A circuit theory of the Kalman filter

This note gives a short heuristic derivation of the discrete Kalman filter by considering simple voltage measurement circuits. The idea is to obtain conclusions about the general estimation problem by reasoning about an electric analog. The usual Kalman filter and the formulation known as the information filter are both quickly derived by this method. A basis for this approach is Nyquist's result (1928) that any resistance R exhibits a thermal noise voltage-the Johnson noise in radio engineering-of constant power spectral density proportional to R. It follows that multivariate white noise may be realized as the thermal noise of a resistive n-port. We model the general noisy measurement problem as a measurement problem on a resistive circuit. Covariance matrices arise in a concrete fashion as resistance matrices.<>