Consistent estimation of autoregressive parameters from noisy observations based on two interacting Kalman filters

The estimation of the parameters of an autoregressive process (AR) from noisy observations is still a challenging problem. In this paper, we propose to sequentially estimate both the signal and the parameters, avoiding a non-linear approach such as the extended Kalman filter. The method is based on two conditionally linked Kalman filters running in parallel. Once a new observation is available, the first filter uses the latest estimated AR parameters to estimate the signal, while the second filter uses the estimated signal to update the AR parameters. This approach can be viewed as a recursive instrumental variable-based method and hence has the advantage of providing consistent estimates of the parameters from noisy observations. A comparative study with existing algorithms illustrates the performances of the proposed method when the additive noise is either white or coloured.