Discrete-Time State Estimation of Analog Double Integrators

The problem of minimum variance discrete-time state estimation of a continuous-time double integrator via noisy continuous-time measurements is considered. The error covariance matrices o this estimation are calculated and analyzed. The relations between these covariance matrices and the error covariance matrix of the optimal continuous-time filter are obtained, and a way for determining the required sampling period is proposed. A commonly used approximated model is investigated; it is shown to be inappropriate unless a specific improvement is introduced in the model.