Global convergence of output error recursions in colored noise

This paper presents a variation on a known extended least squares algorithm of the "output error" or "parallel model" type. Under reasonable conditions, the algorithms achieve global convergence of the one-step-ahead prediction error to the additive independent (possible colored) measurement noise. The convergence of the algorithms proposed is not critically sensitive to the color in the noise as are related extended least squares schemes which require a simultaneous noise model identification, nor is the convergence critically sensitive to the input signals as are realizations of the method of instrumental variables. The algorithms are also simpler to implement than for the competing schemes. In the paper, there is also studied an add on scheme which consists of additional processing of the prediction errors to achieve simultaneous noise model identification, and improved prediction. Such a scheme is attractive from the computational cost point of view. Global convergence results are developed for the algorithms based on martingale convergence theorems as in earlier theories for extended least squares schemes. The key contribution of the paper as far as the theory is concerned is to show how to cope with the colored noise in the martingale framework.