Optimal position and velocity navigation filters with discrete-time delayed measurements

This paper presents the design and performance evaluation of a continuous-time Kalman filter with discrete-time delayed measurements for a class of time-varying kinematic systems with application to the estimation of linear motion quantities, in three dimensions, of mobile platforms. The design is based on the Kalman filter solution for an equivalent linear time invariant realization and allows for the natural use of frequency weights to explicitly achieve adequate disturbance rejection and measurement noise attenuation on the state estimates. Moreover, the proposed solution is optimal with respect to all signals assuming exact angular measurements. Two applications in the field of ocean robotics are presented and simulation results are included that illustrate the achievable performance in the presence of both extreme environmental disturbances and realistic measurements, with noise and delays.