Information geometry is a new mathematical discipline which applies the methodology of differential geometry to statistics. Therefore, families of exponential distributions are considered as embedded manifolds, called statistical manifolds. This includes so important families like the multivariate normal or the gamma distributions. Fisher information — well known in information theory — becomes a metric on statistical manifolds. The Fisher information metric enables a hyperbolic structure on the multivariate normal distributions. Information geometry offers new methods for hypothesis testings, estimation theory or stochastic filtering. These can be used in engineering areas like signal processing or video processing or finance.

http://ieeexplore.ieee.org/iel5/6423297/6450609/06450636.pdf

Information geometry and its applications

Crami??r-Rao bounds on estimation accuracy are established for estimation problems on arbitrary manifolds in which no set of intrinsic coordinates exists. The frequently encountered examples of estimating either an unknown subspace or a covariance matrix are examined in detail. The set of subspaces, called the Grassmann manifold, and the set of covariance (positive-definite Hermitian) matrices have no fixed coordinate system associated with them and do not possess a vector space structure, both of which are required for deriving classical Crami??r-Rao bounds. Intrinsic versions of the Crami??r-Rao bound on manifolds utilizing an arbitrary affine connection with arbitrary geodesics are derived for both biased and unbiased estimators. In the example of covariance matrix estimation, closed-form expressions for both the intrinsic and flat bounds are derived and compared with the root-mean-square error (RMSE) of the sample covariance matrix (SCM) estimator for varying sample support K. The accuracy bound on unbiased covariance matrix estimators is shown to be about (10/log 10)n/K 1/2 dB, where n is the matrix order. Remarkably, it is shown that from an intrinsic perspective, the SCM is a biased and inefficient estimator and that the bias term reveals the dependency of estimation accuracy on sample support observed in theory and practice. The RMSE of the standard method of estimating subspaces using the singular value decomposition (SVD)is compared with the intrinsic subspace Crami??r-Rao bound derived in closed form by varying both the signal-to-noise ratio (SNR) of the unknown p-dimensional subspace and the sample support. In the simplest case, the Crami??r-Rao bound on subspace estimation accuracy is shown to be about (p(n - p)1/2 K-1/2SN-1/2 rad for p-dimensional subspaces. It is seen that the SVD-based method yields accuracies very close to the Crami??r-Rao bound, esta blishing that the principal invariant subspace of a random sample provides an excellent estimator of an unknown subspace. The analysis approach developed is directly applicable to many other estimation problems on manifolds encountered in signal processing and elsewhere, such as estimating rotation matrices in computer vision and estimating subspace basis vectors in blind source separation.

Covariance, Subspace, and Intrinsic CramrRao Bounds

There is an urgent need for radar-measured data to tackle key technologies of radar maritime target detection. The ‘‘Sea-detecting X-band Radar and Data Acquisition Program’’, proposed in 2019, aims to obtain data through radar experiments and share them publicly. In 2020, the program continued to advance and conducted several experiments in three aspects, namely, Radar Cross-Section (RCS) calibration of radar targets, detection of sea clutter and target under different sea conditions, as well as detection and tracking of maneuvering targets in sea. The measurement data of the stainless steel sphere calibrator at different distances in radar slow-scanning mode, sea clutter in radar staring mode in different directions, sea target in radar staring mode, and marine engine speedboat in radar scanning mode are obtained. In addition, wind and wave data, data from the Automatic Identification System (AIS) of targets, visible/infrared data, and other associated sensor data are synchronously obtained.

Annual Progress of the Sea-detecting X-band Radar and Data Acquisition Program

The space environment has become highly congested due to the increasing space debris, seriously threatening the safety of orbiting spacecraft. Space-based situational awareness, as a comprehensive capability of threat knowledge, analysis, and decision-making, is of significant importance to ensure space security and maintain normal order. Various space situational awareness systems have been designed and launched. Data acquisition, target recognition, and monitoring constituting key technologies make major contributions, and various advanced algorithms are explored as technical supports. However, comprehensive reviews of these technologies and specific algorithms rarely emerge. It disadvantages the future development of space situational awareness. Therefore, this paper further reviews and analyzes research advancements in key technologies for space situational awareness, emphasizing target recognition and monitoring. Many mature and emerging methods are presented for these technologies while discussing application advantages and limitations. Specially, the research prospects of multiagent and synergetic constellation technologies are expected for future situational awareness. This paper indicates the future directions of the key technologies, aiming to provide references for space-based situational awareness to realize space sustainability.

https://downloads.spj.sciencemag.org/space/2022/9802793.pdf

Research Advancements in Key Technologies for Space-Based Situational Awareness

This letter proposes the use of neural networks to realize the passive localization by signal time difference of arrival (TDOA). In the face of multiple complex targets with radiation sources in a specific area, real-time localization is an urgent problem. In this letter, positions of the known targets from the prior data are obtained and their time difference is calculated, which will be connected as data pairs and input to the neural network trained to obtain a corresponding model. Subsequently, unknown targets can be localized by this network. It is verified that the localization accuracy of the algorithm is reliable and its robustness is higher than that of traditional algorithms. The proposed method also shows that great reduction of operation time depending on the previous network training can complete real-time goals.

Real-Time Passive Localization of TDOA via Neural Networks

Clutter suppression in heterogeneous environments is a serious challenge for airborne radar. To address this problem, a matrix-manifold-based clutter suppression method is proposed. First, the distributions of training data in heterogeneous environments are analyzed, while the received data are characterized on a Riemannian manifold of Hermitian positive definite matrices. It is indicated that the training data with different distributions with the same power are separated, whereas data with the same distribution are closer together. This implies that the underlying geometry of the data can be better revealed by manifolds than by Euclidean space. Based on these properties, homogeneous training data are selected by establishing a binary hypothesis test such that the negative effects of the use of heterogeneous samples are alleviated. Moreover, as exploiting a geometric metric on manifolds to reveal the underlying information of data, experimental results on both simulated and real data validate that the proposed method has a superior performance with small sample support.

Heterogeneous Clutter Suppression for Airborne Radar STAP Based on Matrix Manifolds

In radar target detection, constant false alarm rate (CFAR), which stands for the adaptive threshold adjustment with variation of clutter to maintain the constant probability of false alarm during the detection, plays an important role. Matrix CFAR detection performed on the manifold of Hermitian positive-definite (HPD) covariance matrices is an efficient detection method that is based on information geometry. However, the HPD covariance matrix, which is constructed by a small bunch of pulses, describes the correlations among received data and suffers from severe information redundancy that limits the improvement of detection performance. This paper proposes a Principal Component Analysis (PCA) based matrix CFAR detection method for dealing with the point target detection problems in clutter. The proposed method can not only reduce dimensionality of HPD covariance matrix, but also reduce the redundant information and enhance the distinguishability between target and clutter. We first apply PCA to the cell under test, and construct a transformation matrix to map higher-dimensional matrix space to a lower-dimensional matrix space. Subsequently, the corresponding detection statistics and detection decision on matrix manifold are derived. Meanwhile, the corresponding signal-to-clutter ratio (SCR) is improved. Finally, the simulation experiment and real sea clutter data experiment show that the proposed method can achieve a better detection performance.

PCA-Based Matrix CFAR Detection for Radar Target.

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.

https://www.mdpi.com/1099-4300/21/1/10/pdf/1

Vector Bundle Model of Complex Electromagnetic Space and Change Detection

Information geometry is the study of the intrinsic geometric properties of manifolds consisting of a probability distribution and provides a deeper understanding of statistical inference. Based on this discipline, this letter reports on the influence of the signal processing on the geometric structure of the statistical manifold in terms of estimation issues. This letter defines the intrinsic parameter submanifold, which reflects the essential geometric characteristics of the estimation issues. Moreover, the intrinsic parameter submanifold is proven to be a tighter one after signal processing. In addition, the necessary and sufficient condition of invariant signal processing of the geometric structure, i.e., isometric signal processing, is given. Specifically, considering the processing with the linear form, the construction method of linear isometric signal processing is proposed, and its properties are presented in this letter.

https://www.mdpi.com/1099-4300/21/4/332/pdf

Isometric Signal Processing under Information Geometric Framework.

Data-driven deep learning has been well applied in radar target detection. However, the performance of the detection network is severely degraded when the detection scene changes, since the trained network with the data from one scene is not suitable for another scene with different data distribution. In order to address this problem, an adaptive network detector combined with scene classification is proposed in this paper. Aiming at maximizing the posterior probability of the feature vectors, the scene classification network is arranged to control the output ratio of a group of detection sub-networks. Due to the uncertainty of classification error rate in traditional machine learning, the classifier with a controllable false alarm rate is constructed. In addition, a new network training strategy, which freezes the parameters of the scene classification network and selectively fine-tunes the parameters of detection sub-networks, is proposed for the adaptive network structure. Comprehensive experiments are carried out to demonstrate that the proposed method guarantees a high detection probability when the detection scene changes. Compared with some classical detectors, the adaptive network detector shows better performance.

Adaptive Network Detector for Radar Target in Changing Scenes

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