Phase-gradient algorithm as an optimal estimator of the phase derivative

1989 ◽  
Vol 14 (20) ◽  
pp. 1101 ◽  
Author(s):  
P. H. Eichel ◽  
C. V. Jakowatz
Keyword(s):  
Gradient Algorithm ◽  
Phase Gradient ◽  
Optimal Estimator ◽  
Phase Derivative

scholarly journals Phase gradient algorithm method for three-dimensional holographic ladar imaging

2016 ◽  
Vol 55 (17) ◽  
pp. 4611 ◽  
Author(s):  
Jason W. Stafford ◽  
Bradley D. Duncan ◽  
David J. Rabb
Keyword(s):  
Three Dimensional ◽  
Gradient Algorithm ◽  
Phase Gradient

scholarly journals Geometric methods for optimal sensor design

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150312 ◽  
Author(s):  
M.-A. Belabbas
Keyword(s):  
Structural Equation ◽  
Optimization Problem ◽  
Dual Problem ◽  
Morse Function ◽  
Ad Hoc ◽  
Signal To Noise Ratio ◽  
Estimation Error ◽  
Gradient Algorithm ◽  
Optimal Estimator ◽  
Actuator Design

The Kalman–Bucy filter is the optimal estimator of the state of a linear dynamical system from sensor measurements. Because its performance is limited by the sensors to which it is paired, it is natural to seek optimal sensors. The resulting optimization problem is however non-convex. Therefore, many ad hoc methods have been used over the years to design sensors in fields ranging from engineering to biology to economics. We show in this paper how to obtain optimal sensors for the Kalman filter. Precisely, we provide a structural equation that characterizes optimal sensors. We furthermore provide a gradient algorithm and prove its convergence to the optimal sensor. This optimal sensor yields the lowest possible estimation error for measurements with a fixed signal-to-noise ratio. The results of the paper are proved by reducing the optimal sensor problem to an optimization problem on a Grassmannian manifold and proving that the function to be minimized is a Morse function with a unique minimum. The results presented here also apply to the dual problem of optimal actuator design.

scholarly journals Implementation of the phase-gradient algorithm

1990 ◽  
Author(s):  
Daniel E. Wahl ◽  
Paul H. Eichel ◽  
Charles V. Jakowatz, Jr.
Keyword(s):  
Gradient Algorithm ◽  
Phase Gradient

scholarly journals Imaging for Small UAV-Borne FMCW SAR

Sensors ◽  
2018 ◽  
Vol 19 (1) ◽  
pp. 87 ◽  
Author(s):  
Xianyang Hu ◽  
Changzheng Ma ◽  
Ruizhi Hu ◽  
Tat Yeo
Keyword(s):  
Continuous Wave ◽  
Target Identification ◽  
Low Cost ◽  
Real Data ◽  
Gradient Algorithm ◽  
Minimum Entropy ◽  
Phase Gradient ◽  
Minimization Technique ◽  
Range Cell Migration ◽  
Synthetic Aperture Radars

Unmanned aerial vehicle borne frequency modulated continuous wave synthetic aperture radars are attracting more and more attention due to their low cost and flexible operation capacity, including the ability to capture images at different elevation angles for precise target identification. However, small unmanned aerial vehicles suffer from large trajectory deviation and severe range-azimuth coupling due to their simple navigational control and susceptibility to air turbulence. In this paper, we utilize the squint minimization technique to reduce this coupling while simultaneously eliminating intra-pulse motion-induced effects with an additional spectrum scaling. After which, the modified range doppler algorithm is derived for second order range compression and block-wise range cell migration correction. Raw data-based motion compensation is carried out with a doppler tracker. Squinted azimuth dependent phase gradient algorithm is employed to deal with azimuth dependent parameters and inexact deramping, with minimum entropy-based autofocusing algorithms. Finally, azimuth nonlinear chirp scaling is used for azimuth compression. Simulation and real data experiment results presented verify the effectiveness of the above signal processing approach.

scholarly journals A Cascaded Approach for Correcting Ionospheric Contamination with Large Amplitude in HF Skywave Radars

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yajun Li ◽  
Yinsheng Wei ◽  
Rujiang Guo ◽  
Rongqing Xu ◽  
Zhuoqun Wang ◽  
...  
Keyword(s):  
Frequency Distribution ◽  
Large Amplitude ◽  
Gradient Algorithm ◽  
Frequency Resolution ◽  
Good Effect ◽  
Distribution Method ◽  
Phase Gradient ◽  
Time Frequency ◽  
Phase Perturbation ◽  
Time Frequency Distribution

Ionospheric phase perturbation with large amplitude causes broadening sea clutter’s Bragg peaks to overlap each other; the performance of traditional decontamination methods about filtering Bragg peak is poor, which greatly limits the detection performance of HF skywave radars. In view of the ionospheric phase perturbation with large amplitude, this paper proposes a cascaded approach based on improved S-method to correct the ionospheric phase contamination. This approach consists of two correction steps. At the first step, a time-frequency distribution method based on improved S-method is adopted and an optimal detection method is designed to obtain a coarse ionospheric modulation estimation from the time-frequency distribution. At the second correction step, based on the phase gradient algorithm (PGA) is exploited to eliminate the residual contamination. Finally, use the measured data to verify the effectiveness of the method. Simulation results show the time-frequency resolution of this method is high and is not affected by the interference of the cross term; ionospheric phase perturbation with large amplitude can be corrected in low signal-to-noise (SNR); such a cascade correction method has a good effect.

Phase gradient algorithm based on co-axis two-step phase-shifting interferometry and its application

2017 ◽  
Vol 405 ◽  
pp. 211-215 ◽  
Author(s):  
Yawei Wang ◽  
Qiong Zhu ◽  
Yuanyuan Xu ◽  
Zhiduo Xin ◽  
Jingye Liu
Keyword(s):  
Phase Shifting ◽  
Gradient Algorithm ◽  
Phase Gradient ◽  
Phase Shifting Interferometry
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