Kalman example implementations

Now that the theory has been covered, how do we actually implement a Kalman filter from a simple basics start?

This article is written thanks to some very good explanations by Tim Babb, Bilgin Esme, Linsday Kleeman, Matthew Rhudy, Roger Salguero and Keaton Holappa. (NOTE: many of the images are copyright of Bilgin Esme).

Some implementations in Excel: KalmanExample.xls; Kalman.xlsm

Some implementations in Simulink: Kalman Filter Implementation In Simulink

Some useful files: Kalman_Excel_Simulink.zip

Example Details & Assumptions

The simplified example system has a constant value but noisy readings.

It is a 1-D signal so every entity becomes a numerical value rather than a matrix. A = 1, H = 1

There is no control signal.

Below is a description of the equation simplifications and a recap of the symbology naming convention:

In the example we use the following measured values (zk):

at k = 1 ms

zk = 0.390

x_hat_k- = 0

Pk- = 1

Kk = 1 / (1 + 0.1) = 0.909

x_hat_k = 0 + 0.909 * (0.390 - 0) = 0.355

Pk = (1 - 0.909) * 1 = 0.091

at k = 2 ms

zk = 0.500

x_hat_k- = 0.355

Pk- = 0.091

Kk = 0.091 / (0.091 + 0.1) = 0.476

x_hat_k = 0.355 + 0.476 * (0.500 - 0.355) = 0.424

Pk = (1 - 0.476) * 0.091 = 0.048

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