Estimation of Space and Time Shifts in Continuous 2-D Systems Using Instrumental Variable

This paper develops an algorithm to estimate the space shift, time shift (or time delay), and parameters in a shifted continuous 2-D system described by a 2-D partial differential equation. Using the linear filter method, the simultaneous estimation of shifts and parameters is achieved. Also, the instrumental variable technique is used to remove the least square estimation bias, which is due to measurement noise. There are some methods to estimate the time shift in 1-D systems. However, no method has been proposed so far to estimate the shifts in 2-D systems. To show the performance of the proposed algorithm, one illustrative numerical example is discussed.