In the field of active noise control (ANC), a popular method is the modified filtered-x LMS algorithm. However, it has two drawbacks: its computational complexity higher than that of the conventional FxLMS, and its convergence rate that could still be improved. Therefore, we propose an adaptive strategy which aims at speeding up the convergence rate of an ANC system dealing with periodic disturbances. This algorithm consists in combining the organization of the filter weights in a hierarchy of subfilters of shorter length and their sequential partial updates (PU). Our contribution is threefold: (1) we provide the theoretical basis of the existence of a frequency-dependent parameter, called gain in step-size. (2) The theoretical upper bound of the step-size is compared with the limit obtained from simulations. (3) Additional experiments show that this strategy results in a fast algorithm with a computational complexity close to that of the conventional FxLMS.
The objective of this study was to evaluate the performance of the different systems and techniques aimed at suppressing vibrations on optical ground-based telescopes. We identified the studies by searching three electronic databases (Science Direct, IEEE library and Web of Science) from the year 2000 to December 2020. The studies were eligible if they proposed systems focused on mitigating the effects of vibrations in optical telescopes and brought performance data. A total of nine studies met our eligibility criteria. Current evidence confirms the feasibility of adaptative optics (AO) systems based on closed-loop control to mitigate vibrations, although variations and additions should be made depending on their nature and characteristics in order to improve the performance of the proposed techniques. This systematic review was conducted to provide a state-of-the-art of the methods and techniques that have been developed over the past two decades. The review also points out some issues that demand future research.
The location of large telescopes, generally far from the data processing centers, represents a logistical problem for the supervision of the capture of images. In this work, we carried out a preliminary study of the vibration signature of the T80 telescope at the Javalambre Astrophysical Observatory (JAO). The study analyzed the process of calculating the displacement that occurs because of the vibration in each of the frequencies in the range of interest. We analyzed the problems associated with very low frequencies by means of simulation, finding the most critical vibrations below 20 Hz, since they are the ones that generate greater displacements. The work also relates previous studies based on simulation with the real measurements of the vibration of the telescope taken remotely when it is subjected to different positioning movements (right ascension and/or declination) or when it performs movement actions such as those related to filter trays or mirror cover. The obtained results allow us to design a remote alarm system to detect invalid images (taken with excess vibration).
Partial updates (PU) of adaptive filters have been successfully applied in different contexts to lower the computational costs of many control systems. In a PU adaptive algorithm, only a fraction of the coefficients is updated per iteration. Particularly, this idea has been proved as a valid strategy in the active control of periodic noise consisting of a sum of harmonics. The convergence analysis carried out here is based on the periodic nature of the input signal, which makes it possible to formulate the adaptive process with a matrix-based approach, the periodic least-mean-square (P-LMS) algorithm In this paper, we obtain the upper bound that limits the step-size parameter of the sequential PU P-LMS algorithm and compare it to the bound of the full-update P-LMS algorithm. Thus, the limiting value for the step-size parameter is expressed in terms of the step-size gain of the PU algorithm. This gain in step-size is the quotient between the upper bounds ensuring convergence in the following two scenarios: first, when PU are carried out and, second, when every coefficient is updated during every cycle. This step-size gain gives the factor by which the step-size can be multiplied so as to compensate for the convergence speed reduction of the sequential PU algorithm, which is an inherently slower strategy. Results are compared with previous results based on the standard sequential PU LMS formulation. Frequency-dependent notches in the step-size gain are not present with the matrix-based formulation of the P-LMS. Simulated results confirm the expected behavior.
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