SOLUTION OF THE DIFFERENTIAL RICCATI EQUATION USING THE TRANSMISSION-LINE MODELING (TLM) TECHNIQUE

In this communication, the application of the transmission line modell ing (TLM) technique to the solution of the differential Riccati equati on is described. A comparison is made between the TLM, fourth-order Ru nge-Kutta and the first-order Gear methods, for the case where one is applying the Kalman filter to the estimation of a voltage in a passive analogue circuit. In the particular example studied, the state equati on is second-order. It is found that, when the system is underdamped, the fourth-order Runge-Kutta method has the best performance, followed by the TLM method. When the system is overdamped and stiff, the TLM m ethod yields results that are closest to the analytical solution. Fina lly, a discussion is presented of the effects of errors in the TLM sol ution of the Riccati equation on the accuracy of the solution to the c ontinuous Kalman filter estimation equation.