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A Reduced-complexity Trajectory Generation Algorithm for Three-Body Regimes With Minimum Predefined Data

IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2025年第2期61卷 2078-2093页

作者： Baker-McEvilly, Brian Aluvihare, Hansaka Perera, Sirani M. Canales, David Embry Riddle Aeronaut Univ Dept Aerosp Engn Daytona Beach FL 32703 USA Embry Riddle Aeronaut Univ Dept Math Daytona Beach FL 32703 USA

Computational limitations and Big Data analysis pose challenges in seeking efficient techniques to predict trajectories in three-body dynamics. Thus, a reduced-complexity classical algorithm is proposed utilizing predefined spacecraft's position and velocity data to achieve precise and accurate orbital trajectories of the spacecraft within three-body dynamics. The proposed algorithm seamlessly solves polynomial interpolation along with the boundary and interior conditions without the need for the spacecraft's acceleration data. Once the algorithm is derived, it will be tested across a diverse variety of periodic trajectories in the Earth-Moon system. Moreover, a comparative analysis is performed to evaluate the time complexity of the proposed algorithm compared with conventional orbit propagators. Finally, the proposed algorithm will be utilized and extended to learn and update distant retrograde orbits (DRO) while training a neural network with several initial conditions composing minimum predefined data. After the training is done, the neural network is used to accurately predict DRO trajectories for a given initial condition, demonstrating the exceptional accuracy and effectiveness of the proposed learning process.

关键词： Trajectory Space vehicles Moon Earth Polynomials Heuristic algorithms Accuracy Cislunar complexity and performance of algorithms circular restricted three-body problem (CR3BP) machine learning (ML) minimum predefined data neural networks (NN) orbital trajectories sparse matrices

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A Low-complexity LSTM Network to Realize Multibeam Beamforming

A Low-Complexity LSTM Network to Realize Multibeam Beamformi...

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2024 International Conference on Wireless for Space and Extreme Environments

作者： Aluvihare, Hansaka Shanahan, Carina Perera, Sirani M. Sivasankar, Sivakumar Kumarasiri, Umesha Madanayake, Arjuna Li, Xianqi Embry Riddle Aeronaut Univ Dept Math Daytona Beach FL 32703 USA Florida Int Univ Dept Elect & Comp Engn Miami FL 33174 USA Florida Inst Technol Dept Math & Syst Engn Melbourne FL 32901 USA

ISBN: (纸本)9798350351118;9798350351125

Massive data structures can be embedded in the form of weight matrices, enabling to design of neural networks with low-complexity learning algorithms. These data can be organized in rows of matrices, containing progressive phase shifts for a specific beam, along with input and output vectors consisting of time-domain signals. In our previous work, we have identified that multi-beam beamformers based on true-time-delays (TTDs) can be mathematically formulated as the elements of delay Vandermonde matrices (DVM). Thus, by adopting a frequency domain variable, we can express TTDs of time delay data in terms of elements of the DVM. Learning from prior work, we propose to present a low-complexity neural network to realize multibeam beamforming leveraging a novel LSTM network. The goal of our work is to reduce the complexity of the multibeam beamforming algorithm from O((NL)-L-2) to O((NL)-L-s), where 1 < s < 2, by imposing factorization of the DVM in an LSTM network having L layers.

关键词： Sparse Matrices delay Vandermonde matrices complexity and performance of algorithms wireless communication Multi-beam beamformers Neural networks Lowcomplexity Networks LSTM

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Sparse Matrix Based Low-complexity, Recursive, and Radix-2 algorithms for Discrete Sine Transforms

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IEEE ACCESS 2021年 9卷 141181-141198页

作者： Perera, Sirani M. Lingsch, Levi E. Embry Riddle Aeronaut Univ Dept Math Daytona Beach FL 32114 USA Embry Riddle Aeronaut Univ Dept Aerosp Engn Daytona Beach FL 32114 USA

This paper presents factorizations of each discrete sine transform (DST) matrix of types I, II, III, and IV into a product of sparse, diagonal, bidiagonal, and scaled orthogonal matrices. Based on the proposed matrix factorization formulas, reduced multiplication complexity, recursive, and radix-2 DST I-IV algorithms are presented. We will present the lowest multiplication complexity DST-IV algorithm in the literature. The paper fills a gap in the self-recursive, exact, and radix-2 DST I-IIII algorithms executed via diagonal, bidiagonal, scaled orthogonal, and simple matrix factors for any input n=2(t) (t >= 1). The paper establishes a novel relationship between DST-II and DST-IV matrices using diagonal and bidiagonal matrices. Similarly, a novel relationship between DST-I and DST-III matrices is proposed using sparse and diagonal matrices. These interweaving relationships among DST matrices enable us to bridge the existing factorizations of the DST matrices with the proposed factorization formulas. We present signal flow graphs to provide a layout for realizing the proposed algorithms in DST-based integrated circuit designs. Additionally, we describe an implementation of algorithms based on the proposed DST-II and DST-III factorizations within a double random phase encoding (DRPE) image encryption scheme.

关键词： Discrete sine transforms self/completely recursive and radix-2 algorithms complexity and performance of algorithms sparse and orthogonal matrices signal flow graphs

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Multi-Beam Beamforming-Based ML Algorithm to Optimize the Routing of Drone Swarms

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DRONES 2024年第2期8卷 57-57页

作者： Myers, Rodman J. Perera, Sirani M. Mclewee, Grace Huang, David Song, Houbing Florida Southern Coll Dept Comp Sci Lakeland FL 33801 USA Embry Riddle Aeronaut Univ Dept Math Daytona Beach FL 32114 USA Coastal Carolina Univ Dept Comp Sci Conway SC 29528 USA Univ Florida Dept Comp & Informat Sci & Engn Gainesville FL 32611 USA Univ Maryland Baltimore Cty Dept Informat Syst Baltimore MD 21250 USA

The advancement of wireless networking has significantly enhanced beamforming capabilities in Autonomous Unmanned Aerial Systems (AUAS). This paper presents a simple and efficient classical algorithm to route a collection of AUAS or drone swarms extending our previous work on AUAS. The algorithm is based on the sparse factorization of frequency Vandermonde matrices that correspond to each drone, and its entries are determined through spatiotemporal data of drones in the AUAS. The algorithm relies on multibeam beamforming, making it suitable for large-scale AUAS networking in wireless communications. We show a reduction in the arithmetic and time complexities of the algorithm through theoretical and numerical results. Finally, we also present an ML-based AUAS routing algorithm using the classical AUAS algorithm and feed-forward neural networks. We compare the beamformed signals of the ML-based AUAS routing algorithm with the ground truth signals to minimize the error between them. The numerical error results show that the ML-based AUAS routing algorithm enhances the accuracy of the routing. This error, along with the numerical and theoretical results for over 100 drones, provides the basis for the scalability of the proposed ML-based AUAS algorithms for large-scale deployments.

关键词： drone swarms UAS MIMO communication complexity and performance of algorithms wireless communications multi-beam beamforming ML algorithm ANN

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Efficient and Self-Recursive Delay Vandermonde Algorithm for Multi-Beam Antenna Arrays

IEEE OPEN JOURNAL OF SIGNAL PROCESSING

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IEEE OPEN JOURNAL OF SIGNAL PROCESSING 2020年 1卷 64-76页

作者： Perera, Sirani M. Madanayake, Arjuna Cintra, Renato J. Embry Riddle Aeronaut Univ Dept Math Daytona Beach FL 32114 USA Florida Int Univ Dept Elect & Comp Engn Miami FL 33174 USA Univ Fed Pernambuco Dept Estat BR-50711970 Recife PE Brazil Univ Calgary Dept Elect & Comp Engn Calgary AB T2N 1N4 Canada

This paper presents a self-contained factorization for the delay Vandermonde matrix (DVM), which is the super class of the discrete Fourier transform, using sparse and companion matrices. An efficient DVM algorithm is proposed to reduce the complexity of radio-frequency (RF) N-beam analog beamforming systems. There exist applications for wideband multi-beam beamformers in wireless communication networks such as 5G/6G systems, system capacity can be improved by exploiting the improvement of the signal to noise ratio (SNR) using coherent summation of propagating waves based on their directions of propagation. The presence of a multitude of RF beams allows multiple independent wireless links to be established at high SNR, or used in conjunction with multiple-input multiple-output (MIMO) wireless systems, with the overall goal of improving system SNR and therefore capacity. To realize such multi-beam beamformers at acceptable analog circuit complexities, we use sparse factorization of the DVM in order to derive a low arithmetic complexity DVM algorithm. The paper also establishes an error bound and stability analysis of the proposed DVM algorithm. The proposed efficient DVM algorithm is aimed at implementation using analog realizations. For purposes of evaluation, the algorithm can be realized using both digital hardware as well as software defined radio platforms.

关键词： Delay vandermonde matrix efficient algorithms self-recursive algorithms complexity and performance of algorithms approximation algorithms wireless communications beamforming software defined radio

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Efficient Split-Radix and Radix-4 DCT algorithms and Applications 1

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Conference on Analysis of Experimental algorithms (SEA2)

作者： Perera, Sirani M. Silverio, Daniel Ogle, Austin Embry Riddle Aeronaut Univ Daytona Beach FL 32114 USA

ISBN: (数字)9783030340292

ISBN: (纸本)9783030340292;9783030340285

This paper proposes efficient split-radix and radix-4 Discrete Cosine Transform (DCT) of types II/III algorithms. The proposed fast split-radix and radix-4 algorithms extend the previous work on the lowest multiplication complexity, self-recursive, radix-2 DCT II/III algorithms. The paper also addresses the self-recursive and stable aspects of split-radix and radix-4 DCT II/III algorithms having simple, sparse, and scaled orthogonal factors. Moreover, the proposed split-radix and radix4 algorithms attain the lowest theoretical multiplication complexity and arithmetic complexity for 8-point DCT II/III matrices. The factorization corresponding to the proposed DCT algorithms contains sparse and scaled orthogonal matrices. Numerical results are presented for the arithmetic complexity comparison of the proposed algorithms with the known fast and stable DCT algorithms. Execution time of the proposed algorithms is presented while verifying the connection to the order of the arithmetic complexity. Moreover, we will show that the execution time of the proposed split-radix and radix-4 algorithms are more efficient than the radix-2 DCT algorithms. Finally, the implementations of the proposed DCT algorithms are stated using signal-flow graphs.

关键词： Discrete cosine transforms Sparse and orthogonal factors Split-radix and radix-4 algorithms Self recursive algorithms complexity and performance of algorithms Signal flow graphs

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