The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

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Basic Biomechanics of the Musculoskeletal System

This paper considers the problem of time difference-of-arrival (TDOA) source localization when the TDOA measurements from multiple disjoint sources are subject to the same sensor position displacements from the available sensor positions. This is a challenging problem and closed-form solution with good localization accuracy has yet to be found. This paper proposes an estimator that can achieve this purpose. The proposed algorithm jointly estimates the unknown source and sensor positions to take the advantage that the TDOAs from different sources have the same sensor position displacements. The joint estimation is a highly nonlinear problem due to the coupling of source and sensor positions in the measurement equations. We introduce the novel idea of hypothesized source locations in the algorithm development to enable the formulation of psuedolinear equations, thereby leading to the establishment of closed-form solution for source location estimates. Besides the advantage of closed-form, the newly developed algorithm is shown analytically, under the condition that the TDOA measurement noise and the sensor position errors are sufficiently small, to reach the CRLB accuracy. For clarity, the localization of two disjoint sources is used in the algorithm development. The developed algorithm is then examined under the special case of a single source and extended to the more general case of more than two unknown sources. The theoretical developments are supported by simulations.

An Approximately Efficient TDOA Localization Algorithm in Closed-Form for Locating Multiple Disjoint Sources With Erroneous Sensor Positions

This paper reviews the topic of true time delay (TTD) and its importance and implications in wideband imaging phased arrays. The paper describes an early analog version of TTD using the “Rotman lens,” discusses various architectures, and talks about photonic implementations. Also emphasized are the differences in design between narrowband arrays which are calibrated at individual frequencies and wideband imaging arrays where TTD is necessary.

True Time Delay in Phased Arrays

Digital beamforming (DBF) has long been heralded as the next frontier in phased array technology, and not without reason. The digitization of transmit and receive signals at the element level opens the door to new processing and beamforming schemes and promises to deliver maximum flexibility and unprecedented dynamic range in large systems. However, it is not without inherent technological risks and practical challenges associated with the amount of data to process and the use of less sophisticated transceivers. This paper provides broad overviews of several interrelated aspects of the resulting DBF trade spaces for these systems. In particular, emerging concepts are highlighted for the roles and interconnection of distributed beamforming/processing for fixed and adaptive beamforming. These are then related to digital array calibration mechanisms that can potentially reduce the need for data- and processing-intensive beamforming algorithms.

Digital Phased Arrays: Challenges and Opportunities

Efficient utilization of resources is an important issue in the operation of modern radar systems. This paper develops a generalized framework for the radar task scheduling problem as an optimization model. In the proposed method, all radar task parameters are treated as variables, thereby allowing greater scheduling flexibility and the ability to handle more targets using a single radar. An efficient heuristic scheduling method is also proposed and computational results are presented to asses the performance of the proposed method. Note to Practitioners - This paper deals with scheduling a sequence of tasks for a radar system in a limited time-window. Previous work in the literature has addressed this problem by modeling each task as having a fixed duration. In an earlier paper of one of the authors, the task duration was modeled as a variable, which allowed for some flexibility in the task duration, enabling enhanced utilization of the radar timeline. However, a simplified radar task model was used that did not account for the internal structure of a radar task. This work adds a practical dimension by further extending the radar task model to allow for some flexibility in the task duration and also explicitly account for the internal structure of the task. It is shown that utilization of the radar timeline can be thus enhanced through monitoring the interplay of adjusting the dwell times of the internal components of a task.

Variable Dwell Time Task Scheduling for Multifunction Radar

This paper presents the first comprehensive review on vigilance enhancement using both conventional and unconventional means, and further discusses the resulting contradictory findings. It highlights the key differences observed between the research findings and argues that variations of the experimental protocol could be a significant contributing factor towards such contradictory results. Furthermore, the paper reveals the effectiveness of unconventional means of enhancement in significant reduction of vigilance decrement compared to conventional means. Meanwhile, a discussion on the challenges of enhancement techniques is presented, with several suggested recommendations and alternative strategies to maintain an adequate level of vigilance for the task at hand. Additionally, this review provides evidence in support of the use of unconventional means of enhancement on vigilance studies, regardless of their practical challenges.

https://www.mdpi.com/2076-3425/9/8/178/pdf

Vigilance Decrement and Enhancement Techniques: A Review

Unlike a conventional phased array that offers directivity only in the angle domain, a frequency diverse array (FDA) is capable of producing a beampattern that is dependent on both angle and range. In this letter, a transmit beamforming method for an FDA is proposed that uses logarithmic frequency increments that have a nonuniform spacing. Compared to existing methods, the proposed architecture offers an improved range–angle localization with reduced sidelobe values. Simulations results for single and multiple target beampatterns are shown in order to assess the efficacy of the proposed architecture.

Frequency Diverse Array Beamforming Using Nonuniform Logarithmic Frequency Increments

This paper describes the design of a dual-channel S-band digital radar test bed. The test bed combines stretch processing with a novel and cost-effective hardware architecture that enables it to achieve an in-band dynamic range of 60 dB over 600 MHz of instantaneous bandwidth. The dual digital receiver channels allow for adaptive digital beamforming which can be used to mitigate a directional source of interference. Experimental test and verification results are presented to demonstrate system performance.

A Low-Cost High-Performance Digital Radar Test Bed

This paper studies direction finding of electromagnetic energy sources using passive vector sensor arrays whose manifold is only nominally known. The problem of direction finding is studied in the context of an airborne array, thus facilitating the observation of a ground-based source from multiple look-angles. A calibration algorithm explicitly accounting for the polarization diverse nature of the vector sensor is developed. It is also shown that the direction finding performance provided by a conventional array calibration algorithm is greatly enhanced with usage of the proposed polarization diverse calibration algorithm

Hasan Mir

Papers

Variable Dwell Time Task Scheduling for Multifunction Radar

Vigilance Decrement and Enhancement Techniques: A Review

Frequency Diverse Array Beamforming Using Nonuniform Logarithmic Frequency Increments

A Low-Cost High-Performance Digital Radar Test Bed

Passive Direction Finding Using Airborne Vector Sensors in the Presence of Manifold Perturbations