Statistical Performance Analysis of Sparse Linear Arrays

Direction-of-arrival (DOA) estimation remains an important topic in array signal processing. With uniform linear arrays (ULAs), traditional subspace-based methods can resolve only up to M-1 sources using M sensors. On the other hand, by exploiting their so-called difference coarray model, sparse linear arrays, such as co-prime and nested arrays, can resolve up to O(M^2) sources using only O(M) sensors. Various new sparse linear array geometries were proposed and many direction-finding algorithms were developed based on sparse linear arrays. However, the statistical performance of such arrays has not been analytically conducted. In this dissertation, we (i) study the asymptotic performance of the MUtiple SIgnal Classification (MUSIC) algorithm utilizing sparse linear arrays, (ii) derive and analyze performance bounds for sparse linear arrays, and (iii) investigate the robustness of sparse linear arrays in the presence of array imperfections. Based on our analytical results, we also propose robust direction-finding algorithms for use when data are missing. We begin by analyzing the performance of two commonly used coarray-based MUSIC direction estimators. Because the coarray model is used, classical derivations no longer apply. By using an alternative eigenvector perturbation analysis approach, we derive a closed-form expression of the asymptotic mean-squared error (MSE) of both estimators. Our expression is computationally efficient compared with the alternative of Monte Carlo simulations. Using this expression, we show that when the source number exceeds the sensor number, the MSE remains strictly positive as the signal-to-noise ratio (SNR) approaches infinity. This finding theoretically explains the unusual saturation behavior of coarray-based MUSIC estimators that had been observed in previous studies. We next derive and analyze the Cramér-Rao bound (CRB) for general sparse linear arrays under the assumption that the sources are uncorrelated. We show that, unlike the classical stochastic CRB, our CRB is applicable even if there are more sources than the number of sensors. We also show that, in such a case, this CRB remains strictly positive definite as the SNR approaches infinity. This unusual behavior imposes a strict lower bound on the variance of unbiased DOA estimators in the underdetermined case. We establish the connection between our CRB and the classical stochastic CRB and show that they are asymptotically equal when the sources are uncorrelated and the SNR is sufficiently high. We investigate the behavior of our CRB for co-prime and nested arrays with a large number of sensors, characterizing the trade-off between the number of spatial samples and the number of temporal samples. Our analytical results on the CRB will benefit future research on optimal sparse array designs. We further analyze the performance of sparse linear arrays by considering sensor location errors. We first introduce the deterministic error model. Based on this model, we derive a closed-form expression of the asymptotic MSE of a commonly used coarray-based MUSIC estimator, the spatial-smoothing based MUSIC (SS-MUSIC). We show that deterministic sensor location errors introduce a constant estimation bias that cannot be mitigated by only increasing the SNR. Our analytical expression also provides a sensitivity measure against sensor location errors for sparse linear arrays. We next extend our derivations to the stochastic error model and analyze the Gaussian case. We also derive the CRB for joint estimation of DOA parameters and deterministic sensor location errors. We show that this CRB is applicable even if there are more sources than the number of sensors. Lastly, we develop robust DOA estimators for cases with missing data. By exploiting the difference coarray structure, we introduce three algorithms to construct an augmented covariance matrix with enhanced degrees of freedom. By applying MUSIC to this augmented covariance matrix, we are able to resolve more sources than sensors. Our method utilizes information from all snapshots and shows improved estimation performance over traditional DOA estimators

Infrared astronomy

The decade of 1990's presents an opportunity to address fundamental astrophysical issues through observations at IR wavelengths made possible by technological and scientific advances during the last decade. The major elements of recommended program are: the Space Infrared Telescope Facility (SIRTF), the Stratospheric Observatory For Infrared Astronomy (SOFIA) and the IR Optimized 8-m Telescope (IRO), a detector and instrumentation program, the SubMilliMeter Mission (SMMM), the 2 Microns All Sky Survey (2MASS), a sound infrastructure, and technology development programs. Also presented are: perspective, science opportunities, technical overview, project recommendations, future directions, and infrastructure

Sensor Array Processing with Manifold Uncertainty

<p>The spatial spectrum, also known as a field directionality map, is a description of the spatial distribution of energy in a wavefield. By sampling the wavefield at discrete locations in space, an estimate of the spatial spectrum can be derived using basic wave propagation models. The observable data space corresponding to physically realizable source locations for a given array configuration is referred to as the array manifold. In this thesis, array manifold ambiguities for linear arrays of omni-directional sensors in non-dispersive fields are considered. </p><p>First, the problem of underwater a hydrophone array towed behind a maneuvering platform is considered. The array consists of many hydrophones mounted to a flexible cable that is pulled behind a ship. The towed cable will bend or distort as the ship performs maneuvers. The motion of the cable through the turn can be used to resolve ambiguities that are inherent to nominally linear arrays. The first significant contribution is a method to estimate the spatial spectrum using a time-varying array shape in a dynamic field and broadband temporal data. Knowledge of the temporal spectral shape is shown to enhance detection performance. The field is approximated as a sum of uncorrelated planewaves located at uniform locations in angle, forming a gridded map on which a maximum likelihood estimate for broadband source power is derived. Uniform linear arrays also suffer from spatial aliasing when the inter-element spacing exceeds a half-wavelength. Broadband temporal knowledge is shown to significantly reduce aliasing and thus, in simulation, enhance target detection in interference dominated environments. </p><p>As an extension, the problem of towed array shape estimation is considered when the number and location of sources are unknown. A maximum likelihood estimate of the array shape using the field directionality map is derived. An acoustic-based array shape estimate that exploits the full 360$^\circ$ field via field directionality mapping is the second significant contribution. Towed hydrophone arrays have heading sensors in order to estimate array shape, but these sensors can malfunction during sharp turns. An array shape model is described that allows the heading sensor data to be statistically fused with heading sensor. The third significant contribution is method to exploit dynamical motion models for sharp turns for a robust array shape estimate that combines acoustic and heading data. The proposed array shape model works well for both acoustic and heading data and is valid for arbitrary continuous array shapes.</p><p>Finally, the problem of array manifold ambiguities for static under-sampled linear arrays is considered. Under-sampled arrays are non-uniformly sampled with average spacing greater than a half-wavelength. While spatial aliasing only occurs in uniformly sampled arrays with spacing greater than a half-wavelength, under-sampled arrays have increased spatial resolution at the cost of high sidelobes compared to half-wavelength sampled arrays with the same number of sensors. Additionally, non-uniformly sampled arrays suffer from rank deficient array manifolds that cause traditional subspace based techniques to fail. A class of fully agumentable arrays, minimally redundant linear arrays, is considered where the received data statistics of a uniformly spaced array of the same length can be reconstructed in wide sense stationary fields at the cost of increased variance. The forth significant contribution is a reduced rank processing method for fully augmentable arrays to reduce the variance from augmentation with limited snapshots. Array gain for reduced rank adaptive processing with diagonal loading for snapshot deficient scenarios is analytically derived using asymptotic results from random matrix theory for a set ratio of sensors to snapshots. Additionally, the problem of near-field sources is considered and a method to reduce the variance from augmentation is proposed. In simulation, these methods result in significant average and median array gains with limited snapshots.</p>Dissertatio

CUSTARD (Cranfield University Space Technology Advanced Research Demonstrator) - A Micro-System Technology Demonstrator Nanosatellite. Summary of the Group Design Project MSc in Astronautics and Space Engineering. 1999-2000, Cranfield University

CUSTARD (Cranfield University Space Technology And Research Demonstrator) was the group design project for students of the MSc in Astronautics and Space Engineering for the Academic Year 1999/2000 at Cranfield University. The project involved the initial design of a nanosatellite to be used as a technology demonstrator for microsystem technology (MST) in space. The students worked together as one group (organised into several subgroups, e.g. system, mechanical), with each student responsible for a set of work packages. The nanosatellite designed had a mass of 4 kg, lifetime of 3 months in low Earth orbit, coarse 3-axis attitude control (no orbit control), and was capable of carrying up to 1 kg of payload. The electrical power available was 18 W (peak). Assuming a single X-band ground station at RAL (UK), a data rate of up to 1 M bit s-1 for about 3000 s per day is possible. The payloads proposed are a microgravity laboratory and a formation flying experiment. The report summarises the results of the project and includes executive summaries from all team members. Further information and summaries of the full reports are available from the College of Aeronautics, Cranfield University

MAX '91: An advanced payload for the exploration of high energy processes on the active sun

The results of a NASA science working group established to study a follow-on to the Solar Maximum Mission are given. A complement of instruments is suggested, with the primary objective of studying the physics of energetic processes in cosmic plasmas by observing high-energy phenomena in solar flares. High-quality flare observations will be possible with these instruments during the next peak in solar activity expected to last from 1990 through at least 1995. The primary objective of MAX '91 is to study energetic processes in cosmic plasmas by observing high-energy phenomena in solar flares. These processes, which are of general astrophysical importance, include energy release, particle acceleration, and energy transport. Results from comprehensive observing programs conducted during the last solar cycle have demonstrated the great scientific potential of high-energy emissions for addressing these central physical processes. Consequently, a payload optimized for observations of high-energy solar flare phenomena is suggested for MAX '91. It consists of the following four specific instruments: (1) a Fourier-transform X-ray and gamma-ray imager covering the energy range from a few keV to 1 MeV with arcsecond spatial resolution; (2) a cooled germanium X-ray and gamma-ray spectrometer with keV spectral resolution covering the energy range from 10 keV to 50 MeV; (3) Bragg spectrometers with high spectral resolution at wavelengths between 1 and 9 angstrons; and (4) a soft X-ray, EUV, or UV imaging instrument with arcsecond spatial resolution

Advanced space system concepts and their orbital support needs (1980 - 2000). Volume 2: Final report

The results are presented of a study which identifies over 100 new and highly capable space systems for the 1980-2000 time period: civilian systems which could bring benefits to large numbers of average citizens in everyday life, much enhance the kinds and levels of public services, increase the economic motivation for industrial investment in space, expand scientific horizons; and, in the military area, systems which could materially alter current concepts of tactical and strategic engagements. The requirements for space transportation, orbital support, and technology for these systems are derived, and those requirements likely to be shared between NASA and the DoD in the time period identified. The high leverage technologies for the time period are identified as very large microwave antennas and optics, high energy power subsystems, high precision and high power lasers, microelectronic circuit complexes and data processors, mosaic solid state sensing devices, and long-life cryogenic refrigerators

Energy-Efficient Recurrent Neural Network Accelerators for Real-Time Inference

Over the past decade, Deep Learning (DL) and Deep Neural Network (DNN) have gone through a rapid development. They are now vastly applied to various applications and have profoundly changed the life of hu- man beings. As an essential element of DNN, Recurrent Neural Networks (RNN) are helpful in processing time-sequential data and are widely used in applications such as speech recognition and machine translation. RNNs are difficult to compute because of their massive arithmetic operations and large memory footprint. RNN inference workloads used to be executed on conventional general-purpose processors including Central Processing Units (CPU) and Graphics Processing Units (GPU); however, they have un- necessary hardware blocks for RNN computation such as branch predictor, caching system, making them not optimal for RNN processing. To accelerate RNN computations and outperform the performance of conventional processors, previous work focused on optimization methods on both software and hardware. On the software side, previous works mainly used model compression to reduce the memory footprint and the arithmetic operations of RNNs. On the hardware side, previous works also designed domain-specific hardware accelerators based on Field Pro- grammable Gate Arrays (FPGA) or Application Specific Integrated Circuits (ASIC) with customized hardware pipelines optimized for efficient pro- cessing of RNNs. By following this software-hardware co-design strategy, previous works achieved at least 10X speedup over conventional processors. Many previous works focused on achieving high throughput with a large batch of input streams. However, in real-time applications, such as gaming Artificial Intellegence (AI), dynamical system control, low latency is more critical. Moreover, there is a trend of offloading neural network workloads to edge devices to provide a better user experience and privacy protection. Edge devices, such as mobile phones and wearable devices, are usually resource-constrained with a tight power budget. They require RNN hard- ware that is more energy-efficient to realize both low-latency inference and long battery life. Brain neurons have sparsity in both the spatial domain and time domain. Inspired by this human nature, previous work mainly explored model compression to induce spatial sparsity in RNNs. The delta network algorithm alternatively induces temporal sparsity in RNNs and can save over 10X arithmetic operations in RNNs proven by previous works. In this work, we have proposed customized hardware accelerators to exploit temporal sparsity in Gated Recurrent Unit (GRU)-RNNs and Long Short-Term Memory (LSTM)-RNNs to achieve energy-efficient real-time RNN inference. First, we have proposed DeltaRNN, the first-ever RNN accelerator to exploit temporal sparsity in GRU-RNNs. DeltaRNN has achieved 1.2 TOp/s effective throughput with a batch size of 1, which is 15X higher than its related works. Second, we have designed EdgeDRNN to accelerate GRU-RNN edge inference. Compared to DeltaRNN, EdgeDRNN does not rely on on-chip memory to store RNN weights and focuses on reducing off-chip Dynamic Random Access Memory (DRAM) data traffic using a more scalable architecture. EdgeDRNN have realized real-time inference of large GRU-RNNs with submillisecond latency and only 2.3 W wall plug power consumption, achieving 4X higher energy efficiency than commercial edge AI platforms like NVIDIA Jetson Nano. Third, we have used DeltaRNN to realize the first-ever continuous speech recognition sys- tem with the Dynamic Audio Sensor (DAS) as the front-end. The DAS is a neuromorphic event-driven sensor that produces a stream of asyn- chronous events instead of audio data sampled at a fixed sample rate. We have also showcased how an RNN accelerator can be integrated with an event-driven sensor on the same chip to realize ultra-low-power Keyword Spotting (KWS) on the extreme edge. Fourth, we have used EdgeDRNN to control a powered robotic prosthesis using an RNN controller to replace a conventional proportional–derivative (PD) controller. EdgeDRNN has achieved 21 μs latency of running the RNN controller and could maintain stable control of the prosthesis. We have used DeltaRNN and EdgeDRNN to solve these problems to prove their value in solving real-world problems. Finally, we have applied the delta network algorithm on LSTM-RNNs and have combined it with a customized structured pruning method, called Column-Balanced Targeted Dropout (CBTD), to induce spatio-temporal sparsity in LSTM-RNNs. Then, we have proposed another FPGA-based accelerator called Spartus, the first RNN accelerator that exploits spatio- temporal sparsity. Spartus achieved 9.4 TOp/s effective throughput with a batch size of 1, the highest among present FPGA-based RNN accelerators with a power budget around 10 W. Spartus can complete the inference of an LSTM layer having 5 million parameters within 1 μs

Mobile graphics: SIGGRAPH Asia 2017 course

Peer ReviewedPostprint (published version