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 Minimax Estimation in Regression under Sample Conformity Constraints

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1080
Author(s):  
Andrey Borisov
Keyword(s):  
Optimization Problem ◽  
Probability Distributions ◽  
Essential Feature ◽  
Estimation Error ◽  
Saddle Points ◽  
Minimax Problem ◽  
Estimation Of Parameters ◽  
Minimax Optimization ◽  
Optimal Estimator ◽  
Regression Parameters

The paper is devoted to the guaranteeing estimation of parameters in the uncertain stochastic nonlinear regression. The loss function is the conditional mean square of the estimation error given the available observations. The distribution of regression parameters is partially unknown, and the uncertainty is described by a subset of probability distributions with a known compact domain. The essential feature is the usage of some additional constraints describing the conformity of the uncertain distribution to the realized observation sample. The paper contains various examples of the conformity indices. The estimation task is formulated as the minimax optimization problem, which, in turn, is solved in terms of saddle points. The paper presents the characterization of both the optimal estimator and the set of least favorable distributions. The saddle points are found via the solution to a dual finite-dimensional optimization problem, which is simpler than the initial minimax problem. The paper proposes a numerical mesh procedure of the solution to the dual optimization problem. The interconnection between the least favorable distributions under the conformity constraint, and their Pareto efficiency in the sense of a vector criterion is also indicated. The influence of various conformity constraints on the estimation performance is demonstrated by the illustrative numerical examples.

A new adaptive variable step size natural gradient BSS algorithm

2021 ◽  
pp. 1-12
Author(s):  
Junqing Ji ◽  
Xiaojia Kong ◽  
Yajing Zhang ◽  
Tongle Xu ◽  
Jing Zhang
Keyword(s):  
Signal To Noise Ratio ◽  
Wavelet Coefficient ◽  
Gradient Algorithm ◽  
Variable Step Size ◽  
Natural Gradient ◽  
Threshold Method ◽  
Step Size ◽  
Morphological Component Analysis ◽  
Variable Step ◽  
Separation Degree

The traditional blind source separation (BSS) algorithm is mainly used to deal with signal separation under the noiseless model, but it does not apply to data with the low signal to noise ratio (SNR). To solve the problem, an adaptive variable step size natural gradient BSS algorithm based on an improved wavelet threshold is proposed in this paper. Firstly, an improved wavelet threshold method is used to reduce the noise of the signal. Secondly, the wavelet coefficient layer with obvious periodicity is denoised using a morphological component analysis (MCA) algorithm, and the processed wavelet coefficients are recombined to obtain the ideal model. Thirdly, the recombined signal is pre-whitened, and a new separation matrix update formula of natural gradient algorithm is constructed by defining a new separation degree estimation function. Finally, the adaptive variable step size natural gradient blind source algorithm is used to separate the noise reduction signal. The results show that the algorithm can not only adaptively adjust the step size according to different signals, but also improve the convergence speed, stability and separation accuracy.

scholarly journals Shearlet-based regularized reconstruction in region-of-interest computed tomography

2018 ◽  
Vol 13 (4) ◽  
pp. 34
Author(s):  
T.A. Bubba ◽  
D. Labate ◽  
G. Zanghirati ◽  
S. Bonettini
Keyword(s):  
Optimization Problem ◽  
Ad Hoc ◽  
Iterative Scheme ◽  
Tomographic Reconstruction ◽  
Region Of Interest ◽  
Projection Data ◽  
Reconstruction Problem ◽  
Convex Optimization Problem ◽  
Scanning Time ◽  
Novel Approach

Region of interest (ROI) tomography has gained increasing attention in recent years due to its potential to reducing radiation exposure and shortening the scanning time. However, tomographic reconstruction from ROI-focused illumination involves truncated projection data and typically results in higher numerical instability even when the reconstruction problem has unique solution. To address this problem, bothad hocanalytic formulas and iterative numerical schemes have been proposed in the literature. In this paper, we introduce a novel approach for ROI tomographic reconstruction, formulated as a convex optimization problem with a regularized term based on shearlets. Our numerical implementation consists of an iterative scheme based on the scaled gradient projection method and it is tested in the context of fan-beam CT. Our results show that our approach is essentially insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.

scholarly journals Design and Optimization for UAV-Enabled Two-Way Relaying System with SWIPT

2020 ◽  
Author(s):  
Jinlong Wang ◽  
Gang Wang ◽  
Guanyi Chen ◽  
Bo Li ◽  
Ruofei Zhou ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Signal To Noise Ratio ◽  
Power Splitting ◽  
Generalized Singular Value Decomposition ◽  
Ratio Requirement ◽  
Design And Optimization ◽  
Aerial Vehicle ◽  
Resource Allocation Scheme ◽  
Value Decomposition ◽  
Relaying System

Abstract In this paper, we investigate the resource allocation scheme for an unmanned-aerial-vehicle-enable (UAV-enabled) two-way relaying system with simultaneous wireless information and power transfer (SWIPT), where two userequipment exchange information with the help of UAV relay and harvest energythrough power splitting (PS) scheme. Under the transmission power constraintsat UEs and UAV relay, a non-convex intractable optimization problem isformulated which maximizes the sum retained energy of two UEs while satisfying the minimum signal-to-noise ratio requirement. We decouple the complicated beamforming and PS factors optimization problem into three solvable subproblems and propose an efficient alternating optimization scheme. Subsequently, in order to reduce the complexity, a robust scheme based on generalized singular value decomposition (GSVD) is designed. Finally, numerical results verify the robustness and effectiveness of two proposed schemes.

scholarly journals Low Complexity Sparse Beamspace DOA Estimation Via Single Measurement Vectors for Uniform Circular Array

2021 ◽  
Author(s):  
Di Zhao ◽  
Weijie Tan ◽  
Zhongliang Deng ◽  
Gang Li
Keyword(s):  
Optimization Problem ◽  
Signal To Noise Ratio ◽  
Estimation Method ◽  
Doa Estimation ◽  
Low Complexity ◽  
Estimation Methods ◽  
Circular Array ◽  
Single Measurement ◽  
Signal Model ◽  
Convex Optimization Problem

Abstract In this paper, we present a low complexity beamspace direction-of-arrival (DOA) estimation method for uniform circular array (UCA), which is based on the single measurement vectors (SMVs) via vectorization of sparse covariance matrix. In the proposed method, we rstly transform the signal model of UCA to that of virtual uniform linear array (ULA) in beamspace domain using the beamspace transformation (BT). Subsequently, by applying the vectorization operator on the virtual ULA-like array signal model, a new dimension-reduction array signal model consists of SMVs based on Khatri-Rao (KR) product is derived. And then, the DOA estimation is converted to the convex optimization problem. Finally, simulations are carried out to verify the eectiveness of the proposed method, the results show that without knowledge of the signal number, the proposed method not only has higher DOA resolution than subspace-based methods in low signal-to-noise ratio (SNR), but also has much lower computational complexity comparing other sparse-like DOA estimation methods.

scholarly journals Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Duality Theorems ◽  
Differentiable Vector

AbstractIn this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

scholarly journals An SNR-Optimized Scanning Strategy for Geostationary Carbon Cycle Observatory (GeoCarb) Instrument

2018 ◽  
Author(s):  
Jeffrey Nivitanont ◽  
Sean Crowell
Keyword(s):  
Carbon Cycle ◽  
Greenhouse Gases ◽  
Optimization Problem ◽  
Signal To Noise Ratio ◽  
Western Hemisphere ◽  
Geostationary Orbit ◽  
Signal To Noise ◽  
Scanning Strategy ◽  
Land Mass ◽  
Error Distributions

Abstract. The Geostationary Carbon Observatory (GeoCarb) will make measurements of greenhouse gases over the land mass in the western hemisphere. The extreme flexibility of observing from geostationary orbit induces an optimization problem, as operators must choose what to observe and when. We express this problem in terms of an optimal subcovering problem, and use an Incremental Optimization (IO) algorithm to create a scanning strategy that minimizes expected error as a function of the signal-to-noise ratio (SNR), and show that this method outperforms the human selected strategy in terms of global error distributions.

Optimal Design of Semisubmersible’s Form Based on Systems Analysis

1984 ◽  
Vol 106 (4) ◽  
pp. 524-530 ◽  
Author(s):  
S. Akagi ◽  
R. Yokoyama ◽  
K. Ito
Keyword(s):  
Optimal Design ◽  
Computer Aided Design ◽  
Optimization Problem ◽  
Design Method ◽  
Gradient Algorithm ◽  
Interpretive Structural Modeling ◽  
Reduced Gradient ◽  
Optimal Design Method ◽  
Generalized Reduced Gradient ◽  
Aided Design

With the objective of developing a computer-aided design method to seek the optimal semisubmersible’s form, hierarchical relationships among many design objectives and conditions are investigated first based on the interpretive structural modeling method. Then, an optimal design method is formulated as a nonlinear multiobjective optimization problem by adopting three mutually conflicting design objectives. A set of Pareto optimal solutions is derived numerically by adopting the generalized reduced gradient algorithm, and it is ascertained that the designer can determine the optimal form more rationally by investigating the trade-off relationships among design objectives.

scholarly journals Actor–Critic-Algorithm-Based Accurate Spectrum Sensing and Transmission Framework and Energy Conservation in Energy-Constrained Wireless Sensor Network-Based Cognitive Radios

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Hurmat Ali Shah ◽  
Insoo Koo ◽  
Kyung Sup Kwak
Keyword(s):  
Cognitive Radio ◽  
Ad Hoc Networks ◽  
Spectrum Sensing ◽  
Optimization Problem ◽  
Ad Hoc ◽  
Cognitive Radios ◽  
Residual Energy ◽  
Current Time ◽  
Energy Constrained ◽  
Hoc Networks

Spectrum sensing is of the utmost importance to the workings of a cognitive radio network (CRN). The spectrum has to be sensed to decide whether the cognitive radio (CR) user can transmit or not. Transmitting on unoccupied spectrum becomes a hard task if energy-constrained networks are considered. CRNs are ad hoc networks, and thus, they are energy-limited, but energy harvesting can ensure that enough energy is available for transmission, thus enabling the CRN to have a theoretically infinite lifetime. The residual energy, along with the sensing decision, determines the action in the current time slot. The transmission decision has to be grounded on the sensing outcome, and thus, a combined sensing–transmission framework for the CRN has to be considered. The sensing–transmission framework forms a Markov decision process (MDP), and solving the MDP problem exhaustively through conventional methods cannot be a plausible solution for ad hoc networks such as a CRN. In this paper, to solve the MDP problem, an actor–critic-algorithm-based solution for optimizing the action taken in a sensing–transmission framework is proposed. The proposed scheme solves an optimization problem on the basis of the actor–critic algorithm, and the action that brings the highest reward is selected. The optimal policy is determined by updating the optimization problem parameters. The reward is calculated by the critic component through interaction with the environment, and the value function for each state is updated, which then updates the policy function. Simulation results show that the proposed scheme closely follows the exhaustive search scheme and outperforms a myopic scheme in terms of average throughput achieved.

Denoising Simulation Study for MEMS Gyro Dynamic Running

2012 ◽  
Vol 518-523 ◽  
pp. 3800-3804 ◽  
Author(s):  
Su Zhen Wang ◽  
Tao Wang ◽  
Zheng Yan Wang
Keyword(s):  
Simulation Study ◽  
Measurement System ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Dynamic Data ◽  
Optimal Estimator ◽  
Fusion Data ◽  
Data Generator ◽  
Segment Data ◽  
Posture Measurement

At present MEMS inertial devices is unable to satisfy the precision request of the inertial posture measurement system. This paper has designed a gyro dynamic data generator for simulation according to the gyro signal characteristics.The signal produced by the generator is specified as the gyro data and the optimal estimator for data fusion is designed by using the Kaman filter algorithm.The multi-segment data is analyzed and identified while the optimal data is estimated .The results show no matter how the correlation of the data is, the fusion data has attenuation of 10dB in noise, with its signal-to-noise ratio being enhanced more than 2 times at least.

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