Correlated System and Measurement Noise Processes

Abstract

In the previous two chapters, Kalman filtering for the model involving uncorrelated system and measurement noise processes was studied. That is, we have assumed all along that

$$ E(\underline{\xi}_k \underline{\eta}_{\ell}^{\mathsf{T}}) = 0 $$

for ${ k, \ell = 0,1, \ldots }$. However, in applications such as aircraft inertial navigation systems, where vibration of the aircraft induces a common source of noise for both the dynamic driving system and onboard radar measurement, the system and measurement noise sequences ${ \{\underline{\xi}_k\} }$ and ${ \{\underline{\eta}_k\} }$ are correlated in the statistical sense, with

$$ E(\underline{\xi}_k \underline{\eta}_{\ell}^{\mathsf{T}}) = S_k \delta_{k\ell} \:, $$

${k, \ell = 0,1, \ldots }$, where each S _k is a known non-negative definite matrix. This chapter is devoted to the study of Kalman filtering for the above model.