In the areas of acoustic research or applications that deal with not-precisely-known or variable conditions, a method of adaptation to the uncertainness or changes is usually necessary. When searching for an adaptation algorithm, it is hard to overlook the least mean squares (LMS) algorithm. Its simplicity, speed of computation, and robustness has won it a wide area of applications: from telecommunication, through acoustics and vibration, to seismology. The algorithm, however, still lacks a full theoretical analysis. This is probabely the cause of its main drawback: the need of a careful choice of the step size - which is the reason why so many variable step size flavors of the LMS algorithm has been developed.

This paper contributes to both the above mentioned characteristics of the LMS algorithm. First, it shows a derivation of a new necessary condition for the LMS algorithm convergence. The condition, although weak, proved useful in developing a new variable step size LMS algorithm which appeared to be quite different from the algorithms known from the literature. Moreover, the algorithm proved to be effective in both simulations and laboratory experiments, covering two possible applications: adaptive line enhancement and active noise control.

The paper presents an iterative identification method dedicated for industrial processes. The method consists of two steps. In the first step, a MISO system is identified with the Modulating Functions Method to obtain sub-models with a common denominator. In the second step, the obtained subsystems are re-identified. This procedure enables to obtain the set of models with different denominators of the transfer functions. The algorithmwas used for on-line identification of a glass conditioning process. Identification window is divided into intervals, in which the models can be updated based on recent process data, with the use of the integral state observer. Results of the performed simulations for the identified models are compared with the historical process data.