Performance of Line Arrays of Vector and Higher Order Sensors

Abstract

Arrays of vector and higher order directional sensors are of current interest in a number of applications. The performance of these arrays as a function of frequency and steering direction is examined. Results are presented for arrays of zero-th order (omni-directional), first order vector (omni + first spatial derivative) and second order combined (omni + first spatial directions derivatives + second spatial derivatives) sensors. The beampattern product theorem provides insight into to contribution of the individual components of the directional sensors. For endfire array steering, previous results are extended to higher order sensors. Only the axial components are important at endfire. Sensors with axial components up to order n can cancel up to n grating lobes providing extra gain up to (n+1) times the design frequency at which the sensors are spaced at one-half wavelength. Away from endfire only the cross-axial components are important. Simple techniques are presented for overcoming left/right ambiguity of horizontal line arrays using only the omni-directional and horizontal cross axial components. The results of simple deterministic processing approaches are found to be near optimum when compared with those achieved by optimum processing based on covariance matrix inversion.

Closed-Form Direction Finding Using Collocated but Orthogonally Oriented Higher Order Acoustic Sensors

“…Indeed, the directivity and the beam-patterns of higher-order directional sensors have been investigated in [1]- [5], [8], [9], [11], [13]- [15], [18]. Moreover, [16] derives the Cramér-Rao bounds (in open form) for direction finding using such higher-order directional sensors.…”

“…(Please see p. 1232 of [15].) For a directional acoustical sensor aligned along the x-axis, its (θ, φ) directivity may be obtained by considering a position-vector of (θ, φ, r ) in the spherical coordinates of Figure 1.…”

Particle velocity gradient based acoustic mode beamforming for short linear vector sensor arrays

“…The filter weights can be chosen to maximize a performance metric such as directivity, front-back (port-starboard) ratio, main beam width, grating and back lobe suppression, and white noise gain (Franklin, 1997;Elko, 2004;Cox and Lai, 2007;Cox and Lai, 2009). An alternative is to choose the filter weights such that the beamformer output corresponds to a certain desired response function.…”

“…The equivalence of differential arrays and gradient based higher order acoustic sensors is briefly mentioned by Olson (1946) and firmly established by Kolundzija et al (2011). Cox and Lai developed design methods based on simultaneous optimization of array and white noise gains for linear arrays of higher order sensors (Cox and Lai, 2007). The authors extended their design methodology to simultaneous grating and back lobe rejection (Cox and Lai, 2009).…”

A directionally tunable but frequency-invariant beamformer on an acoustic velocity-sensor triad to enhance speech perception

“…The acoustic vector sensor's beam pattern and directivity have been investigated. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] This acoustic vector-sensor concept is practical. It has been implemented in hardware in various forms for airacoustic applications.…”