Kalman filter under nonlinear system transformations

This article deals with state estimation and filtering in nonlinear systems. More precisely the design of approximate nonlinear Kalman filter for nonlinear systems linearizable by a nonlinear coordinate transformation with possible application of nonlinear output injection is studied. The main idea is to reduce the errors introduced by the linearization used by the approximate filter using exact full or partial linearization of the system. Underlying transformations of both deterministic and stochastic signals are studied. An example of designing such an approximate nonlinear filter for nonlinear tracking of walking like motion of bipedal robot is given.