Determination of CRLB and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

2021 ◽  
Vol 40 (1) ◽  
pp. 79-86
Author(s):  
Abdi Abdalla
Keyword(s):  
Lower Bound ◽  
Gaussian Noise ◽  
Unbiased Estimator ◽  
Laplace Transformation ◽  
Additive White Gaussian Noise ◽  
Minimum Variance ◽  
Minimum Variance Unbiased Estimator ◽  
Mathematical Background ◽  
Alternative Approach

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions show that the proposed method has almost the same number of steps as the existing method. However, the later requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.

scholarly journals Active Control of Edgewise Vibrations in Wind Turbine Blades Using Stochastic Disturbance Accommodating Control

2017 ◽  
Author(s):  
Cong Cong
Keyword(s):  
Wind Turbine ◽  
Unbiased Estimator ◽  
Turbine Blades ◽  
Minimum Variance ◽  
Aerodynamic Load ◽  
Unknown Input ◽  
Linear Quadratic ◽  
Minimum Variance Unbiased Estimator ◽  
Stochastic Disturbance ◽  
Disturbance Accommodating Control

Vibrations of blades and tower have important impact for wind turbine. This paper presents a active controller design to suppress blade edgewise vibrations under aerodynamic load and gravitational load.Treating the sum of aerodynamic load input in edgewise direction and gravitational load as unknown disturbance input,a stochastic disturbance accommodating control(SDAC) approach is proposed to design a controller which it utilizes a minimum-variance unbiased estimator(MVUE) to estimate both state and unknown input. The stability analysis proved that the proposed SDAC is bounded in mean square.In order to verify the performance of the minimum-variance unbiased estimator and the proposed SDAC, numerical simulations using Matlab/Simulink have been carried out for the National Renewable Energy Laboratory 5-MW wind turbine.Under the different circumstance which exists the random process and measure noise and noise free. It is shown that the estimation value by MVUE can tracking the real state and unknown input. The results are also compared to the traditional linear quadratic regulator(LQR) and show that the proposed stochastic disturbance accommodating control scheme can further reduce displacement in edgewise vibrations direction and the control strategy is more effective than the LQR.

The Cramer–Rao lower bound in a non-AWGN model for the affine phase retrieval

2021 ◽  
pp. 2050089
Author(s):  
Zhitao Zhuang ◽  
Kaixin Wang
Keyword(s):  
Lower Bound ◽  
Mean Square Error ◽  
Gaussian Noise ◽  
Phase Retrieval ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Mean Square ◽  
Cramer Rao Lower Bound ◽  
The Difference

In this paper, we derive the Cramer–Rao lower bound (CRLB) in a non-additive white Gaussian noise (AWGN) model for the affine phase retrieval (APR) and simulate the difference of CRLB and mean square error produced by PhaseLift of phase retrieval and APR in AWGN and non-AWGN cases.

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