A new methodology is proposed for the design of navigation systems for autonomous marine vehicles. Using simple kinematic relationships, the problem of estimating the velocity and position of an autonomous vehicle based on motion sensor data available at different rates is solved byresorting to complementary multirate time-varying filters. The set-up adopted for filter design and analysis builds on Linear Matrix Inequalities(LMIs) and on efficient numerical analysis tools that borrow from convex optimization techniques. The paper describes the key steps involved in the design of a multirate navigation system for a prototype autonomous marine vehicle. Results of tests at sea illustrate the performance of the system developed.