Two-stage information filters for single and multiple sensors, and their square-root versions

Automatica ◽  
2018 ◽  
Vol 98 ◽  
pp. 20-27 ◽  
Author(s):  
Kumar Pakki Bharani Chandra ◽  
Mohamed Darouach
Keyword(s):  
Square Root ◽  
Two Stage ◽  
Multiple Sensors ◽  
Information Filters

An impulsive two-stage predator–prey model with stage-structure and square root functional responses

2016 ◽  
Vol 119 ◽  
pp. 91-107 ◽  
Author(s):  
Xiangmin Ma ◽  
Yuanfu Shao ◽  
Zhen Wang ◽  
Mengzhuo Luo ◽  
Xianjia Fang ◽  
...  
Keyword(s):  
Stage Structure ◽  
Square Root ◽  
Functional Responses ◽  
Two Stage ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Fusion of Elliptical Extended Object Estimates Parameterized with Orientation and Axes Lengths

2020 ◽  
Author(s):  
Kolja Thormann ◽  
Marcus Baum
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Euclidean Distance ◽  
State Of The Art ◽  
Optimal Estimation ◽  
Square Root ◽  
Multiple Sensors ◽  
Practical Algorithms ◽  
Extended Object ◽  
Wasserstein Distances

This article considers the fusion of target estimates stemming from multiple sensors, where the spatial extent of the targets is incorporated. The target estimates are represented as ellipses parameterized with center orientation and semi-axis lengths and width. Here, the fusion faces challenges such as ambiguous parameterization and an unclear meaning of the Euclidean distance between such estimates. We introduce a novel Bayesian framework for random ellipses based on the concept of a Minimum Mean Gaussian Wasserstein (MMGW) estimator. The MMGW estimate is optimal with respect to the Gaussian Wasserstein (GW) distance, which is a suitable distance metric for ellipses. We develop practical algorithms to approximate the MMGW estimate of the fusion result. The key idea is to approximate the GW distance with a modified version of the Square Root (SR) distance. By this means, optimal estimation and fusion can be performed based on the square root of the elliptic shape matrices. We analyze different implementations using, e.g., Monte Carlo methods, and evaluate them in simulated scenarios. An extensive comparison with state-of-the-art methods highlights the benefits of estimators tailored to the Gaussian Wasserstein distances.

scholarly journals Fusion of Elliptical Extended Object Estimates Parameterized with Orientation and Axes Lengths

2020 ◽  
Author(s):  
Kolja Thormann ◽  
Marcus Baum
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Euclidean Distance ◽  
State Of The Art ◽  
Optimal Estimation ◽  
Square Root ◽  
Multiple Sensors ◽  
Practical Algorithms ◽  
Extended Object ◽  
Wasserstein Distances

This article considers the fusion of target estimates stemming from multiple sensors, where the spatial extent of the targets is incorporated. The target estimates are represented as ellipses parameterized with center orientation and semi-axis lengths and width. Here, the fusion faces challenges such as ambiguous parameterization and an unclear meaning of the Euclidean distance between such estimates. We introduce a novel Bayesian framework for random ellipses based on the concept of a Minimum Mean Gaussian Wasserstein (MMGW) estimator. The MMGW estimate is optimal with respect to the Gaussian Wasserstein (GW) distance, which is a suitable distance metric for ellipses. We develop practical algorithms to approximate the MMGW estimate of the fusion result. The key idea is to approximate the GW distance with a modified version of the Square Root (SR) distance. By this means, optimal estimation and fusion can be performed based on the square root of the elliptic shape matrices. We analyze different implementations using, e.g., Monte Carlo methods, and evaluate them in simulated scenarios. An extensive comparison with state-of-the-art methods highlights the benefits of estimators tailored to the Gaussian Wasserstein distances.

scholarly journals Distributed Hybrid Two-Stage Multi-Sensor Fusion for Cooperative Modulation Classification in Large-Scale Wireless Sensor Networks

Sensors ◽  
2019 ◽  
Vol 19 (19) ◽  
pp. 4339 ◽  
Author(s):  
Markovic ◽  
Sokolovic ◽  
Dukic
Keyword(s):  
Large Scale ◽  
Partial Information ◽  
Complete Information ◽  
Decision Fusion ◽  
Fusion Process ◽  
Modulation Classification ◽  
Two Stage ◽  
Multiple Sensors ◽  
Cluster Data ◽  
Large Scale Networks

Recent studies showed that the performance of the modulation classification (MC) is considerably improved by using multiple sensors deployed in a cooperative manner. Such cooperative MC solutions are based on the centralized fusion of independent features or decisions made at sensors. Essentially, the cooperative MC employs multiple uncorrelated observations of the unknown signal to gather more complete information, compared to the single sensor reception, which is used in the fusion process to refine the MC decision. However, the non-cooperative nature of MC inherently induces large loss in cooperative MC performance due to the unreliable measure of quality for the MC results obtained at individual sensors (which causes the partial information loss while performing centralized fusion). In this paper, the distributed two-stage fusion concept for the cooperative MC using multiple sensors is proposed. It is shown that the proposed distributed fusion, which combines feature (cumulant) fusion and decision fusion, facilitate preservation of information during the fusion process and thus considerably improve the MC performance. The clustered architecture is employed, with the influence of mismatched references restricted to the intra-cluster data fusion in the first stage. The adopted distributed concept represents a flexible and scalable solution that is suitable for implementation of large-scale networks.

Maximum likelihood estimation using square root information filters

1990 ◽  
Vol 35 (12) ◽  
pp. 1293-1298 ◽  
Author(s):  
G.J. Bierman ◽  
M.R. Belzer ◽  
J.S. Vandergraft ◽  
D.W. Porter
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Square Root ◽  
Information Filters

A Class of Stable Square-Root Nonlinear Information Filters

2014 ◽  
Vol 59 (7) ◽  
pp. 1893-1898 ◽  
Author(s):  
Shiyuan Wang ◽  
Jiuchao Feng ◽  
Chi K. Tse
Keyword(s):  
Square Root ◽  
Information Filters

scholarly journals Fusion of Elliptical Extended Object Estimates Parameterized with Orientation and Axes Lengths

2020 ◽  
Author(s):  
Kolja Thormann ◽  
Marcus Baum
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Euclidean Distance ◽  
State Of The Art ◽  
Optimal Estimation ◽  
Square Root ◽  
Multiple Sensors ◽  
Practical Algorithms ◽  
Extended Object ◽  
Wasserstein Distances

This article considers the fusion of target estimates stemming from multiple sensors, where the spatial extent of the targets is incorporated. The target estimates are represented as ellipses parameterized with center orientation and semi-axis lengths and width. Here, the fusion faces challenges such as ambiguous parameterization and an unclear meaning of the Euclidean distance between such estimates. We introduce a novel Bayesian framework for random ellipses based on the concept of a Minimum Mean Gaussian Wasserstein (MMGW) estimator. The MMGW estimate is optimal with respect to the Gaussian Wasserstein (GW) distance, which is a suitable distance metric for ellipses. We develop practical algorithms to approximate the MMGW estimate of the fusion result. The key idea is to approximate the GW distance with a modified version of the Square Root (SR) distance. By this means, optimal estimation and fusion can be performed based on the square root of the elliptic shape matrices. We analyze different implementations using, e.g., Monte Carlo methods, and evaluate them in simulated scenarios. An extensive comparison with state-of-the-art methods highlights the benefits of estimators tailored to the Gaussian Wasserstein distances.

scholarly journals Fusion of Elliptical Extended Object Estimates Parameterized with Orientation and Axes Lengths

2019 ◽  
Author(s):  
Kolja Thormann ◽  
Marcus Baum
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Euclidean Distance ◽  
State Of The Art ◽  
Optimal Estimation ◽  
Square Root ◽  
Multiple Sensors ◽  
Practical Algorithms ◽  
Extended Object ◽  
Wasserstein Distances

This article considers the fusion of target estimates stemming from multiple sensors, where the spatial extent of the targets is incorporated. The target estimates are represented as ellipses parameterized with center orientation and semi-axis lengths and width. Here, the fusion faces challenges such as ambiguous parameterization and an unclear meaning of the Euclidean distance between such estimates. We introduce a novel Bayesian framework for random ellipses based on the concept of a Minimum Mean Gaussian Wasserstein (MMGW) estimator. The MMGW estimate is optimal with respect to the Gaussian Wasserstein (GW) distance, which is a suitable distance metric for ellipses. We develop practical algorithms to approximate the MMGW estimate of the fusion result. The key idea is to approximate the GW distance with a modified version of the Square Root (SR) distance. By this means, optimal estimation and fusion can be performed based on the square root of the elliptic shape matrices. We analyze different implementations using, e.g., Monte Carlo methods, and evaluate them in simulated scenarios. An extensive comparison with state-of-the-art methods highlights the benefits of estimators tailored to the Gaussian Wasserstein distances.

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