Application of the transmission line method to the solution of the continuous Kalman filter equations of general order

Abstract

In this paper, the transmission line method (TLM) is applied to the solution of the general, nth order, continuous Kalman filter estimation equations. A comparison is made between this method, the first-order Gear algorithm and the fourth-order Runge-Kutta method, in the estimation of the voltage drop and its derivative across a capacitor in an LCR circuit. An analysis is made of the sensitivity of the algorithms to changing time step and measurement error variance. In most cases, the Runge- Kutta method has the best performance at the expense of computing time. However, in some cases, the new algorithm yields less biased and smoother estimates. The TLM algorithm performs consistently better than the Gear method for the particular problem analysed. The CPU time for the TLM algorithm has also been compared with that required by the Gear and Runge-Kutta methods; the TLM method is found to take approximately 25% of the time required by the Runge-Kutta method to process one measurement. The TLM algorithm appears to present a compromise between accuracy of estimation and computing time. Finally, suggestions are made for further work.