Solution of the continuous Kalman filter equations using the transmission line method

Abstract

A novel method is presented for the solution of the one-dimensional continuous Kalman filter equations implemented on a digital computer. The Kalman filter is implemented in an unusual way as a transmission line circuit. Estimated variables are regarded as discrete pulses bouncing to and from the nodes in the transmission line network at each time step. This approach is tested on a problem of voltage estimation in a passive electrical network in the presence of voltmeter errors. The transmission line method is compared with the results that are obtained using the Gear first- and third-order methods, the fourth-order Runge-Kutta method and the application of the discrete Kalman filter. It is found that the transmission line method has a tendency to yield less biased estimates than the other algorithms as well as providing smoother estimates for sampling times approaching the time constant of the circuit.