Design of a navigation filter by analysis of local observability

This paper presents an inertial navigation filter designed for an automotive vehicle not equipped with any GPS receiver. The task of this filter is to provide relative position information over a relatively long period of time (tens of minutes). The filter consists of several partial state observers that, one after another, reconstruct key information for the whole state estimation. The observer relies on a sufficient condition to guarantee uniform complete observability of a general bounded linear time-varying system using (point-wise) differential rank conditions. From this condition, we construct a collection of filters well-suited for each possible trajectory of the vehicle. This results in temporally interconnected observers which are of the Kalman filter type. It is proven that each of them asymptotically converges to zero. We illustrate this design with trajectory estimation obtained on simulation data. Finally, experimental results using low-cost sensors show the potential and the relevance of the approach.