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T2 Relatives for the Kalman filter for tracking and fusion

Length: 3 hours

Intended Audience and Prerequisites: The tutorial is intendend for listeners interested in non-linear state estimation problems and fundamental aspects of solving them (by other means than sequential Monte-Carlo methods). Prerequisite is a knowledge of probability theory on graduate level plus (linear and non-linear) algebra.

Description: The Kalman filter is well-known as the workhorse of recursive state estimation. For linear state estimation problems under noisy measurements, the Kalman filter provides consistent estimates being optimal in various senses. In many tracking applications however, the equations describing the state propagation and/or that for the measurement process are non-linear. As long as those non-linearities remain mild in a certain sense, relatives of the Kalman filter suffice to provide suitable estimates with at least approximate consistency.
The proposed tutorial focusses on a variety of those relatives. It starts by recalling the basic relationships and properties of the Kalman filter. As a motivation for the later topics, its different optimality properties are shortly discussed as are various ways to write in particular its update equation (e. g., the Joseph form and the information form). The latter then leads over to the aspect of data fusion with convex combination (CC) and covariance intersection (CI) as two prominent approaches. The interacting multiple model (IMM) is presented as a method to deal with jump-Markovian linear systems.
Starting from those results for linear systems, the generalization to non-linear systems is discussed. The best linear unbiased estimator (BLUE) filter is introduced and general-purpose approximations like the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the Gauss filter (GF) are put in its context, detailed for polar measurements. For that same example, converted measurement (CM) filters are examined. While being straight-forward to implement, they come with the inherent problem of generating estimation bias. This problem and proposed solutions are investigated.
An alternative to converting the measurements to state-(sub-)space is given by a conversion of the states to measurement space. For the example of angular-only measurements, log-spherical coordinates (LSCs) are presented as such a suitable statespace representation that is, in particular, capable to deal with the fact that part of the state-space is not observable by the measurements. Filter initialization, propagation, and update are handled. The discussion on how to use those coordinates for fusing state estimates from different types of sensors in sense-and-avoid-applications wraps up the proposed tutorial.

Presenter: Dietrich Fränken

Dietrich Fränken is systems engineer and expert for ground target tracking at Airbus DS Electronics and Border Security GmbH, where he is responsible for tracking and data fusion in various national and international projects. Additionally, he is a lecturer (Privatdozent) at Ulm University. He presents on a regular basis at conferences, universities, and in front of customers. He is member of the technical program comittee for symposia and serves as a reviewer for scientific journals. Research interests include modeling, simulation, and estimation of physical systems, nonlinear filtering, graph and system theory, and digital signal processing. Dr. Fr¨anken holds a Dipl.-Ing. degree from Bochum University and a Dr.-Ing. degree as well as a Habilitation degree from Paderborn University, all of them in electrical engineering.


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