Entropy

Research

17 pages, 7128 KiB

Open AccessArticle

Vector Bundle Model of Complex Electromagnetic Space and Change Detection

by Hao Wu, Yongqiang Cheng, Xiaoqiang Hua and Hongqiang Wang

Entropy 2019, 21(1), 10; https://doi.org/10.3390/e21010010 - 23 Dec 2018

Cited by 6 | Viewed by 4135

Complex Electromagnetic Space (CEMS), which consists of physical space and the complex electromagnetic environment, plays an essential role in our daily life for supporting remote communication, wireless network, wide-range broadcast, etc. In CEMS, the electromagnetic activities might work differently from the ideal situation; [...] Read more.

Complex Electromagnetic Space (CEMS), which consists of physical space and the complex electromagnetic environment, plays an essential role in our daily life for supporting remote communication, wireless network, wide-range broadcast, etc. In CEMS, the electromagnetic activities might work differently from the ideal situation; the typical case is that undesired signal would disturb the echo of objects and overlap into it resulting in the mismatch of matched filter and the reduction of the probability of detection. The lacking mathematical description of CEMS resulting from the complexity of electromagnetic environment leads to the inappropriate design of detection method. Therefore, a mathematical model of CEMS is desired for integrating the electromagnetic signal in CEMS as a whole and considering the issues in CEMS accurately. This paper puts forward a geometric model of CEMS based on vector bundle, which is an abstract concept in differential geometry and proposes a geometric detector for change detection in CEMS under the geometric model. In the simulation, the proposed geometric detector was compared with energy detector and matched filter in two scenes: passive detection case and active detection case. The results show the proposed geometric detector is better than both energy detector and matched filter with 4∼5 dB improvements of SNR (signal-to-noise ratio) in two scenes. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

15 pages, 1088 KiB

Open AccessArticle

Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence

by Xiaoqiang Hua, Yongqiang Cheng, Hongqiang Wang and Yuliang Qin

Entropy 2018, 20(4), 258; https://doi.org/10.3390/e20040258 - 8 Apr 2018

Cited by 12 | Viewed by 4374

Abstract

This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices estimated by the secondary data set. A new class [...] Read more.

This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices estimated by the secondary data set. A new class of total Bregman divergence is presented on the Riemanian manifold of Hermitian positive-definite (HPD) matrix, which is the foundation of information geometry. On the basis of this divergence, total Bregman divergence medians are derived instead of the sample covariance matrix (SCM) of the secondary data. Unlike the SCM, resorting to the knowledge of statistical characteristics of the sample data, the geometric structure of matrix space is considered in our proposed estimators, and then the performance can be improved in a heterogeneous clutter. At the analysis stage, numerical results are given to validate the detection performance of an adaptive normalized matched filter with our estimator compared with existing alternatives. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

18 pages, 1772 KiB

Open AccessArticle

Modulation Signal Recognition Based on Information Entropy and Ensemble Learning

by Zhen Zhang, Yibing Li, Shanshan Jin, Zhaoyue Zhang, Hui Wang, Lin Qi and Ruolin Zhou

Entropy 2018, 20(3), 198; https://doi.org/10.3390/e20030198 - 16 Mar 2018

Cited by 41 | Viewed by 5700

Abstract

In this paper, information entropy and ensemble learning based signal recognition theory and algorithms have been proposed. We have extracted 16 kinds of entropy features out of 9 types of modulated signals. The types of information entropy used are numerous, including Rényi entropy [...] Read more.

In this paper, information entropy and ensemble learning based signal recognition theory and algorithms have been proposed. We have extracted 16 kinds of entropy features out of 9 types of modulated signals. The types of information entropy used are numerous, including Rényi entropy and energy entropy based on S Transform and Generalized S Transform. We have used three feature selection algorithms, including sequence forward selection (SFS), sequence forward floating selection (SFFS) and RELIEF-F to select the optimal feature subset from 16 entropy features. We use five classifiers, including k-nearest neighbor (KNN), support vector machine (SVM), Adaboost, Gradient Boosting Decision Tree (GBDT) and eXtreme Gradient Boosting (XGBoost) to classify the original feature set and the feature subsets selected by different feature selection algorithms. The simulation results show that the feature subsets selected by SFS and SFFS algorithms are the best, with a 48% increase in recognition rate over the original feature set when using KNN classifier and a 34% increase when using SVM classifier. For the other three classifiers, the original feature set can achieve the best recognition performance. The XGBoost classifier has the best recognition performance, the overall recognition rate is 97.74% and the recognition rate can reach 82% when the signal to noise ratio (SNR) is −10 dB. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

24 pages, 1067 KiB

Open AccessArticle

Low Probability of Intercept-Based Radar Waveform Design for Spectral Coexistence of Distributed Multiple-Radar and Wireless Communication Systems in Clutter

by Chenguang Shi, Fei Wang, Sana Salous and Jianjiang Zhou

Entropy 2018, 20(3), 197; https://doi.org/10.3390/e20030197 - 16 Mar 2018

Cited by 16 | Viewed by 6069

Abstract

In this paper, the problem of low probability of intercept (LPI)-based radar waveform design for distributed multiple-radar system (DMRS) is studied, which consists of multiple radars coexisting with a wireless communication system in the same frequency band. The primary objective of the multiple-radar [...] Read more.

In this paper, the problem of low probability of intercept (LPI)-based radar waveform design for distributed multiple-radar system (DMRS) is studied, which consists of multiple radars coexisting with a wireless communication system in the same frequency band. The primary objective of the multiple-radar system is to minimize the total transmitted energy by optimizing the transmission waveform of each radar with the communication signals acting as interference to the radar system, while meeting a desired target detection/characterization performance. Firstly, signal-to-clutter-plus-noise ratio (SCNR) and mutual information (MI) are used as the practical metrics to evaluate target detection and characterization performance, respectively. Then, the SCNR- and MI-based optimal radar waveform optimization methods are formulated. The resulting waveform optimization problems are solved through the well-known bisection search technique. Simulation results demonstrate utilizing various examples and scenarios that the proposed radar waveform design schemes can evidently improve the LPI performance of DMRS without interfering with friendly communications. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

20 pages, 548 KiB

Open AccessArticle

Kullback–Leibler Divergence Based Distributed Cubature Kalman Filter and Its Application in Cooperative Space Object Tracking

by Chen Hu, Haoshen Lin, Zhenhua Li, Bing He and Gang Liu

Entropy 2018, 20(2), 116; https://doi.org/10.3390/e20020116 - 10 Feb 2018

Cited by 19 | Viewed by 4436

Abstract

In this paper, a distributed Bayesian filter design was studied for nonlinear dynamics and measurement mapping based on Kullback–Leibler divergence. In a distributed structure, the nonlinear filter becomes a challenging problem, since each sensor cannot access the global measurement likelihood function over the [...] Read more.

In this paper, a distributed Bayesian filter design was studied for nonlinear dynamics and measurement mapping based on Kullback–Leibler divergence. In a distributed structure, the nonlinear filter becomes a challenging problem, since each sensor cannot access the global measurement likelihood function over the whole network, and some sensors have weak observability of the state. To solve the problem in a sensor network, the distributed Bayesian filter problem was converted into an optimization problem by maximizing a posterior method. The global cost function over the whole network was decomposed into the sum of the local cost function, where the local cost function can be solved by each sensor. With the help of the Kullback–Leibler divergence, the global estimate was approximated in each sensor by communicating with its neighbors. Based on the proposed distributed Bayesian filter structure, a distributed cubature Kalman filter (DCKF) was proposed. Finally, a cooperative space object tracking problem was studied for illustration. The simulation results demonstrated that the proposed algorithm can solve the issues of varying communication topology and weak observability of some sensors. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

16 pages, 6308 KiB

Open AccessArticle

Adaptive Waveform Design for Cognitive Radar in Multiple Targets Situation

by Xiaowen Zhang and Xingzhao Liu

Entropy 2018, 20(2), 114; https://doi.org/10.3390/e20020114 - 9 Feb 2018

Cited by 10 | Viewed by 4867

Abstract

In this paper, the problem of cognitive radar (CR) waveform optimization design for target detection and estimation in multiple extended targets situations is investigated. This problem is analyzed in signal-dependent interference, as well as additive channel noise for extended targets with unknown target [...] Read more.

In this paper, the problem of cognitive radar (CR) waveform optimization design for target detection and estimation in multiple extended targets situations is investigated. This problem is analyzed in signal-dependent interference, as well as additive channel noise for extended targets with unknown target impulse response (TIR). To address this problem, an improved algorithm is employed for target detection by maximizing the detection probability of the received echo on the promise of ensuring the TIR estimation precision. In this algorithm, an additional weight vector is introduced to achieve a trade-off among different targets. Both the estimate of TIR and transmit waveform can be updated at each step based on the previous step. Under the same constraint on waveform energy and bandwidth, the information theoretical approach is also considered. In addition, the relationship between the waveforms that are designed based on the two criteria is discussed. Unlike most existing works that only consider single target with temporally correlated characteristics, waveform design for multiple extended targets is considered in this method. Simulation results demonstrate that compared with linear frequency modulated (LFM) signal, waveforms designed based on maximum detection probability and maximum mutual information (MI) criteria can make radar echoes contain more multiple-target information and improve radar performance as a result. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

1101 KiB

Open AccessArticle

Bayesian Nonlinear Filtering via Information Geometric Optimization

by Yubo Li, Yongqiang Cheng, Xiang Li, Hongqiang Wang, Xiaoqiang Hua and Yuliang Qin

Entropy 2017, 19(12), 655; https://doi.org/10.3390/e19120655 - 1 Dec 2017

Cited by 10 | Viewed by 4446

Abstract

In this paper, Bayesian nonlinear filtering is considered from the viewpoint of information geometry and a novel filtering method is proposed based on information geometric optimization. Under the Bayesian filtering framework, we derive a relationship between the nonlinear characteristics of filtering and the [...] Read more.

In this paper, Bayesian nonlinear filtering is considered from the viewpoint of information geometry and a novel filtering method is proposed based on information geometric optimization. Under the Bayesian filtering framework, we derive a relationship between the nonlinear characteristics of filtering and the metric tensor of the corresponding statistical manifold. Bayesian joint distributions are used to construct the statistical manifold. In this case, nonlinear filtering can be converted to an optimization problem on the statistical manifold and the adaptive natural gradient descent method is used to seek the optimal estimate. The proposed method provides a general filtering formulation and the Kalman filter, the Extended Kalman filter (EKF) and the Iterated Extended Kalman filter (IEKF) can be seen as special cases of this formulation. The performance of the proposed method is evaluated on a passive target tracking problem and the results demonstrate the superiority of the proposed method compared to various Kalman filter methods. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

1190 KiB

Open AccessArticle

The Geometry of Signal Detection with Applications to Radar Signal Processing

by Yongqiang Cheng, Xiaoqiang Hua, Hongqiang Wang, Yuliang Qin and Xiang Li

Entropy 2016, 18(11), 381; https://doi.org/10.3390/e18110381 - 25 Oct 2016

Cited by 50 | Viewed by 7324

Abstract

The problem of hypothesis testing in the Neyman–Pearson formulation is considered from a geometric viewpoint. In particular, a concise geometric interpretation of deterministic and random signal detection in the philosophy of information geometry is presented. In such a framework, both hypotheses and detectors [...] Read more.

The problem of hypothesis testing in the Neyman–Pearson formulation is considered from a geometric viewpoint. In particular, a concise geometric interpretation of deterministic and random signal detection in the philosophy of information geometry is presented. In such a framework, both hypotheses and detectors can be treated as geometrical objects on the statistical manifold of a parameterized family of probability distributions. Both the detector and detection performance are geometrically elucidated in terms of the Kullback–Leibler divergence. Compared to the likelihood ratio test, the geometric interpretation provides a consistent but more comprehensive means to understand and deal with signal detection problems in a rather convenient manner. Example of the geometry based detector in radar constant false alarm rate (CFAR) detection is presented, which shows its advantage over the classical processing method. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

510 KiB

Open AccessArticle

The Constant Information Radar

by Bryan Paul and Daniel W. Bliss

Entropy 2016, 18(9), 338; https://doi.org/10.3390/e18090338 - 19 Sep 2016

Cited by 16 | Viewed by 8776

Abstract

The constant information radar, or CIR, is a tracking radar that modulates target revisit time by maintaining a fixed mutual information measure. For highly dynamic targets that deviate significantly from the path predicted by the tracking motion model, the CIR adjusts by illuminating [...] Read more.

The constant information radar, or CIR, is a tracking radar that modulates target revisit time by maintaining a fixed mutual information measure. For highly dynamic targets that deviate significantly from the path predicted by the tracking motion model, the CIR adjusts by illuminating the target more frequently than it would for well-modeled targets. If SNR is low, the radar delays revisit to the target until the state entropy overcomes noise uncertainty. As a result, we show that the information measure is highly dependent on target entropy and target measurement covariance. A constant information measure maintains a fixed spectral efficiency to support the RF convergence of radar and communications. The result is a radar implementing a novel target scheduling algorithm based on information instead of heuristic or ad hoc methods. The CIR mathematically ensures that spectral use is justified. Full article

(This article belongs to the Special Issue Radar and Information Theory)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Radar and Information Theory

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI