Filtering Problem For Systems Research Articles

Two-stage particle filtering for non-Gaussian state estimation with fading measurements

In this paper, the filtering problem for systems with fading measurements is considered. Taking advantage of the cascaded structure of the system, the original filtering problem is decomposed into two subproblems: 1) recovery of the original measurements from the faded ones, and 2) state estimation based on the recovered signals. A two-stage particle filtering (PF) algorithm is proposed to achieve simultaneous measurement recovery and state estimation. In our scheme, the second-stage resampling procedure can be implemented concurrently, resulting in a significant reduction of execution time. Two examples are provided to demonstrate the effectiveness of our algorithm. A benchmark problem for nonlinear filtering is tackled in the first example and, in the second example, the proposed algorithm is applied to the object tracking problem where the measured signal is distorted by the communication channel. Simulation results show that, compared with the brute force PF, the two-stage PF can strike better balance between tracking accuracy and execution time.

On Pareto set in control and filtering problems under stochastic and deterministic disturbances

We consider two-criteria control or filtering problems for linear systems, where one criterion is the level of suppression for Gaussian white noise with unknown covariance, and another is the level of suppression for a deterministic signal of bounded power. We define a new criterion, the level of suppression for stochastic and deterministic disturbances that act jointly in the general case on different inputs. This criterion is characterized in terms of solutions of Riccati equations or linear matrix inequalities. We establish that for the choice of optimal controller or filter with respect to this criterion relative losses with respect to each of the original criteria compared to Pareto optimal solutions do not exceed the value $$1 - {{\sqrt 2 } \mathord{\left/ {\vphantom {{\sqrt 2 } 2}} \right. \kern-\nulldelimiterspace} 2}$$1ź2/2 . We extend these results to dual control and filtering problems for systems with one input and two outputs, generalize them to the case of N criteria with loss estimate $$1 - {{\sqrt N } \mathord{\left/ {\vphantom {{\sqrt N } N}} \right. \kern-\nulldelimiterspace} N}$$1źN/N, and also apply them for systems with external and initial disturbances. We show a numerical example.

A measurement policy in stochastic linear filtering problems

With reference to a (discrete time) linear system filtering problem, we consider the problem of online deciding at which instant we actually measure and process the output values. We propose a convenient measurement policy, able to sensibly reduce the measurement cost, while keeping the estimate accuracy at satisfactory levels. By some probabilistic arguments we analyse the upper bounds for the measurement and non-measurement time intervals.

Robust filtering: A model matching approach

This paper investigates the robust H filtering problem for linear systems with uncertainties which are described by integral functional constraints. The objective is to design a dynamic filter such that the L2-gain from an exogenous input to an estimate error is minimized or guaranteed to be less than or equal to a prescribed value for all admissable uncertainties. We establish the interconnection between the robust linear H filtering problem and the linear H filtering problem for systems without uncertainties. Using the existing model-matching approach to linear H filtering for known systems results, we obtain a characterization for the family of robust linear H in the form of a state space representation.

Solution in the z-domain to the discrete-time stationary Kalman filtering problem for systems with perfect measurements

The discrete-time stationary Kalman filtering problem is solved in the z -domain for general right invertible linear systems whose measurements are all noise free. A simple expression in closed form is obtained for the transfer function of the optimal filter both for the uniform and the general nonuniform rank cases. It provides an optimal solution also for systems with uniform and nonuniform time delays. The minimum variance error of the estimate is analyzed and the independent contributions to this error of the system zeros outside the unit circle, finite and infinite, and the excess of the number of inputs over the number of measurements are investigated.

Generalized eigenproblem algorithms and software for algebraic Riccati equations

Numerical issues related to the computational solution of the algebraic matrix Riccati equation are discussed. The approach presented uses the generalized eigenproblem formulation for the solution of general forms of algebraic Riccati equations arising in both continuous- and discrete-time applications. These general forms result from control and filtering problems for systems in generalized (or implicit or descriptor) state space form. A Newtontype iterative refinement procedure for the generalized Riccati solution is given. The issue of numerical condition of the Riccati problem is addressed. Balancing to improve numerical condition is discussed. An overview of a software package, RICPACK, coded in portable, reliable Fortran is given. Results of numerical experiments are reported.

Martingale Projection and Linear Filtering in Hilbert Spaces. I: The Theory

Using a theorem on the projection of Hilbertian martingales and a Hilbertian theorem of the Girsanov type, previously established by the author, to study the filtering problem for systems governed by linear evolution equations in Hilbert spaces, we show that if the observation is a function of the state through an unbounded operator and with values in a Hilbert space (under some hypotheses on the observation noise), the filtered state is obtained as the solution of a differential stochastic equation, the coefficients of which are given by a solution of an operator differential Ricatti equation. We show that the linear filtering problem can be solved only if the solution of this equation is unique.If the observation is made through a bounded operator, we find again, with the innovation method, results from A. Bensoussan (1971) in the partial differential equation context, and from R. F. Curtain (1975) and S. K. Mitter–R. Vinter (1974) in the linear hereditary equation context; the application to the linear...

Analysis of stochastic systems with applications to sensitivityt

The paper considers the optimal filtering problem for systems having one or more stochastic parameters as well as an additive stochastic input. A solution is derived by casting the problem into the general form of non-linear stochastic systems with diffusive Markov solutions. The optimal filter is derived assuming linear measurements and additive noise. Simplification of the optimal filter equations is obtained by approximating the second-order error moment of the optimal estimate and defining a sub-optimal filter. Finally a sensitivity of the sub-optimal filter is defined and its formulation is derived. Simulations of systems with stochastic parameters demonstrate the application of both the sub-optimal filter and its sensitivity