• The Journal of the Acoustical Society of Korea
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• v.20 no.1
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• pp.21-29
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• 2001

In order to detect the precise port/starboard direction of arrival of target signal in real noisy ocean environments, Inverse beamforming (IBF) algorithm is surveyed theoretically and the detection performances of IBF are analyzed with simulations. Cardioid Inverse beamforming algorithm was proposed for port/starboard discrimination and the performance was studied with simulations. It is shown that IBF has a 3dB array gain advantage over Conventional beamforming (CBF) under ideal conditions. This 3 dB advantage is proven theoretically and illustrated with simulations. The fact that the IBF beamwidth is narrower than the CBF beamwidth by a factor of 0.68 proves the performance of defection and spatial resolution improvement. Comparing the simulation results of Cardioid Inverse beamforming and Conventional Cardioid beamforming, it is shown that Cardioid Inverse beamformer has enhanced performance in minimum detection level, detection accuracy and resolution. Due to the results of moving target bearing detection test in endfire, it is shown that Cardioid Inverse beamformer has better performance, comparing the Conventional Cardioid beamformer.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.5
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• pp.786-795
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• 1999

To detect the precise of arrival of target signal in real ocean environments, Inverse beamformnig(IBF) solutions to the Inverse beamforming integral equation are surveyed theoretically and the performance properties of the IBF are analyzed with simulations. IBF-Cardioid beamforming algorithm is proposed for port/starboard discrimination and the performance gains are studied with simulations. It is shown that IBF has a 3 dB array noise gain advantage over CBF under ideal conditions. This 3 dB array noise gain advantage is proven by theocratical studies and simulations. This array noise gain advantage leads to a minimum detectable level advantage for IBF output compared with CBF output. The fact that the IBF beamwidth is narrower than the CBF beamwidth by a factor of 0.68 proves the performance of detection and spatial resolution improvement. Comparing the simulation results of IBF-Cardioid beamforming and Conventional Cardioid beamforming, it is shown that IBF-Cardioid beamformer have performance enhancement in minimum detection level, detection accuracy and resolution.

• The Journal of the Acoustical Society of Korea
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• v.22 no.6
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• pp.489-495
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• 2003

Single towed line array receiver contains an ambiguity on conjugate bearings because of lacking aperture in transverse direction. To solve the left/right bearing ambiguity of line array receiver this paper proposed using single line array with fixed cardioid beam. Fixed cardioid beam has problem about back beam gain exists for steering beam inherent. Back beam is makes form on direction that is different from actually source so that reduced the performance of left/right bearing discrimination. In this paper, line way with adaptive cardioid beam for resolve problem of back beam gain is proposed. So the proposed method has more improved left/right bearing discrimination than fixed cardioid beam, Simulation results show the performance of the proposed method.

• The Journal of the Acoustical Society of Korea
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• v.36 no.2
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• pp.115-122
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• 2017

We propose a robust adaptive beamforming algorithm for triplet array sonar. The proposed beamforming algorithm obtains robustness to mismatches, left/right discrimination, and has two steps. The first is a cardioid beamformer, which supports left/right discrimination of target signals. It applies the conventional delay-and-subtract to each triplet's signal with its rotation angle and obtains multiple cardioid beams. The second is a robust adaptive beamforming to minimize nearby interferences. We regard cardioid beams as input signals of a line array and apply an adaptive beamforming algorithm to the cardioid beams. Simulations results show that the proposed algorithm provides significantly better performance than the conventional algorithms, while supporting left/right discrimination of target signals.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.307-319
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• 2022

The present paper deals with the upper bound of third order Hankel determinant for a certain subclass of analytic functions associated with Cardioid domain in the open unit disc E = {z ∈ ℂ : |z| < 1}. The results proved here generalize the results of several earlier works.

• The Journal of the Acoustical Society of Korea
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• v.37 no.1
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• pp.66-72
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• 2018

In this paper, we propose an adaptive beamforming algorithm of triplet arrays for active sonar systems. The proposed algorithm consists of three steps: matched filters, cardioid beamforming, and line array beamforming. First, we apply a matched filter of a transmitted pulse to received individual sensor signals and obtain filterd signals. Then, we perform the fast Fourier transform to the matched filter results, and make a cardioid beam for each triplet data, respectively. Finally, we apply an adaptive beamforming by assuming that the cardioid beams are input signals of a line array. Experimental results demonstrate that the proposed algorithm provides better performances than conventional algorithms.

• The Journal of the Acoustical Society of Korea
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• v.21 no.2E
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• pp.71-80
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• 2002

This paper suggests the Cardioid beamforming algorithm of the doublet sensors employing DIFAR (directional frequency analysis and recording) sensor signals in the frequency domain. The algorithm enables target bearing estimation using the signals from directional sensors. The algorithm verifies its applicability by successfully estimating bearings of a target projecting ten narrow-band signals in shallow water. The estimated bearings agree very well with those from GPS (global positioning system) data. Assuming the bearings from GPS data to be real values, the estimation errors are analyzed statistically. The histogram of estimation errors in each frequency have Gaussian shape, the mean and standard deviation dropping in the ranges -1.1°∼ 6.7°and 13.3∼43.6°, respectively. Estimation errors are caused by SNR (signal to noise ratio) degradation due to propagation loss between the source and receiver, daily fluctuating geo-magnetic fields, and non-stationary background noises. If multiple DIFAR systems are employed, in addition to bearing, range information could be estimated and finally localization or tracking of a target is possible.

• Journal of the Korea Institute of Military Science and Technology
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• v.5 no.2
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• pp.169-184
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• 2002

In order to extract bearing information from the directional sensors of DIFAR(directional frequency analysis and recording) that is a kind of passive sonobuoy, the cardioid beamforming algorithm applicable to DIFAR system was studied in the frequency domain. the algorithm uses narrow-band signals propagated though the media from the acoustic sources such as ship machineries. The proposed algorithm is expected to give signal to noise ratio of 6dB when it uses the maximum response axis(MRA) among the Cardioid beams. The estimated bearings agree very well with those from GPS data. Assuming the bearings from GPS data to be real values, the estimation errors are analyzed statistically. The histogram of estimation errors in each frequency have Gaussian shape, the mean and standard deviation dropping in the ranges -1.1~$6.7^{\circ}$ and 13.3~$43.6^{\circ}$, respectively. Estimation errors are caused by SMR degradation due to propagation loss between the source and receiver, daily fluctuating geo-magnetic fields, and non-stationary background noises. If multiple DIFAR systems are employed, in addition to bearing, range information could be estimated and finally localization or tracking of a target is possible.

• The Journal of the Acoustical Society of Korea
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• v.22 no.6
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• pp.482-488
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• 2003

Line may receiver contains an ambiguity on conjugate bearings, because of lacking aperture in transverse direction. To solve the left/right bearing ambiguity of line-array receiver we used line-array with cardioid beam. In addition, the synthetic aperture method adopts coherent processing of sub-aperture signals at successive time intervals in the beam domain. We presented performances about division of left/right bearing ambiguity according to array synthetic number of times in this paper.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.221-229
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• 2004

It is known that the parametric boundary equation for the main component in the Mandelbrot set represents a cardioid. We derive an epicy-cloidal boundary equation of the main component in the degree-n bifurcation set by extending the parameter which describes the cardioid in the Mandelbrot set. Computational results as well as some useful properties are presented together with the programming source codes written in Mathematica. Various boundaries are displayed for $2\leqn\leq7$7 and show a good agreement with the theory presented here. The known boundary equation enables us to significantly reduce the construction time for the degree-n bifurcation set.