  Most Kalman filter extensions assume Gaussian noise and when the noise is
non-Gaussian, usually other types of filters are used. These filters, such as
particle filter variants, are computationally more demanding than Kalman type
filters. In this paper, we present an algorithm for building models and using
them with a Kalman type filter when there is empirically measured data of the
measurement errors. The paper evaluates the proposed algorithm in three
examples. The first example uses simulated Student-t distributed measurement
errors and the proposed algorithm is compared with algorithms designed
specifically for Student-t distribution. Last two examples use real measured
errors, one with real data from an Ultra Wideband (UWB) ranging system, and the
other using low-Earth orbiting satellite magnetometer measurements. The results
show that the proposed algorithm is more accurate than algorithms that use
Gaussian assumptions and has similar accuracy to algorithms that are
specifically designed for a certain probability distribution.
