Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs
New Orleans, LA
IEEE Conference on Decision and Control
ISSN or ISBN
In this paper we derive a set of approximate but general bilinear Kalman filter equations for a multi- input multi-output bilinear stochastic system driven by general autocorrelated inputs. The derivation is based on a convergent Picard sequence of linear stochastic state-space subsystems. We also derive necessary and sufficient conditions for a steady-state solution to exist. Provided all the eigenvalues of a chain of structured matrices are inside the unit circle, the approximate bilinear Kalman filter equations converge to a stationary value. When the input is a zero-mean white noise process, the approximate bilinear Kalman filter equations coincide with those of the well known bilinear Kalman filter model operating under white noise inputs.
Ramos, Jose A. and Lopes dos Santos, Paulo, "Derivation of a Bilinear Kalman Filter with Autocorrelated Inputs" (2007). CEC Faculty Articles. 397.