Observer for Phased Microphone Array Signal Processing with Nonlinear Output

Abstract

Acoustic arrays have become an important testing tool in noise identification for industry applications, where the typical beamforming algorithm has been adopted as a classical processing technique. In most practical cases the beamforming computations have to be conducted off-line due to the excessive computational requirements. An alternative algorithm with a real-time capability is proposed. The algorithm is similar to a classic observer while array processing is performed in the frequency domain. The performance of this observer-based algorithm is studied here through comparing with the typical beamforming method, particularly for a case of coherent noise sources. In this paper it is shown that the observer-based algorithm could resolve the coherence restriction between the background noise and the signal of interest. The proposed algorithm is also beneficial for its capability of operating over sampling blocks recursively. The convergence rate of this recursive algorithm is fast enough to satisfy the requirements for practical cases. The experimental efforts could be saved extensively as any testing defects could be revealed instantaneously and corrected on site. In addition, this innovative approach provides an alternative perspective, from which many techniques already developed in control and filtering could be extended to this new application area of array processing.

Observer-based beamforming algorithm for acoustic array signal processing

“…12,13 The so-called observer-based algorithm can be recursively applied over sampling blocks and hence holds real-time computational capability. Moreover, the method can reject coherent background noise.…”

“…12,13 Control theory asserts that any state of a linear dynamic system could be estimated using a carefully designed observer, given the measurements of the input and output, and the linear system should be observable. 14 Therefore, it is possible to construct an observer to identify sound sources (i.e., system states) by array measurements (i.e., system outputs).…”

“…(12) is N Â 1, and the notation of (jx) is omitted for brevity. It is easy to confirm that the observability is still maintained.…”

“…Figure 2(a) shows an acoustic image of DAS beamforming with the inclusion of the correlated background noise and signal of interest. Figure 2(b) is the result from DAS beamforming with removal of background noise, 12 where K ¼ 100 (100 sampling blocks are averaged to generate covariance matrix for background noise interference rejection). It is easy to see that DAS beamforming fails to completely reject interferences from the coherent background noise, as Eq.…”

“…[9][10][11] The idea of the observer-based method has been proposed in previous works. 12,13 In this work a detailed theoretical derivation is developed and the performance of the new method is carefully evaluated through conducting a couple of numerical tests. The performance of the new observer-based algorithm is compared with that of the conventional DAS beamforming method in terms of coherent background noise rejection and real-time capability.…”