# SS12 - Advanced Sigma-Point Filters: Analysis, Sigma-Point Set Design, and Applications

The session is aimed at state estimation of nonlinear discrete-time stochastic dynamic systems. In particular, the recent advances in design of the nonlinear state estimation methods providing the estimates in the form of the conditional mean and state estimate error covariance matrix described by a set of sigma-points are of interest.

## Topics of interest

State estimation is a corner-stone of vast majority of navigation, positioning, and tracking systems. Besides these systems, the state estimation is crucial also in various areas and applications where knowledge of the state is required for a (multistep) prediction, control, fault detection, or generally for a decision making. The general solution to the state estimation problem, assuming a stochastic state-space model of a system and the Bayesian approach, is given by the Bayesian recursive relations (BRRs). The BRRs are used for computation of probability density functions (PDFs) of the state conditioned by all available measurements. The conditional PDFs provide a full description of the immeasurable state. The closed form solution to the BRRs is available only for a few special cases, among which a linear Gaussian system is the most significant. The solution results, in terms of the estimation algorithm, in the Kalman filter (KF). In other cases, i.e., for nonlinear or non-Gaussian systems, it is necessary to apply some approximate methods. Many approximate estimation methods have been proposed in the past five decades. Among them, the local methods have attracted considerable attention and currently, they are the widely used in practical estimators. The local methods adopt the KF design technique also for nonlinear systems with the conditional moments of the state estimate being recursively computed instead of its conditional PDF. In particular, the conditional mean and covariance matrix are of interest. The classical local filter is the extended Kalman filter (EKF). The EKF was developed in the seventies and is based on the linearization of the nonlinear functions in the state-space model by the first order Taylor expansion. Later on, the second order Taylor expansion and also other expansions have been used instead. In the late nineties, conceptually different approximations have been proposed. Contrary to the Taylor expansion based linearization, they are predominantly based on the approximation of the state estimate description by a set of deterministically chosen weighted points (so called sigma-points), preserving the nonlinear functions in the state-space model. Such approximations are usually denoted as the unscented transformation (UT) and a number of versions working with different number of points have been proposed so far (e.g., higher-order, scaled, reduced, smart transformations). The resulting filters are then denoted as the unscented Kalman filters. Recently, novel approximations based on various integration rules have been introduced in the local filter framework and attract quite significant attention of researchers. The rules might be either deterministic (e.g., quadrature or cubature) or stochastic, and in fact, they can be viewed as a certain alternative to the UT. As both the unscented Kalman filter and the filters utilizing various integration rules provide estimates in the form of a sigma-point set, the term sigma-point filters have been coined for them.

The proposed session aims to cover the recent advances in the area of the sigma-point filtering with the special emphasis on the following up-to-date topics; design of novel approaches to sigma-point set nonlinear filters, analysis and comparison of sigma-point-based approximations, performance evaluation of sigma-point set filters, and applications of the sigma-point filters.

The proposed special session will bring together leading and active researchers and practitioners in the field of the local estimation methods to present their recent accomplishments, exchange latest experience, and explore future directions in this field. We believe that the subject of this special session is timely, important, and of wide interest to the information fusion community, particularly the participants of FUSION 2014.

## Keywords

State estimation, nonlinear filtering, Bayesian filters, sigma-point filters, numerical integration rules, stochastic systems

## Special Session Organizers

- Jindrich Dunik, University of West Bohemia (Czech Republic)
- Ondrej Straka, University of West Bohemia (Czech Republic)

## Special Session Contact

- Jindrich Dunik ()
- Ondrej Straka ()