Over the last two decades, low-frequency active sonar has become an attractive tool for underwater target detection. The reverberation to signal ratio (RSR) of transmitted waveforms is an important factor affecting the detection capability of low-frequency active sonar. Therefore, reasonable waveform design for reverberation suppression of active sonar is an important topic. Pulse trains of linear frequency-modulated (PTFM) waveforms have been proposed and manifested their good performance in suppressing reverberation. The number of sub-pulses is positively related to the reverberation to signal ratio; the lower the number of sub-pulses, the lower the reverberation to signal ratio. However, to avoid ambiguity in a Doppler measurement, the PTFM waveforms have a requirement for the number of sub-pulses to be satisfied, which prevents its reverberation suppression performance from being further improved. In this paper, we propose a coprime pulse train of linear frequency-modulated (CPTFM) waveform, which reduces the number of sub-pulses to some extent. Therefore, the ability of reverberation suppression of the CPTFM waveform can be improved. The RSR was chosen as the metric to evaluate the waveform’s ability to suppress reverberation, and the theoretical formula for the RSR of the CPTFM waveform was derived in zone A and B. With the overlap of zones A and B brought about by the decrease in the number of sub-pulses, the average RSR of zones A and B is used in this paper to evaluate the reverberation suppression ability of the waveform. The simulation experiment shows that the proposed CPTFM waveform decreases the average RSR by 7 dB and 20 dB in comparison to the reference PTFM waveform and continuous waveform (CW), which is consistent with the theoretical results by the derived formulas.

Towed array shape estimation aided with non‐acoustic sensors is widely used for its rather low computational complexity of solutions and rather explicit results. In addition, previous studies have emphasised that depth sensors’ distribution has a dramatic influence on the accuracy of this kind of array shape estimation method. Established on the basic theory of towed array shape estimation using Kalman Filters, the approximately optimal distribution of a certain number of depth sensors over a certain number of discretised towed arrays yields the approximately best achievable performance in terms of minimum space average mean square error (AMSE), is addressed in this study. The effect of depth sensors’ distribution has been discussed. Then an exact expression for the space AMSE is derived. The expression is simplified in a reasonable way considering the practical issues in order to calculate the minimum space AMSE rapidly and effectively. The performance assessments demonstrate the effectiveness of the newly proposed method.

Most of the non‐acoustic methods for towed array shape estimation are based on the incorrect original Paidoussis equation. A comparison between solution to the original and revised Paidoussis equation is made to prove the significance of utilising the latter. In addition, considering relative characteristics of the revised Paidoussis equation and the critical point which exists on the cylinder, the minimum length of damping section added at the end of the cylinder is derived.