This paper proposes a new recursive least-squares (RLS) estimation algorithm for an impulse response function in linear continuous-time wide-sense stationary stochastic systems. It is assumed that the input signal to the unknown impulse response function is contaminated by additive white Gaussian observation noise. The output signal from the system related with the impulse response function is observed with additive white Gaussian noise. The impulse response function is estimated recursively in terms of the variance of the white Gaussian observation noise included in the input signal, the autocovariance function of the process before the observation noise is added to the input signal, the crosscovariance function between the output observed value and the input observed value, concerning the system based on the unknown impulse response function.
['Seiichi Nakamori']
Recursive estimation of impulse response function using covariance information in linear continuous stochastic systems