Discrete

This article addresses the problem of estimating the position, velocity, and acceleration of a manoeuvring target from noisy position measurements. A discrete-time sliding mode observer is designed to handle unmeasured disturbance input and measurement noise. A first-order linear dynamics is considered for target acceleration. The acceleration input command and the pole of the first-order acceleration dynamics are considered to be unknown parameters with known upper bounds. A finite non-zero boundary layer is employed to reduce the chattering phenomenon typically associated with sliding mode observers. Analysis of estimation error dynamics is presented for the case where the discrete-time sliding mode observer is operating outside the boundary layer and also within the boundary layer. An algorithm is developed for obtaining the observer gain vector that guarantees the stability of the error dynamics. Numerical simulations and experimental results are presented to validate the stability and performance of the proposed observer