New algorithms for estimation with sequentially correlated measurement noise †

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Abstract
This paper derives new estimation algorithms for use with systems with sequentially correlated observation noise. Both single and two-stage correlation are considered. The algorithms appear much like the well known white noise algorithms and are not much more complex. Error analysis algorithms for the analysis of modelling errors made in using those and white noise estimation algorithms are also presented. Those algorithms permit analysis of the effect of making the white noise assumption when the observation noise is really coloured. Examples and associated illustrations are presented to show this effect The newly derived algorithms are compared with existing, more restrictive algorithms, and Bhown to provide equivalent results for problems where both apply.

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