A hybrid time and frequency domain beamforming method for application to source localisation on high-speed trains

To comply with the legislation and certification procedures that limit railway noise, reliable approaches are required to reduce the noise from trains. However, effective noise control can only be achieved if the dominant sources are identified first. Beamforming is a possible experimental solution to achieving source identification on a moving train. However, application of the conventional delay-and-sum beamforming method to moving sources relies on the interpolation, or de-dopplerisation, of the received signals, and is therefore computationally expensive. Frequency-domain methods also exist which have been developed based upon the linearisation of the moving trajectory of the source. These are faster in processing time but can only provide accurate source identification within the validity of the linear approximation. They are typically applied to slowly varying sources such as aircraft flyovers. A hybrid beamforming method is presented for application to moving sources with a short pass-by window, which is a typical situation in railway pass-by measurements. The hybrid method proposed in this paper is based on a combination of features of time- and frequency-domain methods. Delays are applied to the signals as in the time domain method and beamforming is performed as for the frequency domain method. It can provide beamforming estimates over a sub-grid by performing de-dopplerisation based on a single point. Numerical simulations and a field measurement targeting a train pantograph are used to compare the performance of three beamforming methods. The numerical analysis of the proposed method shows that, compared with the frequency-domain method, the hybrid approach has more relaxed requirements for linearisation, and thus results in a better beamforming performance. With appropriate settings, a substantial computational advantage can be achieved. The results also show that the conventional method and the hybrid method have a similar beamforming performance, whereas the frequency-domain method shows higher sidelobe level, especially at high frequencies. The proposed hybrid method can achieve both good beamforming performance and low computational cost and can be used as a good alternative of the conventional time-domain method for identification of moving sources