Publication

A Stable Switching Kalman Smoother

2004
Reports

Abstract

We present a new method for approximate inference in Switching linear Gaussian State Space Models (also known as Switching Kalman Filters. The method is similar in spirit to the Rauch-Tung-Striebel smoother in the Kalman Filter case. Only a single Forward and Backward pass is required, both of which are numerically stable. The algorithm projects at each time, for both the Forward and Backward passes, the approximate Belief states onto either a single or a mixture of Gaussians. Unlike in Expectation Propagation, we find few difficulties with numerical stability.

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2004
Reports

Abstract

Official source

Related concepts (16)

Kalman filter

For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory.

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.