Reduced order unknown input Kalman filter: application for vehicle lateral control

A new optimal filtering formula is derived for stochastic linear systems with structured unknown inputs. The main idea consists in finding a robust sub-system of unknown inputs in which the dynamical and output noises are uncorrelated. Thereby the problem is reduced to the sub-state estimation of an unknown inputs-free reduced system, which can be easily dealt with following the well-known Kalman filter theory. After a change of basis, we can then rebuild the state of the original system. The method developed is applied to the lateral control of a vehicle.