Maximum likelihood approach for localization of sources in 3-D space

Bu çalışmanın amacı, anten dizilimi ile aynı düzlemde bulunmayan 3 boyutlu uzayda bulunan kaynakların konumlarının kestirimidir. Kaynak konumları, 2 boyutlu dikdörtgen anten diziliminde toplanan verileri kullanan en büyük olabilirlik kestirimcisi ile belirlenmiştir. En büyük olabilirlik kestirimcisi, diğer kestirim yöntemlerine göre bir çok avantaja sahip olmasına rağmen işlemsel yoğunluğu olan bir algoritmadır. Bu işlemsel yoğunluk, çok boyutlu arama probleminden kaynaklanmaktadır. Karşılaşılan işlemsel yoğunluk, özyinelemeli beklenti en büyükleme algoritmasının ilgilenilen probleme uyarlanmasıyla ortadan kaldırılmıştır. Ayrıca, geliştirilen kestirimcinin başarımının incelenebilmesi için yansız bir kestirimci için alt sınırı oluşturan Cramer-Rao Sınırları çıkarılmıştır. Benzetim örneklerinden kullanılan yöntemin özellikle yüksek sinyal gürültü oranlarında oldukça iyi sonuçlar verdiği gözlemlenmiştir.  Anahtar Kelimeler: Kaynak yerelleştirme, en büyük olabilirlik, beklenti en büyükleme, Cramer-Rao sınırları.Various estimation methods have been proposed for localization  of passive sources till now. Most of these studies assumed, sources were at the same plane with antenna array. This assumption may be inappropriate for some applications in real world. The goal of this study is to estimate unknown locations of sources that is not at same plane with antenna array but in 3-D space. Locations of the sources are determined by maximum likelihood estimator that uses data collected by a 2-D rectangular array. Maximum Likelihood Method is chosen as the estimator since it has better resolution performance than the conventional methods in the presence of less number and highly correlated source signal samples and low signal to noise ratio. Besides these superiorities, stability, asymptotic unbiasedness, asymptotic minimum variance properties and bringing no restrictions on the antenna array are the additional reasons for the decision of this method. Despite these advantages, Maximum Likelihood Estimator has computational complexity. This problem arises from multidimensional search problem. Computational complexity was overcome by adapting iterative Expectation Maximization algorithm to the problem at hand. Furthermore, Cramer-Rao bounds that is the lower bound of any unbiased estimator are derived for analyzing the accuracy performance of the proposed algorithm. It was observed that the proposed algorithm gave satisfactory results especially for high signal to noise ratios.Keywords: Source localization, maximum likelihood, expectation maximization, Cramer-Rao bounds

Eigenvector-based multidimensional frequency estimation : identifiability, performance, and applications.

Multidimensional frequency estimation is a classic signal processing problem that has versatile applications in sensor array processing and wireless communications. Eigenvalue-based two-dimensional (2-D) and N -dimensional ( N -D) frequency estimation algorithms have been well documented, however, these algorithms suffer from limited identifiability and demanding computations. This dissertation develops a framework on eigenvector-based N -D frequency estimation, which contains several novel algorithms that estimate a structural matrix from eigenvectors and then resolve the N -D frequencies by dividing the elements of the structural matrix. Compared to the existing eigenvalue-based algorithms, these eigenvector-based algorithms can achieve automatic pairing without an extra frequency pairing step, and tins the computational complexity is reduced. The identifiability, performance, and complexity of these algorithms are also systematically studied. Based on this study, the most relaxed identifiability condition for the N -D frequency estimation problem is given and an effective approach using optimized weighting factors to improve the performance of frequency estimation is developed. These results are applied in wireless communication for time-varying multipath channel estimation and prediction, as well as for joint 2-D Direction-of-arrival (DOA) tracking of multiple moving targets

A pre-filtering maximum likelihood approach to multiple source direction estimation.

Imperial Users onl

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

Deprettere, “Azimuth and elevation computation in high resolution DOA estimation

ABSTRACT In this paper, we discuss a number of high-resolution direction finding methods for determining the two-dimensional directions of arrival of a number of plane waves, impinging on a sensor array. The array consists of triplets of sensors that are identical, as an extension of the 1D ESPRIT scenario to two dimensions. New algorithms are devised that yield the correct parameter pairs while avoiding an extensive search over the two separate one-dimensional parameter sets

Sampling methods for parametric non-bandlimited signals:extensions and applications

Sampling theory has experienced a strong research revival over the past decade, which led to a generalization of Shannon's original theory and development of more advanced formulations with immediate relevance to signal processing and communications. For example, it was recently shown that it is possible to develop exact sampling schemes for a large class of non-bandlimited signals, namely, certain signals with finite rate of innovation. A common feature of such signals is that they have a parametric representation with a finite number of degrees of freedom and can be perfectly reconstructed from a finite number of samples. The goal of this thesis is to advance the sampling theory for signals of finite rate of innovation and consider its possible extensions and applications. In the first part of the thesis, we revisit the sampling problem for certain classes of such signals, including non-uniform splines and piecewise polynomials, and develop improved schemes that allow for stable and precise reconstruction in the presence of noise. Specifically, we develop a subspace approach to signal reconstruction, which converts a nonlinear estimation problem into the simpler problem of estimating the parameters of a linear model. This provides an elegant and robust framework for solving a large class of sampling problems, while offering more flexibility than the traditional scheme for bandlimited signals. In the second part of the thesis, we focus on applications of our results to certain classes of nonlinear estimation problems encountered in wideband communication systems, most notably ultra-wideband (UWB) systems, where the bandwidth used for transmission is much larger than the bandwidth or rate of information being sent. We develop several frequency domain methods for channel estimation and synchronization in UWB systems, which yield high-resolution estimates of all relevant channel parameters by sampling a received signal below the traditional Nyquist rate. We also propose algorithms that are suitable for identification of more realistic UWB channel models, where a received signal is made up of pulses with different pulse shapes. Finally, we extend our results to multidimensional signals, and develop exact sampling schemes for certain classes of parametric non-bandlimited 2-D signals, such as sets of 2-D Diracs, polygons or signals with polynomial boundaries