# A Comparison of Optimal SONAR Array Amplitude Shading Coefficients

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## Abstract

**:**

## 1. Introduction

## 2. Physics-Based Weights for a Directional Sensor

#### 2.1. Physics-Based Optimal Weights for a First-Order Directional Vector Sensor

_{a1}and w

_{a2}are the corresponding weights multiplying the two separated pressure sensors. Substituting the physics-based optimal weights, $\widehat{w}=\left\{1,3\right\}$ and chosen parameter values ${c}_{0}=1500\mathrm{m}/\mathrm{s}$, $f=3000\mathrm{Hz}$ and $d=3\mathrm{cm},$ we find that:

#### 2.2. Physics-Based Optimal Weights for a Second-Order Directional Dyadic Sensor

_{0}at midpoint, the beam response (Equation (13)) is rewritten as:

## 3. Adaptive (MVDR) Weights for a Sensor Array

#### 3.1. Adaptive (MVDR) Weights for a First-Order Directional Vector Sensor

#### 3.2. Adaptive (MVDR) Weights for a Second-Order Directional Dyadic Sensor

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Orientation of a single directional sensor or single acoustic pressure sensor (denoted with a solid circle) and adjacent collinear pressure sensors (denoted with open circles). End fire is defined directly down the boresight of the z-axis, $\phi =0$.

**Table 1.**Comparison of First and Second Order Directivity Indices for Incident Signals Arriving at End Fire.

Directivity Index | 1st Order/dB | 2nd Order/dB |
---|---|---|

Directional | 6 | 9.5 |

Adaptive | 5.8 | 9.4 |

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**MDPI and ACS Style**

Cray, B.A.; Kirsteins, I.
A Comparison of Optimal SONAR Array Amplitude Shading Coefficients. *Acoustics* **2019**, *1*, 808-815.
https://doi.org/10.3390/acoustics1040047

**AMA Style**

Cray BA, Kirsteins I.
A Comparison of Optimal SONAR Array Amplitude Shading Coefficients. *Acoustics*. 2019; 1(4):808-815.
https://doi.org/10.3390/acoustics1040047

**Chicago/Turabian Style**

Cray, Benjamin A., and Ivars Kirsteins.
2019. "A Comparison of Optimal SONAR Array Amplitude Shading Coefficients" *Acoustics* 1, no. 4: 808-815.
https://doi.org/10.3390/acoustics1040047