System state estimation in the presence of noise is critical for
control systems, signal processing, and many other applications in
a variety of fields. Developed decades ago, the Kalman filter
remains an important, powerful tool for estimating the variables in
a system in the presence of noise. However, when inundated with
theory and vast notations, learning just how the Kalman filter
works can be a daunting task.
With its mathematically rigorous, "no frills" approach to the
basic discrete-time Kalman filter, A Kalman Filter Primer builds a
thorough understanding of the inner workings and basic concepts of
Kalman filter recursions from first principles. Instead of the
typical Bayesian perspective, the author develops the topic via
least-squares and classical matrix methods using the Cholesky
decomposition to distill the essence of the Kalman filter and
reveal the motivations behind the choice of the initializing state
vector. He supplies pseudo-code algorithms for the various
recursions, enabling code development to implement the filter in
practice. The book thoroughly studies the development of modern
smoothing algorithms and methods for determining initial states,
along with a comprehensive development of the "diffuse" Kalman
filter.
Using a tiered presentation that builds on simple discussions to
more complex and thorough treatments, A Kalman Filter Primer is the
perfect introduction to quickly and effectively using the Kalman
filter in practice.
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