Observer design for a class of kinematic systems

An observer design methodology is introduced for a class of kinematic systems that often arise in the development of Navigation Systems for vehicular applications. At the core of the proposed methodology there is a time varying orthogonal coordinate transformation that renders the observer error dynamics linear time invariant (LTI). The problem is then formulated as a virtual control problem which is solved by resorting to the standard H_infin output feedback control synthesis technique, thus minimizing the L₂ induced norm from a generalized disturbance input to a performance variable. The resulting observer error dynamics are globally exponentially stable (GES) and several input-to-state stability (ISS) properties are derived. A relevant example is provided that demonstrates the potential and usefulness of the proposed design methodology and simulation results are offered to illustrate the filter achievable performance in the presence of extreme environmental disturbances and realistic sensors´ noise.