Multi-innovation least squares parameter estimation algorithms for stochastic regression models

A multi-innovation least-squares (MILS) identification algorithm is presented for linear regression models with unknown parameter vectors by extending the conventional standard least-squares (LS) algorithm from the viewpoint of innovation modification. Because the proposed MILS algorithms use p innovations at each iteration (the integer p > 1 being an innovation length), the accuracy of parameter estimation is improved compared with the standard LS algorithm. The performance analysis and simulation results show that the proposed MILS algorithm is consistently convergent. Moreover, we introduce a new interval-varying MILS algorithm, for which the key is to change the interval dynamically, in order to deal with cases where some sampled data are missing. Further, we derive an auxiliary model based MILS for output error moving average systems with colored noises. The simulation results of an ARX system is included.