UltimateKalman: Flexible Kalman Filtering and Smoothing Using Orthogonal Transformations

TL;DR

UltimateKalman introduces a flexible, numerically superior Kalman filter and smoother implementation in MATLAB, C, and Java, capable of handling complex, time-dependent, and variable-dimension problems with a simple modular interface.

Contribution

It provides a simplified, generalized version of a 1977 Kalman filter algorithm, implemented across multiple languages, enabling flexible and robust state estimation for complex problems.

Findings

Numerically superior and more flexible than previous Kalman filters

Handles time-dependent, variable-dimension, and incomplete observation problems

Provides a modular programming interface for diverse filtering and smoothing tasks

Abstract

UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification and slight generalization of an elegant Kalman filter and smoother that was proposed in 1977 by Paige and Saunders. Their algorithm appears to be numerically superior and more flexible than other Kalman filters and smoothers, but curiously has never been implemented or used before. UltimateKalman is flexible: it can easily handle time-dependent problems, problems with state vectors whose dimensions vary from step to step, problems with varying number of observations in different steps (or no observations at all in some steps), and problems in which the expectation of the initial state is unknown. The programming interface of UltimateKalman is broken into simple building blocks that can be used to construct filters, single or multi-step predictors, multi-step or whole-track smoothers, and combinations. The paper describes the algorithm and its implementation as well as with a test suite of examples and tests.