On Observer Error Linearization for Perspective Dynamic Systems

State estimation in perspective dynamic systems can be performed using different kinds of nonlinear observers. In this paper we investigate observer error linearization for perspective dynamic systems, where the goal is to find a coordinate transformation that results in a system for which a linear observer can be constructed. We present preliminary results in this direction, showing that such linearizing coordinate transformations indeed exist, subject to certain constraints on the angular and linear velocities. Specifically, it is shown that in many situations a linearizing coordinate transformation can be found only when additional states are added to the original system. This results in what is referred to as dynamic observer error linearization. Our investigations further provide additional insight into observability issues for perspective dynamic systems by showing how an observability condition can be interpreted in terms of the focus of expansion, and how the condition is related to the derivation of appropriate coordinate transformations.