bounded are given for most cases, except for general degenerate systems, where only sufficient conditions are given in a closed form.

Stability of Kalman filters subject to intermittent observations

This paper addresses the stability of a Kalman filter when measurements are intermittently available due to the non-transparent communication channel between sensor and estimator. More specifically, we present a method to determine whether the expected value of the estimation error covariance is bounded for a given stochastic network model. The method applies to general discrete-time LTI systems and adopts the finite state Markov channel model.

Optimal PMU placement for power system state estimation with random communication packet losses

Phasor measurement units (PMUs) become important to state estimation for power systems by providing globally synchronized measurements of real-time phasors of voltage and currents with a high sampling rate. However the large quantities of measurement data produced by PMUs brings a serious burden to the communication system, which aggravates communication constraints such as the packet loss rate. In this paper, a novel optimization criterion for choosing PMU placements is proposed, considering random communication packet losses. Based on this criterion, a simplified optimal solution searching algorithm is given. Finally numerical simulations are given to test the validity of this algorithm. The dependence of the optimal PMU placement solution on the packet loss rate is indicated as well.

Local Stability Analysis of Feedback Linearizing Schemes for a Class of Uncertain Nonlinear Systems

Abstract This work presents a (numerical) technique to the local stability analysis of feedback linearizing control schemes for a class of uncertain nonlinear systems. A nonlinear decomposition of vector functions is applied to transform the Lyapunov stability conditions into a set of state-and parameter-dependent LMI (linear matrix inequality) constraints, which are numerically solved in a finite set of points. The proposed method can deal with a large class of nonlinear systems as well as very complex Lyapunov function candidates. In addition, a maximized level set of the Lyapunov function is proposed as an estimate of the system stability region.