A Low Computational Complexity SML Estimation Algorithm of DOA for Wireless Sensor Networks

Abstract

We address the problem of DOA estimation in positioning of nodes in wireless sensor networks. The Stochastic Maximum Likelihood (SML) algorithm is adopted in this paper. The SML algorithm is well-known for its high resolution of DOA estimation. However, its computational complexity is very high because multidimensional nonlinear optimization problem is usually involved. To reduce the computational complexity of SML estimation, we do the following work. (1) We point out the problems of conventional SML criterion and explain why and how these problems happen. (2) A local AM search method is proposed which could be used to find the local solution near/around the initial value. (3) We propose an algorithm which uses the local AM search method together with the estimation of DML or MUSIC as initial value to find the solution of SML. Simulation results are shown to demonstrate the effectiveness and efficiency of the proposed algorithms. In particular, the algorithm which uses the local AM method and estimation of MUSIC as initial value has much higher resolution and comparable computational complexity to MUSIC.

A Novel Modification of PSO Algorithm for SML Estimation of DOA

“…According to [9,22], the SML criteria is derived based on the following assumptions. (A1)

The array configuration is known and any p steering vectors for different q directions are linearly independent, i.e., the matrix $\mathrm{bold-italicA}false(\Theta false)$ has full rank.

(A2)

$\mathrm{bold-italicn}false(t_{i}false)$ are statistically independent samples from a complex Gaussian random vector with zero mean and the covariance matrix ${\sigma }^2{\mathit{I}}_p$, where ${\mathrm{bold-italicI}}_p$ is a $p\times p$ identity matrix and ${\sigma }^2$ is an unknown real number.

(A3)

$\mathrm{bold-italics}false(t_{i}false)$ are independent samples from a complex Gaussian random vector which has zero mean and signal covariance matrix S and is independent of the noise ($\mathrm{bold-italics}false(t_{i}false)$ are independent of $\mathrm{bold-italicn}false(t_{j}false)$ for any i and j ).

…”

General Improvements of Heuristic Algorithms for Low Complexity DOA Estimation

“…Among these algorithms, it is well known that ML and WSF have the highest accuracy of DOA estimation [13][14][15]. However, it is also well demonstrated that the computational complexity of them is also the highest because the criteria of them are nonlinear multi-dimensional optimization [13][14][15][16]. e second step is how to get the DOAs from the criteria, i.e., the estimation process.…”

“…Usually, this kind of algorithm needs a large number of training samples. e second type is heuristic algorithms for simulating biological behaviors in nature such as Genetic Algorithm (GA) [20], Ant Colony Algorithm [21], and Particle Swarm Optimization (PSO) algorithm [16,22,23]. ese algorithms are all population-based iterative techniques.…”