Mathematical Problems in Engineering

Volume 2015, Article ID 231307, 8 pages

http://dx.doi.org/10.1155/2015/231307

## Direction of Arrival Estimation Based on DDOA and Self-Organizing Map

School of Science, North University of China, Taiyuan, Shanxi 030051, China

Received 4 June 2015; Revised 23 July 2015; Accepted 5 August 2015

Academic Editor: Peter Liu

Copyright © 2015 Xiuhui Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

An effective two-level self-organizing map (SOM) neural network for direction of arrival (DOA) of sound signals estimation is proposed. The approach is based on the distance difference of arrival (DDOA) and a uniform linear sensor array in a 2D plane; it performs a nonlinear mapping between the DDOA vectors and angles of arrival (AOA). We found that the topological order of DDOA vectors and AOAs of same signals is uniform; thus, the topological order preserving of SOM network makes it valid to estimate AOA through DDOA. From the results of simulations and lake experiments, it is shown that the network has the advantage of accuracy and robustness, can be trained in advance, and is easy to implement.

#### 1. Introduction

Target detection and localization are important problems in sonar, radar, radio emitter tracking, and mobile communications, and estimation of sound signal source direction is one of the basic issues. In the past few decades, varieties of approaches have been proposed for solving the direction of arrival (DOA) of signal source, such as the multiple signal classification (MUSIC) algorithm [1], the estimation of signal parameters via rotational invariance technique (ESPRIT) [2]. These algorithms are known for the resolution of high accuracy and well performance in case of low signal-to-noise ratios. They decompose the signal observation space into two orthogonal subspaces: signal subspace and noise subspace, and get the estimation of angle of arrival (AOA) by finding the peak of spatial spectrum function. However, MUSIC and ESPRIT need to calculate eigenvalue decomposition (EVD) of the cross-correlation matrix and singular value decomposition (SVD) of the sensor array output data, which makes the time of computation long and limits their practical applicability. Recently, artificial neural networks have been applied successfully in the estimation of DOA with high accuracy [3–9]. A neural network is proposed to approximate the relationship between the outputs of sensor array and the characters of signals to be estimated. First, Hopfield network was used for the signal processing community [3], and radial basis function (RBF) neural is known to be popular and of high accuracy subsequently [4]. Through the network trained in advance the AOA of unknown signal could be obtained immediately. Self-organizing map (SOM) is a self-organizing system: the data received from the sensor array put in it will be mapped automatically onto a set of output with the same topological order as the primary signals [10], and it is a self-organized network of unsupervised training. Recently, the application of SOM appears in the field of DOA estimation. Xun et al. [11] proposed a self-organizing map scheme for mobile location estimation, and the network is set up between the strengths of signals and user’s location. All these neural networks are efficient, blind, and easy to implement in practice. However, little research has been focused on the rationality of these neural networks.

Regardless of the various methods in form, the nature of the issue is to explore the relationship between the time difference of arrival (TDOA) and the DOA of signals. In this paper, we proposed a two-level SOM network to approximate the relationship between the distance difference of arrival (DDOA) and DOA when there is only single signal waveform, and a 2D DOA problem with a uniform linear sensor array is considered. We found that, under this assumption, the topological structure of the DDOA vectors is similar to that of the AOA, but different from the locations of the signals. The similar topological structure decides a consistent correlation between DDOA and AOA. Therefore, we set up a two-level SOM network between them and train the network by simulation data in advance. In practical application, just put the estimated DDOA into the trained network and the corresponding DOA could be estimated immediately.

The rest of this paper is organized into four sections. In Section 2, we introduce the data model and the structure of Kohonen self-organizing map. Then, we analyze the relationship between DDOA vectors and AOA and set up a two-level SOM neural network for the estimation of AOA in Section 3. Section 4 is a simulation study and lake experiments of the proposed network and accuracy analysis. Finally, we conclude the paper in Section 5.

#### 2. Background Material

##### 2.1. Data Model

Assume that there is a uniform linear array of sensors in the 2D plane and a sound source incident on the plane. Establish rectangular coordinate system as shown in Figure 1; let the linear array be placed along the -axis, and the first left sensor is located at the origin; the array element spacing is . Consider the distance from sound source to sensor () is , and thenThe distance difference of sensor and is