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

Approaches to multiharmonic frequency tracking and estimation

The problem of tracking the possibly time-varying fundamental frequency of a noisy multiharmonic signal, along with its time-varying and unknown harmonic amplitudes, is one of great practical interest, and stems, for example, from problems in sonar signal processing. This thesis continues the theoretical and simulation study of a novel frequency tracker for the multiharmonic case, the Extended Kalman Filter (EKF), first reported in [1]. In addition, the single tone and multiharmonic Maximum Likelihood estimators (MLE{u2019}s) are studied, in their application to the problem of estimating a constant frequency for a sinusoidal signal and a multiharmonic signal respectively. The EKF is applied to the multiharmonic estimation problem, and its performance compared with the CR bounds. For high SNR (signal-to-noiseratio), the EKF is shown to be efficient, (i.e., to have performance that meets the CR bounds). An important averaging approximation is introduced and applied in the calculation of the EKF performance. The notion of a complex analytic signal is clarified. Prompted by a key theoretical result of [1], the performance of an EKF applied to the frequency tracking problem (where the harmonic amplitudes are assumed constant and known) is analyzed (with the aid of the averaging approximation). In some cases, the performance is determined explicitly without resorting to bounds. A close relationship to the well known problem of FM (frequency modulation) demodulation and the associated notion of PLL's (phase locked loops) is observed, and an important parameter termed the effective SNR arises. In addition, the existence of a threshold effect (a dramatic collapse in the performance of an estimator, evident as the SNR is lowered) is demonstrated for the EKF. A simplified continuous time model of the EKF, termed the CPLL (coupled phase locked loop), is derived. As a multiharmonic generalization of the well known PLL, it is successfully analyzed using techniques adapted from those for the PLL. The performance of the CPLL is analyzed in the presence and absence of measurement noise, and its rough equivalence to the EKF is demonstrated. The importance of not overestimating the number of harmonics in the received signal, prior to tracking of the signal{u2019}s frequency, is demonstrated by recourse to the CPLL analysis. Two distinct philosophies of analyzing the threshold effect are identified and discussed - the so-called black box and internal philosophies. The importance of understanding the causes of the threshold effect and the practical desirability of being able to predict its occurrence is made clear. The application of these two different approaches gives new and powerful ways of predicting the point at which threshold occurs, for both the single tone and multiharmonic MLE's. One approach, the black box, leads to the discovery of threshold "indicator" quantities that are calculable from readily available, prior information, for both the single tone and significantly, the mutiharmonic MLE{u2019}s. The other approach (internal) leads to a way of theoretically calculating performance curves clearly demonstrating the threshold effect for the multiharmonic MLE, which till now required Monte Carlo simulation. In addition, the success of the black box approach applied to the multiharmonic MLE has enabled the formation of a strong conjecture as to the characterization of threshold for the EKF/CPLL, a difficult and unsolved problem

Power Quality

Electrical power is becoming one of the most dominant factors in our society. Power generation, transmission, distribution and usage are undergoing signifi cant changes that will aff ect the electrical quality and performance needs of our 21st century industry. One major aspect of electrical power is its quality and stability – or so called Power Quality. The view on Power Quality did change over the past few years. It seems that Power Quality is becoming a more important term in the academic world dealing with electrical power, and it is becoming more visible in all areas of commerce and industry, because of the ever increasing industry automation using sensitive electrical equipment on one hand and due to the dramatic change of our global electrical infrastructure on the other. For the past century, grid stability was maintained with a limited amount of major generators that have a large amount of rotational inertia. And the rate of change of phase angle is slow. Unfortunately, this does not work anymore with renewable energy sources adding their share to the grid like wind turbines or PV modules. Although the basic idea to use renewable energies is great and will be our path into the next century, it comes with a curse for the power grid as power fl ow stability will suff er. It is not only the source side that is about to change. We have also seen signifi cant changes on the load side as well. Industry is using machines and electrical products such as AC drives or PLCs that are sensitive to the slightest change of power quality, and we at home use more and more electrical products with switching power supplies or starting to plug in our electric cars to charge batt eries. In addition, many of us have begun installing our own distributed generation systems on our rooft ops using the latest solar panels. So we did look for a way to address this severe impact on our distribution network. To match supply and demand, we are about to create a new, intelligent and self-healing electric power infrastructure. The Smart Grid. The basic idea is to maintain the necessary balance between generators and loads on a grid. In other words, to make sure we have a good grid balance at all times. But the key question that you should ask yourself is: Does it also improve Power Quality? Probably not! Further on, the way how Power Quality is measured is going to be changed. Traditionally, each country had its own Power Quality standards and defi ned its own power quality instrument requirements. But more and more international harmonization efforts can be seen. Such as IEC 61000-4-30, which is an excellent standard that ensures that all compliant power quality instruments, regardless of manufacturer, will produce of measurement instruments so that they can also be used in volume applications and even directly embedded into sensitive loads. But work still has to be done. We still use Power Quality standards that have been writt en decades ago and don’t match today’s technology any more, such as fl icker standards that use parameters that have been defi ned by the behavior of 60-watt incandescent light bulbs, which are becoming extinct. Almost all experts are in agreement - although we will see an improvement in metering and control of the power fl ow, Power Quality will suff er. This book will give an overview of how power quality might impact our lives today and tomorrow, introduce new ways to monitor power quality and inform us about interesting possibilities to mitigate power quality problems. Regardless of any enhancements of the power grid, “Power Quality is just compatibility” like my good old friend and teacher Alex McEachern used to say. Power Quality will always remain an economic compromise between supply and load. The power available on the grid must be suffi ciently clean for the loads to operate correctly, and the loads must be suffi ciently strong to tolerate normal disturbances on the grid

Extraction of Small Boat Harmonic Signatures from Passive Sonar

This paper investigates the extraction of acoustic signatures from small boats using a passive sonar system. Noise radiated from a small boats consists of broadband noise and harmonically related tones that correspond to engine and propeller specifications. A signal processing method to automatically extract the harmonic structure of noise radiated from small boats is developed. The Harmonic Extraction and Analysis Tool (HEAT) estimates the instantaneous fundamental frequency of the harmonic tones, refines the fundamental frequency estimate using a Kalman filter, and automatically extracts the amplitudes of the harmonic tonals to generate a harmonic signature for the boat. Results are presented that show the HEAT algorithms ability to extract these signatures

The evolution of echolocation in bats: a comparative approach

The evolutionary history of echolocation in bats is poorly understood, as fossils provide little direct evidence, and most studies into echolocation have taken an ecological approach. Bats use a wide variety of echolocation call structures despite facing similar sensory challenges, and it is not clear how and why these echolocation call types evolved, or what impact they have on other aspects of the evolution of bats. Here, I use phylogenetic comparative methods and newly-collated echolocation call data from 410 species in 120 genera and all 19 families to investigate the origination and evolution of echolocation in bats (Chiroptera). I construct an updated phylogenetic supertree of the bats using source phylogenies from the literature between 1970 and 2009. I ask three main questions: (1) Are echolocation call structures really a product of present-day ecological conditions, or are they much more constrained by evolutionary history than is currently thought? (2) What did the first echolocation calls sound like? (3) Are echolocation calls ‘key innovations’ that promote diversification? I found that early divergences and subsequent constraints in evolutionary history have resulted in a greater variety of bat call structures than appear to be functionally necessary. The structure of the first echolocation calls was predicted to be short duration, multi-harmonic, and narrowband, suggesting that the proto-bat was a slow and manoeuvrable flier with an opportunistic and omnivorous diet, and may have used a perch-hunting foraging strategy. Finally, some echolocation call types were found to correlate with higher diversification rates such that they may be considered key innovations, but, unexpectedly, the most rapidly diversifying clades were those in which species either did not use echolocation at all (Pteropodidae), or where less sensory reliance was placed on echolocation (Stenodermatinae: Phyllostomidae)

A systematic search for close supermassive black hole binaries in the Catalina Real-Time Transient Survey

Hierarchical assembly models predict a population of supermassive black hole (SMBH) binaries. These are not resolvable by direct imaging but may be detectable via periodic variability (or nanohertz frequency gravitational waves). Following our detection of a 5.2 year periodic signal in the quasar PG 1302-102 (Graham et al. 2015), we present a novel analysis of the optical variability of 243,500 known spectroscopically confirmed quasars using data from the Catalina Real-time Transient Survey (CRTS) to look for close (< 0.1 pc) SMBH systems. Looking for a strong Keplerian periodic signal with at least 1.5 cycles over a baseline of nine years, we find a sample of 111 candidate objects. This is in conservative agreement with theoretical predictions from models of binary SMBH populations. Simulated data sets, assuming stochastic variability, also produce no equivalent candidates implying a low likelihood of spurious detections. The periodicity seen is likely attributable to either jet precession, warped accretion disks or periodic accretion associated with a close SMBH binary system. We also consider how other SMBH binary candidates in the literature appear in CRTS data and show that none of these are equivalent to the identified objects. Finally, the distribution of objects found is consistent with that expected from a gravitational wave-driven population. This implies that circumbinary gas is present at small orbital radii and is being perturbed by the black holes. None of the sources is expected to merge within at least the next century. This study opens a new unique window to study a population of close SMBH binaries that must exist according to our current understanding of galaxy and SMBH evolution.Comment: 29 pages, 10 figures, accepted for publication in MNRAS - this version contains extended table and figur

Rotorcraft Smoothing Via Linear Time Periodic Methods

This research presents the development of an on line linear time periodic rotor vibration controller. The Cramer-Rao bound is developed for a linear time periodic system in order to identify the quality of identified system parameters, which are used in system models for controller development. The methods developed in this work allow model parameters can be verified for accuracy and likewise adjusted to improve controller accuracy

Tracking Rhythmicity in Biomedical Signals using Sequential Monte Carlo methods

Cyclical patterns are common in signals that originate from natural systems such as the human body and man-made machinery. Often these cyclical patterns are not perfectly periodic. In that case, the signals are called pseudo-periodic or quasi-periodic and can be modeled as a sum of time-varying sinusoids, whose frequencies, phases, and amplitudes change slowly over time. Each time-varying sinusoid represents an individual rhythmical component, called a partial, that can be characterized by three parameters: frequency, phase, and amplitude. Quasi-periodic signals often contain multiple partials that are harmonically related. In that case, the frequencies of other partials become exact integer multiples of that of the slowest partial. These signals are referred to as multi-harmonic signals. Examples of such signals are electrocardiogram (ECG), arterial blood pressure (ABP), and human voice. A Markov process is a mathematical model for a random system whose future and past states are independent conditional on the present state. Multi-harmonic signals can be modeled as a stochastic process with the Markov property. The Markovian representation of multi-harmonic signals enables us to use state-space tracking methods to continuously estimate the frequencies, phases, and amplitudes of the partials. Several research groups have proposed various signal analysis methods such as hidden Markov Models (HMM), short time Fourier transform (STFT), and Wigner-Ville distribution to solve this problem. Recently, a few groups of researchers have proposed Monte Carlo methods which estimate the posterior distribution of the fundamental frequency in multi-harmonic signals sequentially. However, multi-harmonic tracking is more challenging than single-frequency tracking, though the reason for this has not been well understood. The main objectives of this dissertation are to elucidate the fundamental obstacles to multi-harmonic tracking and to develop a reliable multi-harmonic tracker that can track cyclical patterns in multi-harmonic signals

Centre for Information Science Research Annual Report, 1987-1991

Annual reports from various departments of the AN