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Iterative computing algorithms implemented in FPGA using ALTERA_CORDIC library as an example

Procedia Computer Science 2024年 246卷 2380-2389页

作者： Paweł Poczekajło Koszalin University of Technology. ul Śniadeckich 2 75-453 Koszalin Poland

The article discusses the general issues of implementing pipelined and iterative algorithms. These are typical solutions for engineering algorithms implemented in hardware like reprogrammable systems. The authors focused on the implementation of such algorithms in field-programmable gate array (FPGA) circuits. Key aspects and advantages of pipelined processing were discussed. The focus was on an example CORDIC algorithm. Analyses of the iterative implementation using the ALTERA_CORDIC library were performed. Key parameters such as frequency and circuit occupancy were measured. Also, the obtained results were compared with the exact values - the errors were determined. Realizations based on 8-, 12- and 16-bits of fractional in fixed-position notation were analyzed.

关键词： iterative algorithms pipelined algorithms computing algorithms engineering computing CORDIC FPGA Altera library finite precision implementation occupation frequency

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Biologically Inspired Model with Feature Selection for Target Recognition Using Biogeography-Based Optimization

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JOURNAL OF AEROSPACE INFORMATION SYSTEMS 2014年第7期11卷 433-446页

作者： Duan, Haibin Deng, Yimin Beihang Univ State Key Lab Virtual Real Technol & Syst Beijing 100191 Peoples R China

To detect salient ground targets precisely and rapidly during aerial reconnaissance, this paper describes a novel object recognition method based on the feature selection of a biologically inspired model and biogeography-based optimization. As a promising approach to object recognition, the biologically inspired model is a hierarchical system of building an increasingly complex and invariant feature representation, which closely follows the process of object recognition in the visual cortex. These scale-and position-tolerant features are constructed by alternating between a template-matching and a maximum-pooling operation. Because of the many patches extracted in the standard biologically inspired model, the random mechanism may extract patches from irrelevant parts of an image and consume a lot of time. In this work, a feature selection method is proposed based on a new population-based evolutionary algorithm called biogeography-based optimization to choose the proper set of patches with high accuracy of classification and recognition. A support vector machine classifier is used for evaluation of the fitness function in biogeography-based optimization and to calculate the recognition rate in testing. A series of experiments are conducted, and the comparative results demonstrate the feasibility and effectiveness of the approach.

关键词： Particle Swarm Optimization Support Vector Machine Aerial Reconnaissance Aeroplane Helicopters Aspect Ratio Optimization Algorithm Feedforward computing algorithms Automatic Target Recognition

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Partitioned component mode synthesis via a flexibility approach

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AIAA JOURNAL 2004年第6期42卷 1236-1245页

作者： Park, KC Park, YH Univ Colorado Ctr Aerosp Struct Boulder CO 80309 USA Univ Colorado Dept Aerosp Engn Sci Boulder CO 80309 USA Samsung Elect Co Ltd Suwon 443742 South Korea

A new flexibility-based component mode synthesis method is presented, which is derived by approximating the partitioned equations of motion that employ a localized method of Lagrange multipliers. The use of the localized Lagrange multipliers leads to, unlike the classical Lagrange multipliers, a linearly independent set of interface forces without any redundancies at multiply connected interface nodes. Hence, the resulting interface flexibility matrices are uniquely determined and well suited for the present method development. An attractive feature of the present method is its substructural mode selection criterion that is independent of loading conditions. Numerical experiments show that the present modal selection criterion is reliable and that the proposed flexibility-based component mode synthesis method performs well relative to the classical Craig-Bampton method in terms of accuracy and of its ability to include dominant substructural modes for simple plates and a relatively complex solid ring.

关键词： Lagrange Multipliers Three Dimensional Elements Structural Dynamics Parallel Computers Transient Response computing algorithms Structural Health Monitoring Sandia National Laboratories Structural Analysis Structural System

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Penalized weighted residual method for the initial value problems

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AIAA JOURNAL 1997年第1期35卷 172-177页

作者： Kim, SJ Cho, JY Seoul National University Seoul 151-742 Republic of Korea

To satisfy the need for network parallel computing in the whole time domain, a penalized weighted residual formulation for the second-order initial value problems is developed and its time finite element approximation is presented. To impose properly both the initial displacement and velocity, the initial velocity is imposed to the weighted residual equation as a penalized form that is constructed such that the approximated initial velocity can satisfy the initial condition in the average sense. By this procedure, the penalized weighted residual formulation makes it possible to handle the whole time domain of investigation and to use the conventional displacement-based finite element technique without any other artificial routine. Through several numerical tests, it is confirmed that the present method gives very accurate solutions for various systems arising in the second-order initial value problems and presents promising characteristics for network parallel computation in the whole time domain of investigation.

关键词： Network Parallel computing Stiffness Matrices Boundary Value Problems Numerical Simulation Conjugate Gradient Method Numerical Integration computing algorithms Structural Dynamics Oscillating Motions Optimal Control

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Fast and Reliable Computation of Instantaneous Orbital Collision Probability

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第8期47卷 1660-1673页

作者： Masson, Matthieu Arzelier, Denis Brehard, Florent Joldes, Mioara Salvy, Bruno Toulouse Univ ROC Team LAAS CNRS 07 Ave Colonel Roche F-31400 Toulouse France Lille Univ Crystal Lab CNRS F-59655 Lille France ENS Ecole Normale Super INRIA Natl Inst Res Digital Sci & Technol LIP ENS Lyon F-69000 Lyon France

Because of the increasing number of objects in low Earth orbit, the fast and reliable estimation of the collision risk is an important challenge for spacecraft owners/operators. Among the available risk indicators, this paper focuses on computing the instantaneous probability of collision, which can be modeled as the integral of a three-dimensional Gaussian probability density function over a Euclidean ball. The authors propose an efficient and accurate method for evaluating this integral. It is based on the combination of two complementary strategies. For the first one, convergent series and numerical error bounds are computed. These bounds provide a tradeoff between the accuracy needed and the number of terms to compute. The second one, using divergent series, approximates the value of the integral with a good accuracy in most cases with only a few terms computed. Based on those two methods, a hybrid algorithm is tested on cases borrowed from the literature and compared against existing methods. Several numerical results and comparisons confirm both the efficiency and robustness of this paper's approach.

关键词： Active Satellites computing algorithms series expansions Space Vehicle Risk Assessment instantaneous collision probability long-term encounters Gaussian Mixture Models saddle-point method

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Coning Algorithm Design by Explicit Frequency Shaping

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2010年第4期33卷 1123-1132页

作者： Savage, Paul G. Strapdown Associates Inc Maple Plain MN 55359 USA

A new optimum approach is presented for strapdown coning algorithm design based on Explicit matching of desired response to expected coning input magnitude as a function of coning frequency. Unlike previous time or frequency Taylor series expansion techniques, the new method achieves optimization through minimum least-squares estimation over a user selected design frequency range. The error being minimized is the square of the weighted algorithm error, the weighting factor being user specified coning amplitude over frequency. This methodology allows the coning algorithm coefficients to be independently designed for each coning axis to achieve optimal balanced performance over the frequency range of expected coning inputs. Performance of the new algorithm design technique is evaluated by comparison with previous time and frequency-series approaches, in discrete and stochastic coning environments, and over a time based extreme dynamic maneuvering profile. A generalized method is presented for translating system performance requirements into expected coning amplitude versus frequency profiles for calculating Explicit algorithm coefficients, and for evaluating coning algorithm accuracy. The paper includes derivations of generalized formulas for calculating algorithm coefficients for previous time and frequency-series design approaches.

关键词： Algorithm Performance Taylor Series Resonance Frequencies computing algorithms Strapdown Inertial Navigation System Dynamic Response Angular Motion Strapdown System Kalman Filter Numerical Optimization

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ZEROTH-ORDER FEEDBACK-STRATEGIES FOR MEDIUM-RANGE INTERCEPTION IN A HORIZONTAL PLANE

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1985年第1期8卷 9-15页

作者： SHINAR, J Technion—Israel Institute of Technology Haifa Israel

A zeroth-order feedback solution of a variable-speed interception game between two aircraft in the horizontal plane, obtained by using the method of forced singular perturbations, is compared with the exact open-loop solution. The comparison indicates that the forced singular-perturbation approximation, based on multiple time-scale separation of the state variables, is satisfacton . Nevertheless, in cases where the interception terminates at speeds much lower than the maximum speed predicted by the reduced-order game, a rough estimate of these final speeds is needed to improve the accuracy. Using such estimates, a payoff error of 1% or less is demonstrated in all examples with sufficiently large initial distances of separation (greater than 6-8 times the best initial turning radius of the pursuer). The results validate the zeroth-order forced singular-perturbation approximation for medium-range air combat analysis. This explicit feedback strategy is a very attractive candidate for airborne implementation. © 1985 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Singular Perturbation Open Loop Aeroplane Zero Lift Drag Coefficient Air to Air Missiles Aircraft Dynamics Feedback Control Boundary Value Problems Flight Control System computing algorithms

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Dynamic Stochastic Model for Converging Inbound Air Traffic

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2016年第10期39卷 2273-2283页

作者： Chen, Jun DeLaurentis, Daniel Sun, Dengfeng Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47906 USA

Weather accounts for the majority of congestion in the National Airspace System, which highlights the importance of addressing weather uncertainty to mitigate delays. First, this paper presents a new dynamic stochastic integer programming model that studies the single-airport ground-holding problem with respect to uncertainty in the separation between flights instead of airport acceptance rate. The current model is able to provide a more accurate schedule expressed in minutes for the individual flight. Second, a converging in bound air traffic model is formulated based on the current model. This paper addresses a problem involving the merging of two in bound streams into a single airport in which uncertainty in separation from minutes-in-trail restrictions is considered. Although the "first-come/first-served" policy is still obeyed by flights on the same path, the experimentation has shown that allowing flights on different paths to switch arrival orders can help reduce the total delays. Finally, in order to tackle the computational burden posed by the disaggregate integer model, this paper introduces a dual decomposition method to reduce computation time. The original problem is decomposed scenario by scenario into several subproblems;then, a parallel computing algorithm is developed to handle these subproblems. Such a combination increases the model's computational efficiency.

关键词： National Airspace System computing algorithms Hartsfield Jackson Atlanta International Airport Air Traffic Flow Management Lagrange Multipliers Stochastic Optimization Mathematical Models Weather Forecasting Mathematical Analysis Parallel computing

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ANALYTIC TIME-OPTIMAL CONTROL SYNTHESIS OF 4TH-ORDER SYSTEM AND MANEUVERS OF FLEXIBLE STRUCTURES

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1994年第6期17卷 1171-1178页

作者： LI, FY BAINUM, PM Howard University Washington DC 20059

The analytic solution to the problem of minimum-time control of a fourth-order linear system near the origin is obtained by using Gulko's subsystem strategy. This system has two real eigenvalues (zeros) and two imaginary eigenvalues (vibrational. frequency), which represents a flexible structure with one rigid-body mode and one flexible mode. The complete solution including the optimal switching times for the second-order subsystem is first obtained. Next, the geometry of the control switching surface near the origin for the third-order subsystem is analyzed through the phase-plane and phase-space technique. Then, the switching function for the full fourth-order system is constructed by using the roots of a quartic algebraic equation. This solution can be used to synthesize the feedback time-optimal control for the maneuvers of flexible structures. Numerical examples with one and more flexible modes are illustrated to show the applications of the solution.

关键词： Flexible Structures Time Optimal Control Closed Loop Control Flexible Spacecrafts Feedback Control Harmonic Oscillator Structural Damping Structural Modeling Influence Coefficients computing algorithms

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Robust Bayesian Particle Filter for Space Object Tracking Under Severe Uncertainty

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2021年第3期45卷 481-498页

作者： Greco, Cristian Vasile, Massimiliano Univ Strathclyde Dept Mech & Aerosp Engn Aerosp Ctr Excellence James Weir Bldg Glasgow G1 1XJ Lanark Scotland

This paper introduces a robust Bayesian particle filter that can handle epistemic uncertainty in the measurements, dynamics, and initial conditions. The robust filter returns robust bounds on the output quantity of interest, rather than a crisp value. Particles are generated with an importance sampling technique and propagated only one time during the estimation process. The proposal distribution is constructed by running a parallel unscented Kalman filter to drive particles in regions of high expected likelihood and achieve a high effective sample size. The bounds are then computed by an inexpensive tuning of the importance weights via numerical optimization. A Branch & Bound algorithm over simplexes with a Lipschitz bounding function is employed to achieve guaranteed convergence to the lower and upper bounds in a finite number of steps. The filter is applied to the robust computation of the collision probability of SENTINEL 2B with a FENGYUN 1C debris in different operational instances, all characterized by a mix of aleatory and epistemic uncertainty on initial conditions and observation likelihoods.

关键词： Unscented Kalman Filter Sentinel Fengyun Branch and Bound Algorithm Numerical Optimization Satellite Collision Cumulative Distribution Function Number of Particles computing algorithms Resident Space Object

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