A Review of the Frequency Estimation and Tracking Problems

This report presents a concise review of some frequency estimation and frequency tracking problems. In particular, the report focusses on aspects of these problems which have been addressed by members of the Frequency Tracking and Estimation project of the Centre for Robust and Adaptive Systems. The report is divided into four parts: problem specification and discussion, associated problems, frequency estimation algorithms and frequency tracking algorithms. Part I begins with a definition of the various frequency estimation and tracking problems. Practical examples of where each problem may arise are given. A comparison is made between the frequency estimation and tracking problems. In Part II, block frequency estimation algorithms, fast block frequency estimation algorithms and notch filtering techniques for frequency estimation are dealt with. Frequency tracking algorithms are examined in Part III. Part IV of this report examines various problems associated with frequency estimation. Associated problems include Cramer-Rao lower bounds, theoretical algorithm performance, frequency resolution, use of the analytic signal and model order selection

Rational invariant subspace approximations with applications

Includes bibliographical references.Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algorithms approximate the required subspace using rational and power-like methods applied to the direct data or the sample covariance matrix. Several ESPRIT- as well as MUSIC-type methods are developed based on these approximations. A substantial computational saving can be gained comparing with those associated with the eigendecomposition-based methods. These methods are demonstrated to have performance comparable to that of MUSIC yet will require fewer computation to obtain the signal subspace matrix

A unified approach to sparse signal processing

A unified view of the area of sparse signal processing is presented in tutorial form by bringing together various fields in which the property of sparsity has been successfully exploited. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common potential benefits of significant reduction in sampling rate and processing manipulations through sparse signal processing are revealed. The key application domains of sparse signal processing are sampling, coding, spectral estimation, array processing, compo-nent analysis, and multipath channel estimation. In terms of the sampling process and reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding i

Super-Resolution of Positive Sources: the Discrete Setup

In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by $f_c$, which is just about the frequency of natural light. This paper rigorously establishes that this super-resolution problem can be solved via linear programming in a stable manner. We prove that the quality of the reconstruction crucially depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within a square of side length about $1/f_c$. The theoretical performance guarantee is complemented with a converse result showing that our simple convex program convex is nearly optimal. Finally, numerical experiments illustrate our methods.Comment: 31 page, 7 figure

High-resolution sonar DF system

One of the fundamental problems of sonar systems is the determination of the bearings of underwater sources/targets. The classical solution to this problem, the 'Conventional Beamformer', uses the outputs from the individual sensors of an acoustic array to form a beam which is swept across the search sector. The resolution of this method is limited by the beam width and narrowing this beam to enhance the resolution may have some practical problems, especially in low frequency sonar, because of the physical size of the array needed. During the past two decades an enormous amount of work has been done to develop new algorithms for resolution enhancements beyond that of the Conventional Beamformer. However, most of these methods have been based on computer simulations and very little has been published on the practical implementation of these algorithms. One of the main reasons for this has been the lack of hardware that can handle the relatively heavy computational load of these algorithms. However, there have been great advances in semiconductor and computer technologies in the last few years which have led to the availability of more powerful computational and storage devices. These devices have opened the door to the possibility of implementing these high-resolution Direction Finding (DF) algorithms in real sonar systems. The work presented in this thesis describes a practical implementation of some of the high-resolution DF algorithms in a simple sonar system that has been designed and built for this purpose. [Continues.

Study on a miniaturized satellite payload for atmospheric temperature measurements

The atmospheric temperature reflects the thermal balance of the atmosphere and is a valuable indicator of climate change. It has been widely recognized that the atmospheric gravity wave activity has a profound effect on the large-scale circulation, thermal and constituent structures in the mesosphere and lower thermosphere (MLT). Temperature distribution in this region is an essential component to identify and quantify gravity waves. Observation from remote sensing instruments on satellite platforms is an effective way to measure the temperature in the MLT region. A miniaturized satellite payload is developed to measure the atmospheric temperature in the MLT region via observing the O2A-band emission. Following a Boltzmann distribution, the relative intensities of the emission lines can be used to derive the temperature profile. Based on the spatial heterodyne spectroscopy, this instrument is capable of resolving individual emission lines in the O2A-band for the spatial and spectral information simultaneously. The monolithic and compact feature of this spectrometer makes it suitable for operating on satellite platforms. In this work, the characterization of the instrument is investigated for the purpose of simultaneously measuring multiple emission lines of the O2A-band. The instrument is explored through a series of experimental methods, providing characteristics of the instrument and evaluation of its performance. In spatial and spectral domain, Level- 0 and Level-1 data processors are developed to convert the raw data to the calibrated spectral radiance for further temperature and gravity wave characterization. Within this framework, the performance of the utilized detector is evaluated along with its radiation tolerance in space environment. In the processor, the detector artifacts are corrected based on the measurements in laboratory or in space. The radiometric response of the instrument is characterized on a pixel-by-pixel basis using a blackbody. An interferogram distortion correction algorithm is developed to correct for the spatial and phase distortion induced by the detector optics. Further, localized phase distortion correction is implemented to correct for the remaining phase error. Unwanted ghost emission lines are removed based on two dimensional Fourier transform. In the spectral domain, the processing steps mainly consist of wavelength calibration and instrument spectral response correction, including filter response correction and modulation efficiency correction. As an in-orbit verification, the AtmoSHINE instrument was successfully deployed in space on 22th of December, 2018. In the first test phase, the functionality and the performance of the instrument in space were verified. The detector dark current measurement in orbit is consistent with the ground-based results. Based on the the calibration procedures and the developed data processing algorithms, the O2A-band emission lines can be successfully resolved. A cross-verification of the AtmoSHINE limb radiance profile with other satellite payload measurements indicates that the radiometric performance of the instrument is within the expectation. The retrieved temperature parameters are studied with respect to different number of samples and different objective functions in the optimization. This work verifies the ability of the instrument to derive the atmospheric temperature in the MLT region and its potential application in gravity wave detections