Joint Diagonalization Applied to the Detection and Discrimination of Unexploded Ordnance

Efforts to discriminate buried unexploded ordnance from harmless surrounding clutter are often hampered by the uncertainty in the number of buried targets that produce a given detected signal. We present a technique that helps determine that number with no need for data inversion. The procedure is based on the joint diagonalization of a set of multistatic response (MSR) matrices measured at different time gates by a time-domain electromagnetic induction sensor. In particular, we consider the Naval Research Laboratory’s Time-Domain Electromagnetic Multisensor Towed Array Detection System (TEMTADS), which consists of a 5×5 square grid of concentric transmitter/receiver pairs. The diagonalization process itself generalizes one of the standard procedures for extracting the eigenvalues of a single matrix; in terms of execution time, it is comparable to diagonalizing the matrices one by one. We present the method, discuss and illustrate its mathematical basis and physical meaning, and apply it to several actual measurements carried out with TEMTADS at a test stand and in the field at the former Camp Butner in North Carolina. We find that each target in a measurement is associated with a set of nonzero time-dependent MSR eigenvalues (usually three), which enables estimation of the number of targets interrogated. These eigenvalues have a characteristic shape as a function of time that does not change with the location and orientation of the target relative to the sensor. We justify analytically and empirically that symmetric targets have pairs of eigenvalues with constant ratios between them

THE GERMAN-GEORGIAN MODEL OF PENALTY REGULATION (Comparative-Legal Analysis)

The present article reviews the Penalty as an additional claim securing tool that has been adopted in private or public-legal relations and nowadays, it is characteristic to the laws of all countries belonging to the Roman-German (continental) or Anglo-American systems of law. This is why the thorough study of the issue is performed by making the focus on the comparative-legal analysis of the Georgian model and the German system of law. It is noteworthy that the Georgian legislation has been significantly amended with regards to the Penalty. Since 2017, the Civil Code of Georgia has provided a new definition of a statutory penalty (article 625) within the loan obligations, which was positioned on the 150%-scale that was inappropriate and unreasonable from the very beginning, and thus, it finally diverged from the overall practice adopted in the European countries. The article provides the review of a complex of issues like the need for defining the form of a penalty, the prerequisites for charging and canceling a penalty within the enforcement of decisions, court’s rulings on inappropriately high penalties, criticism of a statutory penalty determined under the new standard of article 625 of the Civil Code of Georgia, and the discretionary authorities of the judge to rule an inappropriately high penalty. The article also presents the analysis of a generalized practice applied by judicial authorities, the analysis of high-profile court judgments, and along with outlining the flaws, the article has also drafted interim findings and recommendations, which are crucially important for harmonizing and improving the law

Realistic Subsurface Anomaly Discrimination Using Electromagnetic Induction and an SVM Classifier

The environmental research program of the United States military has set up blind tests for detection and discrimination of unexploded ordnance. One such test consists of measurements taken with the EM-63 sensor at Camp Sibert, AL. We review the performance on the test of a procedure that combines a field-potential (HAP) method to locate targets, the normalized surface magnetic source (NSMS) model to characterize them, and a support vector machine (SVM) to classify them. The HAP method infers location from the scattered magnetic field and its associated scalar potential, the latter reconstructed using equivalent sources. NSMS replaces the target with an enclosing spheroid of equivalent radial magnetization whose integral it uses as a discriminator. SVM generalizes from empirical evidence and can be adapted for multiclass discrimination using a voting system. Our method identifies all potentially dangerous targets correctly and has a false-alarm rate of about 5%.</p