A Robust Continuous Time Fixed Lag Smoother for Nonlinear Uncertain Systems

This paper presents a robust fixed lag smoother for a class of nonlinear uncertain systems. A unified scheme, which combines a nonlinear robust estimator with a stable fixed lag smoother, is presented to improve the error covariance of the estimation. The robust fixed lag smoother is based on the use of Integral Quadratic Constraints and minimax LQG control. The state estimator uses a copy of the system nonlinearity in the estimator and combines an approximate model of the delayed states to produce a smoothed signal. In order to see the effectiveness of the method, it is applied to a quantum optical phase estimation problem. Results show significant improvement in the error covariance of the estimator using fixed lag smoother in the presence of nonlinear uncertainty.Comment: 8 pages, will be presented in 52nd Conference on Decision and Contro

A Probabilistic Perspective on Gaussian Filtering and Smoothing

We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances of joint probabilities. This implies that novel filters and smoothers can be derived straightforwardly by providing methods for computing these moments. Based on this insight, we derive the cubature Kalman smoother and propose a novel robust filtering and smoothing algorithm based on Gibbs sampling

Robust RLS Wiener Fixed-Interval Smoother in Linear Discrete-Time Stochastic Systems with Uncertain Parameters

This paper proposes the robust RLS Wiener filter and fixed-interval smoothing algorithms based on the innovation approach. As a result, the robust RLS Wiener filtering algorithm is same as the existing robust RLS Wiener filtering algorithm. The estimation accuracy of the fixed-interval smoother is compared with the robust RLS Wiener filter and the following fixed-interval smoothers. In the proposed robust RLS Wiener fixed-interval smoother, the case, where the observed value is replaced with the robust filtering estimate of the signal, is also simulated. (1) The RLS Wiener fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate. (2) The RTS (Rauch-Tung-Striebel) fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate. (3) The  RLS Wiener fixed-interval smoother and the  RLS Wiener filter. (4) The RLS Wiener fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate and the observed value is replaced with the robust RLS Wiener filtering estimate of the signal. From the simulation results, the most feasible estimation technique for the fixed-interval smoothing estimate is the RLS Wiener fixed-interval smoother. Here, the robust filtering estimate is used and the observed value is replaced with the robust filtering estimate

Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances

Unified Forms for Kalman and Finite Impulse Response Filtering and Smoothing

The Kalman filter and smoother are optimal state estimators under certain conditions. The Kalman filter is typically presented in a predictor/corrector format, but the Kalman smoother has never been derived in that format. We derive the Kalman smoother in a predictor/corrector format, thus providing a unified form for the Kalman filter and smoother. We also discuss unbiased finite impulse response (UFIR) filters and smoothers, which can provide a suboptimal but robust alternative to Kalman estimators. We derive two unified forms for UFIR filters and smoothers, and we derive lower and upper bounds for their estimation error covariances

Robust Filtering and Smoothing with Gaussian Processes

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of "system identification" is more robust than finding point estimates of a parametric function representation. In this article, we present a principled algorithm for robust analytic smoothing in GP dynamic systems, which are increasingly used in robotics and control. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail.Comment: 7 pages, 1 figure, draft version of paper accepted at IEEE Transactions on Automatic Contro

Robust Smoothing for Estimating Optical Phase Varying as a Continuous Resonant Process

Continuous phase estimation is known to be superior in accuracy as compared to static estimation. The estimation process is, however, desired to be made robust to uncertainties in the underlying parameters. Here, homodyne phase estimation of coherent and squeezed states of light, evolving continuously under the influence of a second-order resonant noise process, are made robust to parameter uncertainties using a robust fixed-interval smoother, designed for uncertain systems satisfying a certain integral quadratic constraint. We observe that such a robust smoother provides improved worst-case performance over the optimal smoother and also performs better than a robust filter for the uncertain system.Comment: 6 pages, 7 figures, Proceedings of the 2014 European Control Conference, pp. 896-90