One of the biggest challenges in any airborne radar is to distinguish a target from a strong ground echo. The main problem is that the ground echo, called ground clutter, can be up to a million times stronger than the response from the target in question. Today many different filtering methods are used in airborne radar systems to separate the target signal from the ground clutter. All of them with their own advantages and shortcomings. In an ideal world the optimum filter would completely filter out the unwanted ground echo. But as ideal filters don't exist in reality a filter with low sidelobes and minimum loss in signal-to-interference ratio is sought after. A type of filter which exhibit this behaviour are discrete prolate spheroidal sequences (DPSS). This thesis investigated if DPSS could be used as weight functions in multitaper spectrum estimation to filter out ground clutter in the radar signal. A simple clutter model was developed for generating simulated ground clutter which was then filtered out by multitaper and a traditional method. Results showed that it is possible to use DPSS in multitaper spectrum estimation and that it outperforms a basic traditional method in clutter filtration as long as parameters such as bandwidth and the number of sequences used are chosen properly. The increase in performance against the traditional method comes at a cost of increased computational load with each additional DPSS order used. A full factorial experiment was also performed to investigate which parameters were important for maximising improvement factor and minimum detectable velocity. The results from these showed that a low bandwidth in the generation of the DPSS was preferable and that a high number of time samples and DPSS used improved performance. They also showed that for an increase in number of time samples the bandwidth and number of sequences used need to be adjusted to maintain the same level of the improvement factor. It was concluded that future work should focus on validation with more advanced clutter models and MTI filters in simulations as well as validation against real radar data. If proved successful, optimisation of calculation speeds as well as implementation of adaptive choice of DPSS bandwidth would be beneficial before being implemented in a radar system. / En av de största utmaningarna i ett flygburet radarsystem är att urskilja ett mål från markekot. Problem uppstår eftersom markekot, kallat markklotter, kan vara upp emot en miljon gånger starkare än svaret från målet i fråga. I dagsläget används flera olika filtreringmetoder i flyburna radarsystem för att urskilja målet från markklottret, alla har sina fördelar och nackdelar. I en ideal värld skulle det optimala filtret filtrera ut markklottret fullständigt och endast bevara målsignalen. Eftersom dessa filter inte existerar i verkligheten eftersträvas istället ett filter med låga sidlober och minimal förlust i signal-till-interferens ration. En typ av filter som uppvisar detta beteende är diskreta prolata sfäroid sekvenser (DPSS). Denna uppsats undersöker ifall DPSS kan användas som viktfunktioner i multitaper spektralestimering för att filtrera ut markklotter i en radarsignal. En enkel klottermodell utvecklades för generering av simulerat markklotter som sedan filtrerades ut med multitaper metoden och en traditionell metod. Resultatet visade att det var möjligt att använda DPSS i multitaper spektralestimering och att metodens prestanda överstiger den traditionella meteoden, så länge parametrar som bandbredd och antal använda sekvenser väljs korrekt. Prestandaförbättringen mot den traditionella metoden uppstår mot en kostnad i beräkningstid som ökar med varje DPSS ordning som används. Ett full factorial experiment utfördes också för att undersöka vilka parametrar som hade störst påverkan för att maximera förbättringsfaktorn och minsta detekterbara hastighet. Resultated visade att låg bandbredd vid generering av DPSS var att föredra, samt att ett stort antal använda DPSS och tidssamples ökade prestandan. Resultaten visade också att för ett ökat antal tisdssamples så måste bandbredd och antal sekvenser som används justeras för att bibehålla samma nivå av förbättringsfaktorn. Slutligen rekommenderades det att framtida arbete borde fokusera på validering med mer avancerade klottermodeller och MTI filter i simuleringar, samt validering mot verklig radar data. Om detta visar sig framgångsrikt bör optimering av beräkningstid och implementation av ett adaptivt val av DPSS bandbredd göras före implementering i ett radarsystem.

Four contributions to the multitaper method of applied spectrum estimation are presented. These are a generalization of the multitaper method of spectrum estimation to time-series possessing irregularly spaced samples, a robust spectrum estimate suitable for cyclostationary, or quasi cyclostationary time-series, an improvement over the standard, multitaper spectrum estimates using quadratic inverse theory, and finally a method of scan-free spectrum estimation using a rotational shear-interferometer. Each of these topics forms a chapter in this thesis. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-02-05 18:01:45.187

Surgical scheduling is complicated by naturally occurring, and human-induced variability in the demand for surgical services. We used time series methods to detect, model and forecast these behaviors in surgical demand time series to help improve the scheduling of scarce surgical resources. With institutional approval, we studied 47,752 surgeries undertaken at a large academic medical center over a six-year time frame. Each daily sample in this time series represented the aggregate total hours of surgeries worked on a given day. Linear terms such as periodic cycles, trends, and serial correlations explained approximately 80 percent of the variance in the raw data. We used a moving variance filter to help explain away a large share of the heteroscedastic behavior mainly attributable to surgical activities on specific US holidays, which we defined as holiday variance. In the course of this research, we made a thoughtful attempt to understand the time series structure within our surgical demand data. We also laid a foundation, for further development, of two time series techniques, the multiwindow variance filter and cyclostatogram that can be applied not only to surgical demand time series, but also to other time series problems from other disciplines. We believe that understanding the non-stationarity, in surgical demand time series, may be an important initial step in helping health care managers save critical health care dollars. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-02-09 11:55:42.494

No description available.

Robust nonparametric spectral estimation includes generating an accurate estimate of the Power Spectral Density (PSD) for a given set of data while trying to minimize the bias due to data outliers. Robust nonparametric spectral estimation is applied in the domain of electrical communications and digital signal processing when a PSD estimate of the electromagnetic spectrum is desired (often for the goal of signal detection), and when the spectrum is also contaminated by Impulsive Noise (IN). Power Line Communication (PLC) is an example of a communication environment where IN is a concern because power lines were not designed with the intent to transmit communication signals. There are many different noise models used to statistically model different types of IN, but one popular model that has been used for PLC and various other applications is called the Middleton Class A model, and this model is extensively used in this thesis. The performances of two different nonparametric spectral estimation methods are analyzed in IN: the Welch method and the multitaper method. These estimators work well under the common assumption that the receiver noise is characterized by Additive White Gaussian Noise (AWGN). However, the performance degrades for both of these estimators when they are used for signal detection in IN environments. In this thesis basic robust estimation theory is used to modify the Welch and multitaper methods in order to increase their robustness, and it is shown that the signal detection capabilities in IN is improved when using the modified robust estimators. / Master of Science / One application of blind spectral estimation is blind signal detection. Unlike a car radio, where the radio is specifically designed to receive AM and PM radio waves, sometimes it is useful for a radio to be able to detect the presence of transmitted signals whose characteristics are not known ahead of time. Cognitive radio is one application where this capability is useful. Often signal detection is inhibited by Additive White Gaussian Noise (AWGN). This is analogous to trying to hear a friend speak (signal detection) in a room full of people talking (background AWGN). However, some noise environments are more impulsive in nature. Using the previous analogy, the background noise could be loud banging caused by machinery; the noise will not be as constant as the chatter of the crowd, but it will be much louder. When power lines are used as a medium for electromagnetic communication (instead of just sending power), it is called Power Line Communication (PLC), and PLC is a good example of a system where the noise environment is impulsive. In this thesis, methods used for blind spectral estimation are modified to work reliably (or robustly) for impulsive noise environments.

During processing of data received by an airborne radar one of the issues is that the typical signal echo from the ground produces a large perturbation. Due to this perturbation it can be difficult to detect targets with low velocity or a low signal-to-noise ratio. Therefore, a filtering process is needed to separate the large perturbation from the target signal. The traditional method include a tapered Fourier transform that operates in parallel with a MTI filter to suppress the main spectral peak in order to produce a smoother spectral output. The difference between a typical signal echo produced from an object in the environment and the signal echo from the ground can be of a magnitude corresponding to more than a 60 dB difference. This thesis presents research of how the multitaper approach can be utilized in concurrence with the minimum variance estimation technique, to produce a spectral estimation that strives for a more effective clutter suppression. A simulation model of the ground clutter was constructed and also a number of simulations for the multitaper, minimum variance estimation technique was made. Compared to the traditional method defined in this thesis, there was a slight improvement of the improvement factor when using the multitaper approach. An analysis of how variations of the multitaper parameters influence the results with respect to minimum detectable velocity and improvement factor have been carried out. The analysis showed that a large number of time samples, a large number of tapers and a narrow bandwidth provided the best result. The analysis is based on a full factorial simulation that provides insight of how to choose the DPSS parameters if the method is to be implemented in a real radar system.

No description available.

L'échographie est aujourd'hui une technique d'imagerie de diagnostic répandue. Si l'imagerie dite ‘classique' basée sur la réponse linéaire des tissus est couramment utilisée, l'imagerie harmonique, basée sur la réponse non linéaire des tissus, est maintenant aussi utilisée en routine clinique. L'estimation du paramètre de non linéarité d'un milieu par une technique ultrasonore amène de nouvelles perspectives en termes d'imagerie et de diagnostic. Cependant, la méthode de mesure du paramètre de non linéarité est limitée par deux facteurs, la présence du speckle et la concentration de l'énergie à une profondeur donnée (la zone focale). Cette thèse a pour objectifs de répondre aux deux limitations mentionnées précédemment en proposant de nouvelles méthodes de lissage de l'image pour réduire le speckle et d'améliorer l'estimation du paramètre de non linéarité en mode écho par de nouvelles méthodes d'émission. Dans un premier temps, il a été proposé d'utiliser une méthode de filtrage spatiale basée sur des filtres orthogonaux (filtres de Thomson) lors de la formation de voie en réception pour lisser le speckle. Ce filtrage spatiale intervient après la transmission d'ondes planes sous différents angles pour améliorer la résolution spatiale et le contraste tout en accélérant la cadence d'imagerie. Dans un deuxième temps, l'estimation du paramètre de non linéarité est faite avec une méthode comparative. Le champ de pression du second harmonique d'une zone de référence est comparé avec le champ de pression d'une zone dont le paramètre de non linéarité est inconnu. Cependant, dans le cas des images échographiques, le champ de pression du second harmonique n'est pas accessible. Nous faisons l'hypothèse que la pression acoustique locale est liée à l'intensité de l'image échographique si le speckle est réduit et lissé. La transmission d'ondes planes et l'application de filtres orthogonaux permet de mieux délimiter le paramètre de non linéarité par rapport à une transmission focalisée / Nowadays, ultrasound imaging is a common diagnostic tool thanks to its non-invasive behavior and relatively cheap equipment. Classic medical echographic imaging is based on the linear response of the biological tissue. However harmonic imaging, based on the harmonic frequencies generated by the nonlinear properties of the tissue, is more and more used for clinical application. The quantification of nonlinearity is based on the evaluation of the nonlinearity parameter which strongly influences the harmonics generation. The nonlinearity parameter estimation using an echographic approach would bring new modalities for imaging and diagnosis. However the echographic method for nonlinearity estimation is limited by two factors: the presence of speckles in the image and the focalization used during transmission, which concentrates the energy at one particular depth. The objectives of this thesis work are developing novel approaches to reduce the speckle noise using original smoothing techniques and improving the nonlinearity parameter estimation in echo mode using new transmission-reception strategies. Firstly, new speckle noise reduction approaches were investigated. The Thomson’s multitaper approach was proposed, consisting in using several different orthogonal apodizations during beamforming. This method was combined to a coherent plane-wave compounding transmission-reception strategy improving the spatial resolution and the contrast while improving the frame rate. In a second time, the nonlinearity parameter was estimated using a comparative method. The second-harmonic pressure field of a reference area was compared to the pressure field of an area where the nonlinearity parameter is unknown. However in echo-mode, the pressure field of the medium is unknown. It is assumed in this thesis work that the local pressure can be derived from envelope image local amplitude if the speckle noise is smoothed. The nonlinearity parameter estimation has been improved using plane-wave transmission and orthogonal apodizations compared to the use of a single focalization transmission / Oggigiorno, le tecniche di imaging ad ultrasuoni sono un comune strumento di diagnosi, grazie alla loro non invasività e alla relativa economicità dei sistemi. La risposta lineare dei tessuti biologici è la base per le tecniche di imaging ecografico tradizionali. La generazione di frequenze ad armoniche superiori da parte dei tessuti può essere sfruttata per sviluppare tecniche di imaging innovative (i.e., imaging armonico), che sono sempre più utilizzate per applicazioni cliniche. Tali tecniche sono basate sul metodo di valutazione del parametro di non linearità che influenza fortemente la generazione delle armoniche all’interno dei tessuti. I metodi per la stima dei suddetti parametri sfruttano solitamente un approccio ecografico tradizionale. Di conseguenza, gli effetti legati alla focalizzazione impiegata durante la trasmissione, che concentra l’energia ad una particolare profondità, e la presenza di speckle nell’immagine finale, rendono più incerta la stima del parametro di non linearità. In questa tesi sono proposti metodi innovativi finalizzati a due scopi: ridurre, nelle immagini, il rumore dovuto a speckle, tramite l’adozione di nuove tecniche di smoothing; migliorare la stima dei parametri di non linearità, tramite l’impiego di nuove strategie di beamforming in trasmissione e ricezione. Per ridurre il rumore dovuto a speckle, è stato proposto un approccio di filtraggio spaziale basato sull’impiego dei filtri di Thomson. Tale tecnica consiste nell’impiego di numerose apodizzazioni ortogonali fra di loro in fase di beamforming. Il metodo è stato in particolare combinato con la tecnica di imaging coherent plane-wave compounding, con lo scopo di migliorare la risoluzione spaziale e il contrasto e, al contempo, incrementare il frame rate. Il parametro di non linearità è stato misurato tramite un approccio comparativo. Il campo di pressione della seconda armonica in un’area di riferimento dell’immagine è stato confrontato con quello di un’area in cui il parametro di non linearità è ignoto. In questa tesi, grazie alla riduzione del rumore speckle, è stato possibile assumere che il campo di pressione

In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper methods and statistics, and estimate the variance of the estimates by the weighted jackknife method. I will discuss its applicability and usefulness in nonlinear quadratic phase coupling detection and analysis for multivariate random processes. Furthermore, I will develop the time-varying canonical bicoherence for the nonlinear analysis of non-stationary random processes. In this thesis, the canonical bicoherence is mainly applied in two types of data: a) three-component geomagnetic field data, and b) high-dimensional brain electroencephalogram data. Both results obtained will be linked with physical or physiological interpretations. In particular, this thesis is the first work where the novel method of ``canonical bicoherence'' is introduced and applied to the nonlinear quadratic phase coupling detection and analysis for multivariate random processes. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-10-31 15:03:57.596

Cognitive radio is a technology that aims to maximize the current usage of the licensed frequency spectrum. Cognitive radio aims to provide services for license-exempt users by making use of dynamic spectrum access (DSA) and opportunistic spectrum sharing strategies (OSS). Cognitive radios are defined as intelligent wireless devices capable of adapting their communication parameters in order to operate within underutilized bands while avoiding causing interference to licensed users. An underused band of frequencies in a specific location or time is known as a spectrum hole. Therefore, in order to locate spectrum holes, reliable spectrum sensing algorithms are crucial to facilitate the evolution of cognitive radio networks. Since a large and growing body of literature has mainly focused into the conventional time domain (TD) energy detector, throughout this thesis the problem of spectrum sensing is investigated within the context of a frequency domain (FD) approach. The purpose of this study is to investigate detection based on methods of nonparametric power spectrum estimation. The considered methods are the periodogram, Bartlett's method, Welch overlapped segments averaging (WOSA) and the Multitaper estimator (MTE). Another major motivation is that the MTE is strongly recommended for the application of cognitive radios. This study aims to derive the detector performance measures for each case. Another aim is to investigate and highlight the main differences between the TD and the FD approaches. The performance is addressed for independent and identically distributed (i.i.d.) Rayleigh channels and the general Rician and Nakagami fading channels. For each of the investigated detectors, the analytical models are obtained by studying the characteristics of the Hermitian quadratic form representation of the decision statistic and the matrix of the Hermitian form is identified. The results of the study have revealed the high accuracy of the derived mathematical models. Moreover, it is found that the TD detector differs from the FD detector in a number of aspects. One principal and generalized conclusion is that all the investigated FD methods provide a reduced probability of false alarm when compared with the TD detector. Also, for the case of periodogram, the probability of sensing errors is independent of the length of observations, whereas in time domain the probability of false alarm is increased when the sample size increases. The probability of false alarm is further reduced when diversity reception is employed. Furthermore, compared to the periodogram, both Bartlett method and Welch method provide better performance in terms of lower probability of false alarm but an increased probability of detection for a given probability of false alarm. Also, the performance of both Bartlett's method and WOSA is sensitive to the number of segments, whereas WOSA is also sensitive to the overlapping factor. Finally, the performance of the MTE is dependent on the number of employed discrete prolate spheroidal (Slepian) sequences, and the MTE outperforms the periodogram, Bartlett's method and WOSA, as it provides the minimal probability of false alarm.