System Identification I

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Statistical Signal Processing Detection Estimation And Time Series Analysis

This paper is devoted to the maximum likelihood estimation of multiple sources in the presence of unknown noise. With the spatial noise covariance modeled as a function of certain unknown parameters, e.g., an autoregressive (AR) model, a direct and systematic way is developed to find the exact maximum likelihood (ML) estimates of all parameters associated with the direction finding problem, including the direction-of-arrival (DOA) angles /spl Theta/, the noise parameters /spl alpha/, the signal covariance /spl Phi//sub s/, and the noise power /spl sigma//sup 2/. We show that the estimates of the linear part of the parameter set /spl Phi//sub s/ and /spl sigma//sup 2/ can be separated from the nonlinear parts /spl Theta/ and /spl alpha/. Thus, the estimates of /spl Phi//sub s/ and /spl sigma//sup 2/ become explicit functions of /spl Theta/ and /spl alpha/. This results in a significant reduction in the dimensionality of the nonlinear optimization problem. Asymptotic analysis is performed on the estimates of /spl Theta/ and /spl alpha/, and compact formulas are obtained for the Cramer-Rao bounds (CRB's). Finally, a Newton-type algorithm is designed to solve the nonlinear optimization problem, and simulations show that the asymptotic CRB agrees well with the results from Monte Carlo trials, even for small numbers of snapshots. >

Maximum likehood DOA estimation and asymptotic Cramer-Rao bounds for additive unknown colored noise

We propose a new subspace-based localization of far-field (FF) and near-field (NF) narrowband signals (LOFNS) without eigendecomposition impinging on a symmetrical uniform linear array, where the oblique projection operator is utilized to isolate the NF signals from the FF ones, and the procedures of computationally burdensome eigendecomposition are not required in the estimation of the NF and FF location parameters and the computation of oblique projection operator. As a measure against the impact of finite array data, an alternating iterative scheme is presented to improve the estimation accuracy of the oblique projection operator and, hence, that of the NF location parameters, where the “saturation behavior” encountered in most of localization methods is overcome. Furthermore, the statistical analysis of the proposed LOFNS is studied, and the asymptotic mean-squared-error expressions of the estimation errors are derived for the FF and NF location parameters. Finally, the effectiveness and the theoretical analysis of the proposed LOFNS are substantiated through numerical examples, and the simulation results demonstrate that the LOFNS provides remarkable and satisfactory estimation performance for both the NF and FF signals compared with some existing localization methods even with eigendecomposition.

Subspace-Based Localization of Far-Field and Near-Field Signals Without Eigendecomposition

Nested arrays have recently attracted a growing concern owing to their ability of achieving extended aperture and enhanced degrees of freedom (DOFs) compared to conventional uniform linear arrays (ULAs). In this paper, we devise a source localization scheme under the simultaneous existence of near-field (NF) and far-field (FF) sources using a symmetric double-nested array (SDNA). First, the direction-of-arrivals (DOAs) of FF sources are estimated using 1-D MUSIC spectrum. Then, the NF components can be extracted by applying the oblique projection technique. By constructing a special NF cumulant matrix and performing vectorization to generate the virtual array signal, the DOAs of NF sources can be estimated by the spatial smoothing MUSIC (SS-MUSIC) algorithm. Finally, with the NF DOA estimates, the range estimates of NF sources are obtained via 1-D peak searching. We also derive the consecutive range of the difference coarray and optimum array configurations for the SDNA, under a given number of sensors. The proposed algorithm exploits the large coarray aperture to enhance the localization performance and can distinguish correctly the types of the sources. The numerical results demonstrate that our proposed method significantly outperforms the existing methods for both DOA and range estimations.

Localization of Mixed Near-Field and Far-Field Sources Using Symmetric Double-Nested Arrays

This paper investigates the localization of multiple near-field narrowband sources with a symmetric uniform linear array, and a new linear prediction approach based on the truncated singular value decomposition (LPATS) is proposed by taking an advantage of the anti-diagonal elements of the noiseless array covariance matrix. However, when the number of array snapshots is not sufficiently large enough, the “saturation behavior” is usually encountered in most of the existing localization methods for the near-field sources, where the estimation errors of the estimated directions-of-arrival (DOAs) and ranges cannot decrease with the signal-to-noise ratio. In this paper, an oblique projection based alternating iterative scheme is presented to improve the accuracy of the estimated location parameters. Furthermore, the statistical analysis of the proposed LPATS is studied, and the asymptotic mean-square-error expressions of the estimation errors are derived for the DOAs and ranges. The effectiveness and the theoretical analysis of the proposed LPATS are verified through numerical examples, and the simulation results show that the LPATS provides good estimation performance for both the DOAs and ranges compared to some existing methods.

Localization of Near-Field Sources Based on Linear Prediction and Oblique Projection Operator

In this paper, we investigate the problems of estimating and tracking the location parameters [i.e., directions-of-arrival (DOAs) and ranges] of multiple near-field (NF) narrowband sources impinging on a symmetric uniform linear array, and a simple subspace-based algorithm for localization of NF sources (SALONS) is presented, where the computationally burdensome eigendecomposition and spectrum peak searching are avoided. In the SALONS, the DOAs and ranges are estimated separately with a one-dimensional subspace-based estimation technique, where the null spaces are obtained through the linear operation of the correlation matrices formed from the antidiagonal elements of the noiseless array covariance matrix, and the estimated DOAs and ranges are automatically paired without any additional procedure. Then the statistical analysis of the presented batch SALONS is studied, and the asymptotic mean-squared-error expressions of the estimated DOAs and ranges are derived. Furthermore, an online algorithm is developed for tracking the multiple moving NF sources with crossover points on their trajectories. The effectiveness and the theoretical analysis of the presented algorithms are verified through numerical examples, and the simulation results show that the proposed algorithms provide good estimation and tracking performance for DOAs and show satisfactory estimation and tracking performance for ranges.

Subspace-Based Algorithms for Localization and Tracking of Multiple Near-Field Sources

Source localization for near-field narrowband signal is an important topic in array signal processing. Deep neural network (DNN) based methods are data-driven and free of pre-assumptions about data model and are expected to learn the intricate nonlinear structure in large data sets. This paper proposes a framework of DNN where a regression layer is utilized to address the problem of near-field source localization. Unlike previous studies in which DOA estimation is modeled as a classification problem and have a relatively low resolution, we exploit a regression model and aim to improve the estimation accuracy. In the training stage, we propose a novel form of feature representation to take full advantage of the convolution networks. In addition, the architecture of deep neural networks is well designed taking in to consideration the trade-off between the expression ability and under-training risks. The simulation results show that the proposed approach has a rather high validation accuracy with a high resolution, and also outperforms some conventional methods in adverse environments such as low signal to noise ratio (SNR) or small number of snapshots.

Deep Learning Based Localization of Near-Field Sources with Exact Spherical Wavefront Model

In this paper, we consider the source localization for a mixed near-field (NF) and far-field (FF) narrowband signals impinging on a uniform linear array (ULA) with the symmetrical geometric configuration. A computationally efficient direction-of-arrivals (DOAs) and range estimation method for the mixed NF and FF signals is proposed, where the DOAs of the NF and FF signals are estimated separately, and the computationally burdensome eigendecomposition is avoided. Comparing to some existent methods, the proposed method can separate the NF signals from the FF signals more efficiently, and consequently the estimation performance is improved. The effectiveness of the proposed method is verified though numerical examples.

Nanning Zheng

Papers

Subspace-Based Localization of Far-Field and Near-Field Signals Without Eigendecomposition

Localization of Near-Field Sources Based on Linear Prediction and Oblique Projection Operator

Subspace-Based Algorithms for Localization and Tracking of Multiple Near-Field Sources

Deep Learning Based Localization of Near-Field Sources with Exact Spherical Wavefront Model

A computationally efficient source localization method for a mixture of near-field and far-field narrowband signals