A New Algorithm for Solving the Best-Fit Sphere of Optical Aspherical Surface

2011 ◽  
Vol 418-420 ◽  
pp. 1472-1477 ◽  
Author(s):  
Jie Qiong Lin ◽  
Jin Song Yang ◽  
Ming Ming Lu
Keyword(s):  
Material Removal ◽  
Radius Of Curvature ◽  
Variable Step Size ◽  
Rapid Convergence ◽  
Step Size ◽  
Cubic Surface ◽  
Variable Step ◽  
Speed Up ◽  
Best Fit ◽  
Best Fit Sphere

To solve the best-fit sphere (BFS) accurately is one of the technological keys for the generating and testing of optical aspherical surfaces. This paper presents a new algorithm for solving the BFS of aspherical surfaces to suppress some deficiencies in the existing BFS algorithms. In the proposed approach, a BFS is constructed, which passes through both sides of endpoints in the section of the aspherical surfaces, the center of the BFS is shifted along the x-axis, and its radius of curvature is automatically computed. The variable step size method is proposed to speed up the convergence of the iteration. Through numerically solving the BFS of conic and cubic surface, the advantages of the proposed approach are verified. The results show that the proposed approach is of rapid convergence, and high accuracy; it is not only suitable for the conic surface, but also for higher order aspheres. The obtained asphericity and material removal function is more suitable for the machining and test.

scholarly journals Improvement of Stripmap SAR Autofocus Based on Minimum-Entropy Criterion

2021 ◽  
Author(s):  
Tao Li ◽  
Yaowen Fu ◽  
Jianfeng Zhang ◽  
Wenpeng Zhang ◽  
Wei Yang
Keyword(s):  
Phase Error ◽  
Variable Step Size ◽  
Minimum Entropy ◽  
Step Size ◽  
Algorithm Performance ◽  
Variable Step ◽  
Speed Up ◽  
Autofocus Algorithm ◽  
Entropy Criterion ◽  
New Phase

Autofocus is an essential part of the SAR imaging process. Multi-subaperture autofocus algorithm is a commonly used autofocus algorithm for processing SAR stripmap mode data. The multi-subaperture autofocus algorithm has two main steps, the first is to estimate the phase error gradient within the subaperture, the second is to splice the phase error gradient, that is, to remove the shift amount between the estimated adjacent subapertures’ error gradients. Previous gradient-splicing algorithms assume that the estimation of subaperture error is accurate, but when the estimation of subaperture phase error gradients is not accurate enough, these algorithm performance will be degraded. A new phase error gradient splicing algorithm is proposed in this paper. It roughly estimates the shift amount first, and then finely estimates the shift amount based on the minimum-entropy criterion, which can improve the robustness of splicing especially when the estimation of the phase error gradients of the subaperture is not accurate enough. To speed up the algorithm, a variable-step-size search method is used. Simulation and experimental results show that the algorithm has enough accuracy and still has good performance when other splicing algorithms doesn’t perform well.

Performance Comparison of Variable Step Size Techniques of Sato and Godard-Based Blind Equalizer

2015 ◽  
Vol 14 (03) ◽  
pp. 1550024
Author(s):  
K. Suthendran ◽  
T. Arivoli
Keyword(s):  
Convergence Rate ◽  
High Speed ◽  
Blind Equalization ◽  
Pulse Amplitude ◽  
Performance Comparison ◽  
Variable Step Size ◽  
Step Size ◽  
Variable Step ◽  
Speed Up ◽  
Equalization Technique

The modern digital high speed wireless communication system demands quick convergence rate and low steady state error. The balancing between the demands can be achieved by opting step size. Thus, it is essential to define new algorithms to equalize channels and mitigate noise in communications. It is renowned that time varying step size blind equalization technique can speed up the convergence rate and minimize the misadjustment. This work presents a variable step size (VSS) approach based on godard blind equalization algorithm to resolve the conflict between the convergence rate and precision of the fixed step-size godard algorithm. The results of this projected approach is compared with the existing variable step size sato algorithm for a pulse amplitude modulated (PAM) input symbol.

A Variable Step-Size for Sparse Nonlinear Adaptive Filters

2021 ◽  
Author(s):  
Alberto Carini ◽  
Markus V. S. Lima ◽  
Hamed Yazdanpanah ◽  
Simone Orcioni ◽  
Stefania Cecchi
Keyword(s):  
Adaptive Filters ◽  
Variable Step Size ◽  
Step Size ◽  
Variable Step

Active control for vehicle interior noise using the improved iterative variable step-size and variable tap-length LMS algorithms

2019 ◽  
Vol 67 (6) ◽  
pp. 405-414 ◽  
Author(s):  
Ningning Liu ◽  
Yuedong Sun ◽  
Yansong Wang ◽  
Hui Guo ◽  
Bin Gao ◽  
...  
Keyword(s):  
Steady State ◽  
Noise Control ◽  
Convergence Speed ◽  
Interior Noise ◽  
Lms Algorithm ◽  
Variable Step Size ◽  
Step Size ◽  
Vehicle Interior ◽  
Vehicle Interior Noise ◽  
Variable Step

Active noise control (ANC) is used to reduce undesirable noise, particularly at low frequencies. There are many algorithms based on the least mean square (LMS) algorithm, such as the filtered-x LMS (FxLMS) algorithm, which have been widely used for ANC systems. However, the LMS algorithm cannot balance convergence speed and steady-state error due to the fixed step size and tap length. Accordingly, in this article, two improved LMS algorithms, namely, the iterative variable step-size LMS (IVS-LMS) and the variable tap-length LMS (VT-LMS), are proposed for active vehicle interior noise control. The interior noises of a sample vehicle are measured and thereby their frequency characteristics. Results show that the sound energy of noise is concentrated within a low-frequency range below 1000 Hz. The classical LMS, IVS-LMS and VT-LMS algorithms are applied to the measured noise signals. Results further suggest that the IVS-LMS and VT-LMS algorithms can better improve algorithmic performance for convergence speed and steady-state error compared with the classical LMS. The proposed algorithms could potentially be incorporated into other LMS-based algorithms (like the FxLMS) used in ANC systems for improving the ride comfort of a vehicle.

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