Navigation system design using time-varying complementary filters

A new methodology for the design of navigation systems for autonomous vehic les is introduced. Using simple kinematic relationships, the problem of est imating the velocity and position of an autonomous vehicle is solved by res orting to special bilinear time-varying tilters, These are the natural gene ralization of linear time-invariant complementary filters that are commonly used to properly merge sensor information available at low frequency with that available in the complementary region. Complementary filters lend them selves to frequency domain interpretations that provide valuable insight in to the filtering design process, This work extends these properties to the time-varying setting by resorting to the theory of linear differential incl usions and by converting the problem of weighted filter performance analysi s into that of determining the feasibility of a related set of linear matri x inequalities (LMIs). Using this set-up, the stability of the resulting fi lters as well as their "frequency-like" performance can be assessed using e fficient numerical analysis tools that borrow from convex optimization tech niques. The mathematical background that is required for complementary time -varying filter analysis and design is introduced. Its application to the d esign of a navigation system that estimates position and velocity of an aut onomous vehicle by complementing position information available from SPS wi th the velocity information provided by a Doppler sonar system is described .