Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots

Alonso-Martín, Fernándo; Moreno, Luís; Garrido, Santiago; Blanco, Dolores

doi:10.3390/s150923431

Cited by 12 publications

(4 citation statements)

References 51 publications

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“…In fact, different sample sizes contain different propensities of probability information. Here we use the Kullback-Leibler (KL) divergence [38] to quantify the difference in probability information between 100 elements of sampled data (initial dataset) and other sample sizes (N = 20, 30, 40, 50, 60, and 80) of stagger-angle error data. These measured data have been shown in Section 4.1.…”

Section: Kullback-leibler Divergence Analysismentioning

confidence: 99%

Critical Sample-Size Analysis for Uncertainty Aerodynamic Evaluation of Compressor Blades with Stagger-Angle Errors

Wang,

Gao,

2023

Aerospace

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Many probability-based uncertainty quantification (UQ) schemes require a large amount of sampled data to build credible probability density function (PDF) models for uncertain parameters. Unfortunately, the amounts of data collected as to compressor blades of aero-engines are mostly limited due to the expensive and time-consuming tests. In this paper, we develop a preconditioner-based data-driven polynomial chaos (PDDPC) method that can efficiently deal with uncertainty propagation of limited amounts of sampled data. The calculation accuracy of a PDDPC method is closely related to the sample size of collected data. Therefore, the influence of sample size on this PDDPC method is investigated using a nonlinear test function. Subsequently, we consider the real manufacturing errors in stagger angles for compressor blades. Under three different operating conditions, the PDDPC method is applied to investigate the effect of stagger-angle error on UQ results of multiple aerodynamic parameters of a two-dimensional compressor blade. The results show that as the sample-size of measured data increases, UQ results regarding aerodynamic performance obtained by the PDDPC method gradually converge. There exists a critical sample size that ensures accurate UQ analysis of compressor blades. The probability information contained in the machining error data is analyzed through Kullback–Leibler divergence, and the critical sample size is determined. The research results can serve as a valuable reference for the fast and cheap UQ analysis of compressor blades in practical engineering.

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Section: Kullback-leibler Divergence Analysismentioning

confidence: 99%

Critical Sample-Size Analysis for Uncertainty Aerodynamic Evaluation of Compressor Blades with Stagger-Angle Errors

Wang,

Gao,

2023

Aerospace

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“…Also, quotient distance is used (with normalization which results in non-symmetry) in the Shannon's or entropy-type metrics, e.g., Kullback-Leibler Divergence (KLD) and Jeffreys Divergence (JD) (Cha, 2007;Kullback and Leibler, 1951). Martin, Moreno, Garrido and Blanco (2015) found that the KLDbased method in the presence of contaminated noise outperformed the L2-based measure in the global localization of mobile robots experiment.…”

Section: Error (Magnitude Of Error): 1 = −mentioning

confidence: 99%

A New Typology Design of Performance Metrics to Measure Errors in Machine Learning Regression Algorithms

Botchkarev

2019

IJIKM

352

148

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Aim/Purpose: The aim of this study was to analyze various performance metrics and approaches to their classification. The main goal of the study was to develop a new typology that will help to advance knowledge of metrics and facilitate their use in machine learning regression algorithms Background: Performance metrics (error measures) are vital components of the evaluation frameworks in various fields. A performance metric can be defined as a logical and mathematical construct designed to measure how close are the actual results from what has been expected or predicted. A vast variety of performance metrics have been described in academic literature. The most commonly mentioned metrics in research studies are Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), etc. Knowledge about metrics properties needs to be systematized to simplify the design and use of the metrics. Methodology: A qualitative study was conducted to achieve the objectives of identifying related peer-reviewed research studies, literature reviews, critical thinking and inductive reasoning. Contribution: The main contribution of this paper is in ordering knowledge of performance metrics and enhancing understanding of their structure and properties by proposing a new typology, generic primary metrics mathematical formula and a visualization chart Findings: Based on the analysis of the structure of numerous performance metrics, we proposed a framework of metrics which includes four (4) categories: primary metrics, extended metrics, composite metrics, and hybrid sets of metrics. The paper identified three (3) key components (dimensions) that determine the structure and properties of primary metrics: method of determining point distance, method of normalization, method of aggregation of point distances over a data set. For each component, implementation options have been identified. The suggested new typology has been shown to cover a total of over 40 commonly used primary metrics Recommendations for Practitioners: Presented findings can be used to facilitate teaching performance metrics to university students and expedite metrics selection and implementation processes for practitioners Recommendation for Researchers: By using the proposed typology, researchers can streamline development of new metrics with predetermined properties Impact on Society: The outcomes of this study could be used for improving evaluation results in machine learning regression, forecasting and prognostics with direct or indirect positive impacts on innovation and productivity in a societal sense Future Research: Future research is needed to examine the properties of the extended metrics, composite metrics, and hybrid sets of metrics. Empirical study of the metrics is needed using R Studio or Azure Machine Learning Studio, to find associations between the properties of primary metrics and their “numerical” behavior in a wide spectrum of data characteristics and business or research requirements

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“…The proposal distribution of the particle filter algorithm is regenerated using the KL divergence after containing the latest measurement values, so the new proposal distribution approaches the actual posterior distribution [ 8 ]. Martin et al proposed the Kullback–Leibler divergence-based differential evolution Markov chain filter for global localization for mobile robots in a challenging environment [ 9 ], where the KL-divergence is the basis of the cost function for minimization. The work in [ 3 ] provides a better measurement method for estimating the posterior distribution to apply KL minimization to the prediction and updating of the filtering algorithm, but it only provides the proof of the KL divergence minimization.…”

Section: Related Workmentioning

confidence: 99%

A Non-Linear Filtering Algorithm Based on Alpha-Divergence Minimization

Luo

Guo

Zheng

et al. 2018

Sensors

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A non-linear filtering algorithm based on the alpha-divergence is proposed, which uses the exponential family distribution to approximate the actual state distribution and the alpha-divergence to measure the approximation degree between the two distributions; thus, it provides more choices for similarity measurement by adjusting the value of α during the updating process of the equation of state and the measurement equation in the non-linear dynamic systems. Firstly, an α-mixed probability density function that satisfies the normalization condition is defined, and the properties of the mean and variance are analyzed when the probability density functions pfalse(xfalse) and qfalse(xfalse) are one-dimensional normal distributions. Secondly, the sufficient condition of the alpha-divergence taking the minimum value is proven, that is when α≥1, the natural statistical vector’s expectations of the exponential family distribution are equal to the natural statistical vector’s expectations of the α-mixed probability state density function. Finally, the conclusion is applied to non-linear filtering, and the non-linear filtering algorithm based on alpha-divergence minimization is proposed, providing more non-linear processing strategies for non-linear filtering. Furthermore, the algorithm’s validity is verified by the experimental results, and a better filtering effect is achieved for non-linear filtering by adjusting the value of α.

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Kullback-Leibler Divergence-Based Differential Evolution Markov Chain Filter for Global Localization of Mobile Robots

Cited by 12 publications

References 51 publications

Critical Sample-Size Analysis for Uncertainty Aerodynamic Evaluation of Compressor Blades with Stagger-Angle Errors

Critical Sample-Size Analysis for Uncertainty Aerodynamic Evaluation of Compressor Blades with Stagger-Angle Errors

A New Typology Design of Performance Metrics to Measure Errors in Machine Learning Regression Algorithms

A Non-Linear Filtering Algorithm Based on Alpha-Divergence Minimization

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