Directionality of generalized acoustic sensors of arbitrary order

Abstract

For several decades there has been a great deal of interest in acoustic sensors that can make multiple measurements at a single point in the ocean. The order of such sensors has been defined by linking it to the order of the Taylor series approximation of the pressure field at that point. Following this definition, the pressure, vector, and dyadic sensor is of order zero, one, and two, respectively. For this theoretical study, a multichannel three-dimensional spatial filter is derived for a directional acoustic sensor of arbitrary order. Explicit formulas are found for the filter coefficients that maximize the array gain (directivity index) of the filter as well as an explicit expression for the maximum array gain (directivity index). This process is repeated for the case of a first-order null placed in the direction opposite to the look direction of the multichannel filter. Finally, an example is presented which tracks the array gain and beamwidth of a third-order acoustic sensor as the order of the null is assigned values 0, 1, 2, and 3.

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

“…These new results will allow high-order directional acoustic sensors to be straight-forwardly adopted in the direction-finding methods cited in [17], [19], [21]. For example, the subsequently derived (5)-(7) or (12)- (14) may directly substitute for the direction-cosine estimation equations (15)- (17) in [12]. These new results will retain the many advantages in those earlier direction-finding methods.…”

“…Even if k x , k y , k z are all odd,ˆ c in (11) would still require prior information that reduces the unambiguous validity-region to an hemisphere. If exactly one of k x , k y , k z is even, the unambiguous validityregion would remain at an hemisphere, because prior information would become necessary in (12)- (14) whereasˆ c in (11) would need no prior information. For each additional k x , k y , k z is also even, the unambiguous validity-region would be further halved once again.…”

Direction-Selective Filters for Sound Localization

“…Note that the discriminating function is a monotonic function of ψ . This is not true for discriminating functions of directional acoustic sensors (Schmidlin, 2007). …”

“…The optimum directivity index is ( ) Schmidlin, 2007). It is a very difficult matter to implement the operations ( ) L, n p tr ⎡⎤ ⎣⎦ for 2 n ≥ .…”

“…Cray (2002) and Cray et al (2003) presented theory for acoustic receivers of order greater than two. Schmidlin (2007) extended the multichannel filtering approach of Silvia (2001) to directional acoustic sensors of arbitrary order ν . It was shown that the maximum directivity index is ( ) 20 log 1 ν + , and explicit expressions were derived for the optimum weights.…”