Using two separate algorithms, called Kalman's recursive and Vaughan's nonrecursive, exact closed-form solutions of the steady-state two-state exponentially correlated velocity (ECV) and three-state exponentially correlated acceleration (ECA) target-tracking filters are derived for discrete position measurements. For this particular application, the superiority of Vaughan's nonrecursive over Kalman's recursive algorithm is observed.

Closed-Form Solutions of Target-Tracking Filters with Discrete Measurements

This paper considers a new application of fixed-lag smoothing algorithms for identification. It could be used online in conjunction with the extended recursive least-squares identification algorithm. This offers a scheme for identifying time-varying process models with unknown dead time from sampled input-output records. Application to short records with time-varying dynamics, where recursive algorithms without smoothing may not give a clear indication of the time variation, is of particular interest. Optimal Kalman-filter and fixed-lag smoothing algorithms are reviewed, and their computational requirements and stability in an identification context are examined. The most attractive measures of model structure obtained from identification algorithms are tested on artificial and real records. It is concluded that the innovation and adjoint variables are feasible and effective indicators for identifying model structure goodness.

Fixed-lag smoothing in the identification of time-varying systems with unknown dead time

This paper is based on an alternative approach to system theory and deals with optimal filters for continuous linear dynamic systems with measurements disturbed by a ”colored” noise or a ”white” noise vector with a singular covariance matrix. It is shown that the optimal filter proposed in this paper is a slight modification of the Kalman-Bucy filter which can generally contain integrators as well as (backward) differentiators. The classical formulation was, however, reformulated in order to obtain a tractable mathematical interpretation of stochastic differential equations describing given processes and random errors.

http://www.wseas.us/e-library/conferences/venice2004/papers/472-337.pdf

Singular Kalman filtering: New aspects based on an alternative system theory

Thompson Sampling (TS) is a popular method for decision-making under uncertainty, where an action is sampled from a carefully constructed distribution based on the data collected. In this work, we study the problem of adaptive control in partially observable linear quadratic Gaussian, i.e., LQG, control systems using TS, when the model dynamics are unknown. Prior works have established an $\tilde O(\sqrt T )$ regret upper bound for the adaptive control of such systems, after T time steps. However, the algorithms that achieve this result employ computationally intractable policies. We propose an efficient TS-based adaptive control algorithm, Thompson Sampling under Partial Observability TSPO, to effectively balance the exploration vs. exploitation trade-off and minimize the overall control cost in epochs. TSPO utilizes closed-loop system identification to estimate the underlying model parameters up to their confidence intervals. It then deploys the optimal policy of a sampled system, which is selected at random from the distribution constructed with the model estimates and their confidence intervals. We show √that using only logarithmic policy updates, TSPO attains $\tilde O(\sqrt T )$ regret against the optimal control policy that knows the system dynamics. To the best of our knowledge, TSPO is the first computationally efficient algorithm that achieves $\tilde O(\sqrt T )$ regret in adaptive control of unknown partially observable LQG control systems with convex cost. Further, we empirically study the performance of TSPO in an adaptive measurement-feedback control problem.

Thompson Sampling for Partially Observable Linear-Quadratic Control

Bounds on the Miss of Radar-Guided Missiles with Discrete Guidance

An exact solution is presented of the matrix Riccati difference equation associated with a time-invariant discrete Kalman filter. The time-varying solution is expressed by means of the corresponding steady-state algebraic solution. An exact solution of the closed-loop transition matrix is also presented.

http://ieeexplore.ieee.org/iel5/9/24188/01102836.pdf

S. Orfanidis

Papers

An exact solution of the time-invariant discrete Kalman filter