Influence of noise on the estimation method to reject damped sinusoidal vibrations in Adaptive Optics Systems

摘要

Damped sinusoidal signals occur in many fields of science and practical issues. One of them are adaptive optics systems where such signals are undesirable and often diminish the system performance. One of solutions to reject these signals is a method called AVC which is based on the estimation of vibrations parameters. In recent years, an universal, fast and accurate estimation method has been presented. It can be used to estimate multifrequency signals and can be useful in many various cases where the estimation method plays a crucial role. The main idea of this paper is using it in the AVC method to increase the system performance. There can be distinguished several measurement parameters that affect the accuracy and the speed of the estimation method: CiR (number of signal cycles in the estimation process). N (number of signal samples in a measurement window), H (time window order). There are also parameters that are especially important in practical situations (damped signals with noise and harmonics): SNR, THD, y (changed in time a damping ratio). Total estimation errors consist of systematic errors and random errors. This paper is focusing on the second component, i.e. when the signal with γ ≠ 0 is distorted by noise. Results can be very useful from a practical point of view because they give information about the estimation accuracy in dependence of noise power for various damping ratio values. The value of the empirical MSE of the frequency estimator is approximately 10^-3 Hz for SNR = 30 dB H=2 and γ = 0.01%.