Continuous-Time Kalman Filtering with Implicit Discrete Measurement Times

lter is applicable to radio navigation problems in which a state-dependent range delay must be subtracted from a measured reception time in order to compute the relevant Kalman lter measurement update time. The new lter can be implemented by incorporating three elements. The rst element is a dense output numerical integration method that outputs a continuous description of the state over an interval. The second element is a nite dimensional approximation of the underlying continuous-time white process noise, for example, a nite order piecewise polynomial approximation. The third element is a new dynamic propagation/measurement update calculation that sensibly combines the implicit denition of the measurement update time with the dense output numerical integration scheme, the nite approximation of the process noise, and the statistical model of that approximation. After developing the necessary theory, the method is demonstrated in simulation for an example tracking problem.