Abstract: In geodetic,seismic and geodynamic data processing,a function is often required to simulate a group of measured data.That is the simulation of a function.The principle of the least squares being usually applied for this purpose,so it is called the least squares simulation,In the current literatures,the measured data are assumed to be independent with one another.In prance,however,we are frequently confronted with problems of handling correlated data.For solving such problems a method of simulation is suggested based upon the theory of least square correlation estimution.In addition,a comprehensive demonstration of the optimality of this method is made.In view of the fact that the new measured data are frequently to be supplemented to the data processing and also for economizing the data storage so as to reduce the workload in the computer,a recursion formula for the least squares simulation is derived according to the kalman filtering theory.