In this letter, an improved version of the popular two-stage weighted least squares (TSWLS) algorithm is presented to determine the position and velocity of a moving source using time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements in a wireless sensor network. A closed-form solution is obtained from the minimization of the weighted least squares (WLS) criterion in each stage. The estimator accuracy is shown analytically to attain the Cramer-Rao lower bound (CRLB) under the small Gaussian noise assumption. Numerical simulations are included to support and corroborate the theoretical developments.

Abstract—In recent years, convolutional neural networks (CNNs) have drawn considerable attention for the analysis of synthetic aperture radar (SAR) data. In this study, major subareas of SAR data analysis that have been tackled by CNNs are systematically reviewed, such as automatic target recognition, land use and land cover classification, segmentation, change detection, object detection and image denoising. Special emphasis has been given to practical techniques such as data augmentation and transfer learning. Complex-valued CNNs, which have been introduced to exploit phase information embedded in SAR complex images, have also been extensively reviewed. To conclude this review paper, open challenges and future research directions are highlighted.

The closed set assumption in conventional classifiers, such as the Softmax, constrains deep networks to select an output from the given known classes. However, classification in a real-world scenario should account for open sets where a new class of targets, which has not been included in the training phase, can easily confuse the classifier. Therefore, it is necessary to not only correctly classify known classes, but also fundamentally deal with unknown ones. In this paper, we extend the Openmax approach, which has been introduced for open set recognition in the optical domain, by offering solutions to its inherent limitations. The motivation behind the work is to propose a more accurate and robust classifier for the open set recognition problem in synthetic aperture radar (SAR) images, without having any prior knowledge about the incoming unknown data. A number of real data experiments are conducted to demonstrate the effectiveness of the proposed method on the basis of selected performance metrics. In particular, the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset, which contains SAR images of ten military vehicles, is used for training and inference of a Convolutional Neural Network (CNN), with an option to recognize open set images.

Most of the existing Non-Cooperative Target Recognition (NCTR) systems follow the “closed world” assumption, i.e., they only work with what was previously observed. Nevertheless, the real world is relatively “open” in the sense that the knowledge of the environment is incomplete. Therefore, unknown targets can feed the recognition system at any time while it is operational. Addressing this issue, the Openmax classifier has been recently proposed in the optical domain to make convolutional neural networks (CNN) able to reject unknown targets. There are some fundamental limitations in the Openmax classifier that can end up with two potential errors: (1) rejecting a known target and (2) classifying an unknown target. In this paper, we propose a new classifier to increase the robustness and accuracy. The proposed classifier, which is inspired by the limitations of the Openmax classifier, is based on proportional similarity between the test image and different training classes. We evaluate our method by radar images of man-made targets from the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset. Moreover, a more in-depth discussion on the Openmax hyper-parameters and a detailed description of the Openmax functioning are given.

Integrating an automatic target recognition (ATR) system into real-world applications presents a challenge as it may frequently encounter new samples from unseen classes. To overcome this challenge, it is necessary to adopt incremental learning, which enables the continuous acquisition of new knowledge while retaining previous knowledge. This paper introduces a novel, multi-purpose interpretability metric for ATR systems that employ synthetic aperture radar (SAR) images. The metric leverages the Local Interpretable Model-Agnostic Explanation (LIME) algorithm, enhancing human decision-making by providing a secondary measure alongside the conventional classification score. Additionally, the proposed metric is employed to analyze the robustness of Convolutional Neural Networks (CNNs) by examining the impact of target features and irrelevant background correlations on recognition results. Finally, we demonstrate the effectiveness of the proposed metric in the context of incremental learning. By utilizing the proposed interpretability metric, we select exemplars in an incremental learning scenario, resulting in improved performance and showcasing the application potential of our proposed methodology. The network is fine-tuned sequentially with unknown samples recognized by the Openmax classifier and exemplars from the old known classes, which are selected based on the proposed interpretability metric. The effectiveness of this approach is demonstrated using the publicly available MSTAR dataset.