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A model for the execution time of parallel algorithms on processor arrays is described. The model is validated for the conjugate gradient algorithm on the eight processor Finite Element Machine at NASA Langley Research Center. Model predictions are also included for this algorithm on a larger array as the number of processors and system parameters are varied.
A digital-signal-processing algorithm (somewhat arbitrarily) called SUMPLE has been devised as a means of aligning the outputs of multiple receiving radio antennas in a large array for the purpose of receiving a weak signal transmitted by a single distant source. As used here, aligning signifies adjusting the delays and phases of the outputs from the various antennas so that their relatively weak replicas of the desired signal can be added coherently to increase the signal-to-noise ratio (SNR) for improved reception, as though one had a single larger antenna. The method was devised to enhance spacecraft-tracking and telemetry operations in NASA's Deep Space Network (DSN); the method could also be useful in such other applications as both satellite and terrestrial radio communications and radio astronomy. Heretofore, most commonly, alignment has been effected by a process that involves correlation of signals in pairs. This approach necessitates the use of a large amount of hardware most notably, the N(N - 1)/2 correlators needed to process signals from all possible pairs of N antennas. Moreover, because the incoming signals typically have low SNRs, the delay and phase adjustments are poorly determined from the pairwise correlations. SUMPLE also involves correlations, but the correlations are not performed in pairs. Instead, in a partly iterative process, each signal is appropriately weighted and then correlated with a composite signal equal to the sum of the other signals (see Figure 1). One benefit of this approach is that only N correlators are needed; in an array of N much greater than 1 antennas, this results in a significant reduction of the amount of hardware. Another benefit is that once the array achieves coherence, the correlation SNR is N - 1 times that of a pair of antennas.
Appendix 5 of the Study of One- and Two-Dimensional Filtering and Deconvolution Algorithms for a Streaming Array Computer includes a resume of the professional background of the Principal Investigator on the project, lists of this publications and research papers, graduate thesis supervised, and grants received.
Flight test results for two fault-tolerance algorithms developed for a redundant strapdown inertial measurement unit consisting of four 2-DOF gyros and accelerometers mounted on the faces of a semioctahedron are presented. Although both algorithms provided timely detection and isolation of flight control level failures, the generalized likelihood test algorithm provided more timely detection and isolation of low-level sensor failures than the edge vector test algorithm. The generalized likelihood test produced a false isolation for the case of a dual low-level failure applied to the sensitive axes of an accelerometer. Both of the algorithms were shown to provide dual fail-operational performance for the skewed array of inertial sensors.
Algorithms for matrix vector multiplication are implemented using acousto-optic cells for multiplication and input data transfer and using charge coupled devices detector arrays for accumulation and output of the results. No two dimensional matrix mask is required; matrix changes are implemented electronically. A system for multiplying a 50 component nonnegative real vector by a 50 by 50 nonnegative real matrix is described. Modifications for bipolar real and complex valued processing are possible, as are extensions to matrix-matrix multiplication and multiplication of a vector by multiple matrices.
Results on efficient forms of decoding convolutional codes based on the Viterbi algorithm by using systolic arrays are presented. Various properties of convolutional codes are discussed. A technique called strongly connected trellis decoding is introduced to increase the efficient utilization of all the systolic array processors. Issues dealing with the composite branch metric generation, survivor updating, overall system architecture, throughput rate, and computational overhead ratio also investigated. The scheme is applicable to both hard and soft decoding of any rate b/n convolutional code. It is shown that as the length of the code becomes large, the systolic Viterbi decoder maintains a regular and general interconnection structure as well as moderate throughput rate gain over the sequential Viterbi decoder.
An approach to modelling the execution time of algorithms on parallel arrays is presented. This time is expressed as a function of the number of processors and system parameters. The resulting model has been applied to a parallel implementation of the conjugate-gradient algorithm on NASA's FEM. Results of experiments performed to compare the model predictions against actual behavior show that the floating-point arithmetic, communication, and synchronization components of the parallel algorithm execution time were correctly modelled. The results also show that the overhead caused by the interaction of the system software and the actual parallel hardware must be reflected in the model parameters. The model has been used to predict the performance of the conjugate gradient algorithm on a given problem as the number of processors and machine characteristics varied.
Lattice algorithm has been employed in numerous adaptive filtering applications such as speech analysis/synthesis, noise canceling, spectral analysis, and channel equalization. In this paper the application to adaptive-array processing is discussed. The advantages are fast convergence rate as well as computational accuracy independent of the noise and interference conditions. The results produced by this technique are compared to those obtained by the direct matrix inverse method.
An algorithm for estimating the optimum combining weights for the Ka-band (33.7-GHz) array feed compensation system was developed and analyzed. The input signal is assumed to be broadband radiation of thermal origin, generated by a distant radio source. Currently, seven video converters operating in conjunction with the real-time correlator are used to obtain these weight estimates. The algorithm described here requires only simple operations that can be implemented on a PC-based combining system, greatly reducing the amount of hardware. Therefore, system reliability and portability will be improved.
Interpolar algorithm, simple enough to hard-wire by hand, improves resolution by factor of 5 to 20.
The development of vector processing computers of the streaming array architectures has made possible a dramatic decrease in the time required for the solution of problems, i.e., for those algorithms which readily lend themselves to sequential operations on long vectors. There has concurrently been rapid growth in the applications of the techniques generally known as mathematical digital filtering, also called signal analysis, digital signal processing, time series analysis, and digital image processing. The best known applications of these techniques is to seismic data and two-dimensional images, data types consisting of very large collections of numbers. A major limitation for these cases is the size and speed of the computer available. Therefore, a move to the streaming array architecture can result in marked improvement in the data analysis techniques which may be employed.
Development of software tools for designing supercomputing systems is highly complex and cost ineffective. To tackle this a special purpose PAcube silicon compiler which integrates different design levels from cell to processor arrays has been proposed. As a part of this, we present in this paper a novel methodology which unifies the problems of Layout Automation and Algorithm Mapping.
A Large array of small antennas can be used to enhance signals with very low signal-to-noise ratio and can also be used to replace large apertures. In this paper, a fast combining algorithm is proposed and analyzed to maximize the combined output signal-to-noise ratio.
The present paper provides a description of recent and continuing work related to the development of tracking systems possessing artificial intelligence. It is pointed out that artificial intelligence is being used to provide trackers with the abilities to sense environmental changes which can affect tracker performance, to optimize tracker performance in a changing environment, and to report on the accuracy and stability of the pointing data. The implementation of artificial intelligence in tracking systems is based on the use of adaptive algorithms which correct for tracking errors by applying polynomial corrections to raw tracking output data. The basic operation of a centroid tracking system is discussed, taking into account the limitations on accuracy and stability which exist in the absence of intelligence. Attention is given to the correction method and the implementation of artificial intelligence to improve tracking.
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Arrays of multiple, nominally identical sensors with sensor-output-processing electronic hardware and software are being developed in order to obtain accuracy, reliability, and lifetime greater than those of single sensors. The conceptual basis of this development lies in the statistical behavior of multiple sensors and a multisensor-array (MSA) algorithm that exploits that behavior. In addition, advances in microelectromechanical systems (MEMS) and integrated circuits are exploited. A typical sensor unit according to this concept includes multiple MEMS sensors and sensor-readout circuitry fabricated together on a single chip and packaged compactly with a microprocessor that performs several functions, including execution of the MSA algorithm. In the MSA algorithm, the readings from all the sensors in an array at a given instant of time are compared and the reliability of each sensor is quantified. This comparison of readings and quantification of reliabilities involves the calculation of the ratio between every sensor reading and every other sensor reading, plus calculation of the sum of all such ratios. Then one output reading for the given instant of time is computed as a weighted average of the readings of all the sensors. In this computation, the weight for each sensor is the aforementioned value used to quantify its reliability. In an optional variant of the MSA algorithm that can be implemented easily, a running sum of the reliability value for each sensor at previous time steps as well as at the present time step is used as the weight of the sensor in calculating the weighted average at the present time step. In this variant, the weight of a sensor that continually fails gradually decreases, so that eventually, its influence over the output reading becomes minimal: In effect, the sensor system "learns" which sensors to trust and which not to trust. The MSA algorithm incorporates a criterion for deciding whether there remain enough sensor readings that approximate each other sufficiently closely to constitute a majority for the purpose of quantifying reliability. This criterion is, simply, that if there do not exist at least three sensors having weights greater than a prescribed minimum acceptable value, then the array as a whole is deemed to have failed.
A numerical technique is presented to optimize the performance of arbitrary antenna arrays under realistic conditions. An experimental-computational algorithm is formulated in which n-dimensional minimization methods are applied to measured data obtained from the antenna array. A numerical update formula is used to induce partial derivative information without requiring special perturbations of the array parameters. The algorithm provides a new design for the antenna array, and the method proceeds in an iterative fashion. Test case results are presented showing the effectiveness of the algorithm.
Two approaches are used to characterize how accurately the North Alabama Lightning Mapping Array (LMA) is able to locate lightning VHF sources in space and in time. The first method uses a Monte Carlo computer simulation to estimate source retrieval errors. The simulation applies a VHF source retrieval algorithm that was recently developed at the NASA Marshall Space Flight Center (MSFC) and that is similar, but not identical to, the standard New Mexico Tech retrieval algorithm. The second method uses a purely theoretical technique (i.e., chi-squared Curvature Matrix Theory) to estimate retrieval errors. Both methods assume that the LMA system has an overall rms timing error of 50 ns, but all other possible errors (e.g., multiple sources per retrieval attempt) are neglected. The detailed spatial distributions of retrieval errors are provided. Given that the two methods are completely independent of one another, it is shown that they provide remarkably similar results. However, for many source locations, the Curvature Matrix Theory produces larger altitude error estimates than the (more realistic) Monte Carlo simulation.