A technique is presented here to obtain the best estimates of states and parameters of a dynamic system based on the least squares of the errors between the observed output and the output computed for the dynamic mathematical model simulated on the digital computer. It is assumed that the form of the differential equations of the plant is known. The least-squares problem is interpreted as the Lagrange problem which needs to satisfy the necessary Euler-Lagrange conditions posing a two-point boundary value problem. This is then solved numerically by using the steepest descent method,