Parametric Estimation of Harmonically Related Sinusoids

Mud-pulse telemetry is a method used for measurement-while-drilling (MWD)in the oil industry. The telemetry signals are corrupted by spurious mud pump noise consisting of a large number of harmonically related sinusoids. In order to denoise the signal, the noise parameters have to be tracked accurately in real time. There are well established parametric estimation techniques for determining various parameters of independent sinusoids. The iterative methods based on the linear prediction properties of the sinusoids provide a computationally e±cient way of solving the non linear optimization problem presented by these methods. However, owing to the large number of these sinusoids, incorporating the harmonic relationship in the problem becomes important. This thesis is aimed at solving the problem of estimating parameters of harmonically related sinusoids. We examine the efficacy of IQML algorithm in estimating the parameters of the telemetry signal for varying SNRs and data lengths. The IQML algorithm proves quite robust and successfully tracks both stationary and slowly varying frequency signals. Later, we propose an algorithm for fundamental frequency estimation which relies on the initial harmonic frequency estimate. The results of tests performed on synthetic data that imitates real field data are presented. The analysis of the simulation results shows that the proposed method manages to remove noise causing sinusoids in the telemetry signal to a great extent. The low computational complexity of the algorithm also makes for an easy implementation on field where computational power is limited

Filtering on DOA estimation using array of sensors

Orientador: Amauri LopesDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho aborda o problema de estimação da direção de chegada (DOA) de ondas planas usando arranjo de sensores. Existem diversos estimadores para DOA relatados na literatura. Dentre os estimadores de alta resolução, se destacam os métodos MODE e MODEX, que possuem como base o estimador de máxima verossimilhança (MLE). Este trabalho apresenta o desenvolvimento dos métodos MODE, MODEX e de uma versão melhorada do MODEX, o método MODEX Modi?ed. Estes dois últimos estimadores produzem várias estimativas candidatas e usam o critério de máxima verossimilhança para selecionar aquelas que representam as melhores estimativas para os ângulos de chegada. Entretanto, para uma relação sinalruído baixa, estes métodos sofrem uma forte degradação na escolha das candidatas. Na busca de reduzir esta degradação, é apresentada uma proposta de ?ltragem nos sinais captados pelos sensores, com o objetivo de melhorar a relação sinalruído. São propostos dois projetos de ?ltro FIR: um por alocação de pólos e zeros, e outro por amostragem em freqüência. Os resultados obtidos mostram que esta proposta de ?ltragem é válida e que se consegue reduzir signi?cativamente a SNR do limiar de desempenho apresentado pelos métodos MODEX e MODEX Modi?ed.Abstract: This work deals with the estimation of the direction of arrival (DOA) of plane waves using array of sensors. There are various estimators for DOA reported in literature. The MODE and MODEX methods, based on the maximum likelihood criterion, are the best high resolution DOA estimators. This work presents the development of these methods as well as of an improved version of the MODEX, named MODEX Modi?ed. MODEX and MODEX Modi?ed produce some estimates that are candidates for the DOA estimation and use the maximum likelihood criterion to select the best ones. However, for low signaltonoise ratio, the selection process suffers a strong performance degradation. In order to reduce this degradation, this work proposes to ?lter the received signals aiming to improve the signaltonoise ratio. Two FIR ?lters are considered: one composed by poles and zeros and another obtained by sampling in the frequency domain. Simulation results show that this proposal improves signi?cantly the performance of both MODEX and MODEX Modi?ed.MestradoTelecomunicações e TelemáticaMestre em Engenharia Elétric

Efficient Beamspace Eigen-Based Direction of Arrival Estimation schemes

The Multiple SIgnal Classification (MUSIC) algorithm developed in the late 70\u27s was the first vector subspace approach used to accurately determine the arrival angles of signal wavefronts impinging upon an array of sensors. As facilitated by the geometry associated with the common uniform linear array of sensors, a root-based formulation was developed to replace the computationally intensive spectral search process and was found to offer an enhanced resolution capability in the presence of two closely-spaced signals. Operation in beamspace, where sectors of space are individually probed via a pre-processor operating on the sensor data, was found to offer both a performance benefit and a reduced computationa1 complexi ty resulting from the reduced data dimension associated with beamspace processing. Little progress, however, has been made in the development of a computationally efficient Root-MUSIC algorithm in a beamspace setting. Two approaches of efficiently arriving at a Root-MUSIC formulation in beamspace are developed and analyzed in this Thesis. In the first approach, a structura1 constraint is placed on the beamforming vectors that can be exploited to yield a reduced order polynomial whose roots provide information on the signal arrival angles. The second approach is considerably more general, and hence, applicable to any vector subspace angle estimation algorithm. In this approach, classical multirate digital signal processing is applied to effectively reduce the dimension of the vectors that span the signal subspace, leading to an efficient beamspace Root-MUSIC (or ESPRIT) algorithm. An auxiliaay, yet important, observation is shown to allow a real-valued eigenanalysis of the beamspace sample covariance matrix to provide a computational savings as well as a performance benefit, particularly in the case of correlated signal scenes. A rigorous theoretical analysis, based upon derived large-sample statistics of the signal subspace eigenvectors, is included to provide insight into the operation of the two algorithmic methodologies employing the real-valued processing enhancement. Numerous simulations are presented to validate the theoretical angle bias and variance expressions as well as to assess the merit of the two beamspace approaches

On the Resolution Probability of Conditional and Unconditional Maximum Likelihood DoA Estimation

After decades of research in Direction of Arrival (DoA) estimation, today Maximum Likelihood (ML) algorithms still provide the best performance in terms of resolution capabilities. At the cost of a multidimensional search, ML algorithms achieve a significant reduction of the outlier production mechanism in the threshold region, where the number of snapshots per antenna and/or the signal to noise ratio (SNR) are low. The objective of this paper is to characterize the resolution capabilities of ML algorithms in the threshold region. Both conditional and unconditional versions of the ML algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude. By using random matrix theory techniques, the finite dimensional distributions of both cost functions are shown to be Gaussian distributed in this asymptotic regime, and a closed form expression of the corresponding asymptotic covariance matrices is provided. These results allow to characterize the asymptotic behavior of the resolution probability, which is defined as the probability that the cost function evaluated at the true DoAs is smaller than the values that it takes at the positions of the other asymptotic local minima

Signal Subspace Processing in the Beam Space of a True Time Delay Beamformer Bank

A number of techniques for Radio Frequency (RF) source location for wide bandwidth signals have been described that utilize coherent signal subspace processing, but often suffer from limitations such as the requirement for preliminary source location estimation, the need to apply the technique iteratively, computational expense or others. This dissertation examines a method that performs subspace processing of the data from a bank of true time delay beamformers. The spatial diversity of the beamformer bank alleviates the need for a preliminary estimate while simultaneously reducing the dimensionality of subsequent signal subspace processing resulting in computational efficiency. The pointing direction of the true time delay beams is independent of frequency, which results in a mapping from element space to beam space that is wide bandwidth in nature. This dissertation reviews previous methods, introduces the present method, presents simulation results that demonstrate the assertions, discusses an analysis of performance in relation to the Cramer-Rao Lower Bound (CRLB) with various levels of noise in the system, and discusses computational efficiency. One limitation of the method is that in practice it may be appropriate for systems that can tolerate a limited field of view. The application of Electronic Intelligence is one such application. This application is discussed as one that is appropriate for a method exhibiting high resolution of very wide bandwidth closely spaced sources and often does not require a wide field of view. In relation to system applications, this dissertation also discusses practical employment of the novel method in terms of antenna elements, arrays, platforms, engagement geometries, and other parameters. The true time delay beam space method is shown through modeling and simulation to be capable of resolving closely spaced very wideband sources over a relevant field of view in a single algorithmic pass, requiring no course preliminary estimation, and exhibiting low computational expense superior to many previous wideband coherent integration techniques

Signal Subspace Processing in the Beam Space of a True Time Delay Beamformer Bank

A number of techniques for Radio Frequency (RF) source location for wide bandwidth signals have been described that utilize coherent signal subspace processing, but often suffer from limitations such as the requirement for preliminary source location estimation, the need to apply the technique iteratively, computational expense or others. This dissertation examines a method that performs subspace processing of the data from a bank of true time delay beamformers. The spatial diversity of the beamformer bank alleviates the need for a preliminary estimate while simultaneously reducing the dimensionality of subsequent signal subspace processing resulting in computational efficiency. The pointing direction of the true time delay beams is independent of frequency, which results in a mapping from element space to beam space that is wide bandwidth in nature. This dissertation reviews previous methods, introduces the present method, presents simulation results that demonstrate the assertions, discusses an analysis of performance in relation to the Cramer-Rao Lower Bound (CRLB) with various levels of noise in the system, and discusses computational efficiency. One limitation of the method is that in practice it may be appropriate for systems that can tolerate a limited field of view. The application of Electronic Intelligence is one such application. This application is discussed as one that is appropriate for a method exhibiting high resolution of very wide bandwidth closely spaced sources and often does not require a wide field of view. In relation to system applications, this dissertation also discusses practical employment of the novel method in terms of antenna elements, arrays, platforms, engagement geometries, and other parameters. The true time delay beam space method is shown through modeling and simulation to be capable of resolving closely spaced very wideband sources over a relevant field of view in a single algorithmic pass, requiring no course preliminary estimation, and exhibiting low computational expense superior to many previous wideband coherent integration techniques

Direction of Arrival Estimation and Tracking with Sparse Arrays

Direction of Arrival (DOA) estimation and tracking of a plane wave or multiple plane waves impinging on an array of sensors from noisy data are two of the most important tasks in array signal processing, which have attracted tremendous research interest over the past several decades. It is well-known that the estimation accuracy, angular resolution, tracking capacity, computational complexity, and hardware implementation cost of a DOA estimation and/or tracking technique depend largely on the array geometry. Large arrays with many sensors provide accurate DOA estimation and perfect target tracking, but they usually suffer from a high cost for hardware implementation. Sparse arrays can yield similar DOA estimates and tracking performance with fewer elements for the same-size array aperture as compared to the traditional uniform arrays. In addition, the signals of interest may have rich temporal information that can be exploited to effectively eliminate background noise and significantly improve the performance and capacity of DOA estimation and tracking, and/or even dramatically reduce the computational burden of estimation and tracking algorithms. Therefore, this thesis aims to provide some solutions to improving the DOA estimation and tracking performance by designing sparse arrays and exploiting prior knowledge of the incident signals such as AR modeled sources and known waveforms. First, we design two sparse linear arrays to efficiently extend the array aperture and improve the DOA estimation performance. One scheme is called minimum redundancy sparse subarrays (MRSSA), where the subarrays are used to obtain an extended correlation matrix according to the principle of minimum redundancy linear array (MRLA). The other linear array is constructed using two sparse ULAs, where the inter-sensor spacing within the same ULA is much larger than half wavelength. Moreover, we propose a 2-D DOA estimation method based on sparse L-shaped arrays, where the signal subspace is selected from the noise-free correlation matrix without requiring the eigen-decomposition to estimate the elevation angle, while the azimuth angles are estimated based on the modified total least squares (TLS) technique. Second, we develop two DOA estimation and tracking methods for autoregressive (AR) modeled signal source using sparse linear arrays together with Kalman filter and LS-based techniques. The proposed methods consist of two common stages: in the first stage, the sources modeled by AR processes are estimated by the celebrated Kalman filter and in the second stage, the efficient LS or TLS techniques are employed to estimate the DOAs and AR coefficients simultaneously. The AR-modeled sources can provide useful temporal information to handle cases such as the ones, where the number of sources is larger than the number of antennas. In the first method, we exploit the symmetric array to transfer a complex-valued nonlinear problem to a real-valued linear one, which can reduce the computational complexity, while in the second method, we use the ordinary sparse arrays to provide a more accurate DOA estimation. Finally, we study the problem of estimating and tracking the direction of arrivals (DOAs) of multiple moving targets with known signal source waveforms and unknown gains in the presence of Gaussian noise using a sparse sensor array. The core idea is to consider the output of each sensor as a linear regression model, each of whose coefficients contains a pair of DOAs and gain information corresponding to one target. These coefficients are determined by solving a linear least squares problem and then updating recursively, based on a block QR decomposition recursive least squares (QRD-RLS) technique or a block regularized LS technique. It is shown that the coefficients from different sensors have the same amplitude, but variable phase information for the same signal. Then, simple algebraic manipulations and the well-known generalized least squares (GLS) are used to obtain an asymptotically-optimal DOA estimate without requiring a search over a large region of the parameter space