Graph clustering for localization within a sensor array

Abstract

We develop a model-free technique to identify weak sources within dense sensor arrays using graph clustering. No knowledge about the propagation medium is needed except that signal strengths decay to insignificant levels within a scale that is shorter than the aperture. We then reinterpret the spatial coherence matrix of a wave field as a matrix whose support is a connectivity matrix of a graph with sensors as vertices. In a dense network, well-separated sources induce clusters in this graph. The support of the covariance matrix is estimated from limited-time data using a hypothesis test with a robust phase-only coherence test statistic combined with a physical distance criterion. The method is applied to a dense 5200 element geophone array that blanketed 7 km ⇥10 km of the city of Long Beach (CA). The analysis exposes a helicopter traversing the array.

Graph Signal Processing for Narrowband Direction of Arrival Estimation

“…Since the introduction of graph signal processing [1], a large number of studies on various applications of graph signal processing (GSP) have emerged, especially for massive data with irregular sensor structures [2]. For example, the filtering operation in GSP can be applied to smoothing [3], denoising [4] and classification [5] of irregular signals and the clustering of graphs can be used to identify weak sources in dense sensor arrays [6]. The result from the classical signal time-frequency uncertainty principle was extended to graph signal processing and the use of eigenvectors of the graph Laplacian matrix is justified as the base for the graph Fourier transform in [7].…”