5.2 Derivation of the Kalman Filter Correction (Update) Equations Revisited

In this section, we provide an alternate derivation of the Kalman filter correction equations (3.43), (3.44), and (3.47), based on the assumption that all conditional densities are Gaussian. Bayes' law provides a link between the posterior density and the joint density of xn with zn resulting in

(5.10) equation

Now defining the joint vector

(5.11) equation

(5.10) can be written as

(5.12) equation

The general form for a multivariate Gaussian distribution can be written as

(5.13) equation

Let all densities in (5.12) be Gaussian so that

(5.14) equation

(5.15) equation

(5.16) equation

Ignoring the factor of img, the exponent of the exponential in the analytical expression for the ...

Get Bayesian Estimation and Tracking: A Practical Guide now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.