Moving microphone arrays to reduce spatial aliasing in the beamforming technique: Theoretical background and numerical investigation

2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

2011

Abstract-Classical sampling theory for sampling and reconstructing bandlimited fields in R d addresses the problem of sampling on lattice points. We consider a generalization of this problem, in which one samples the field along 1-dimensional spatial trajectories in R d rather than at points. The process of sampling records the value of the field at all points on the sampling trajectories. Such a sampling setup is relevant in the problem of spatial sampling using mobile sensors. We study various possible designs of sampling trajectories and discuss necessary and sufficient conditions for perfect reconstruction. We introduce a density metric for trajectories which we call path density, that quantifies the total length of these trajectories per unit volume in R d . We formulate the problem of identifying optimal sampling trajectories that admit perfect reconstruction of bandlimited fields and are minimal in terms of the path density metric. We identify optimal sampling trajectories from a restricted class of trajectories.

Section: Introductionmentioning

confidence: 99%

Sampling trajectories for mobile sensing

2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

2011

“…Since is bandlimited we can write Now, if the sensor takes samples every time units, we essentially get uniform noisy samples of the field at intervals of spatial units. We know from classical sampling theory [17] that when noise is absent the field can be exactly recovered from these samples using sinc interpolation as (6) provided that the sampling interval satisfies . In the noisy case, this reconstructed field is completely devoid of out-of-band noise which is suppressed by the sinc 2 pre-filtering.…”

Section: ) One-dimensional Fieldmentioning

confidence: 99%

“…Consequently much of the literature on spatial sampling and reconstruction have focused on such static sensing schemes [3], [4]. An emerging paradigm in spatial sampling is the use of mobile sensors that move through the area of interest, taking measurements along their paths [5], [6]. Mobile sensing schemes have several advantages over static schemes, the chief of which is the fact that a single mobile sensor can be used to take measurements at several distinct positions in space.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, one has to account for the Doppler effect while sensing with moving sensors (see e.g., [ potential applications in limiting spatial aliasing in certain sampling problems, e.g., wave-field synthesis [10]. The advantage of mobile sensing over static sensing in suppressing spatial aliasing has been noted in the context of audio source localization in [6] where the authors show that using a planar rotating array of microphones, the effective number of measurement points can be increased thus reducing the amount of spatial aliasing while using the beamforming technique. In some other works moving microphones have been used for estimating room impulse responses [12] and head related impulse responses [13].…”

Section: Introductionmentioning

confidence: 99%

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Sampling and Reconstruction of Spatial Fields Using Mobile Sensors

IEEE Trans. Signal Process.

2013

Abstract-Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper, we study the emerging paradigm of sampling and reconstructing spatial fields using sensors that move through space. We show that mobile sensing offers some unique advantages over static sensing in sensing bandlimited spatial fields. Since a moving sensor encounters such a spatial field along its path as a time-domain signal, a time-domain anti-aliasing filter can be employed prior to sampling the signal received at the sensor. Such a filtering procedure, when used by a configuration of sensors moving at constant speeds along equispaced parallel lines, leads to a complete suppression of spatial aliasing in the direction of motion of the sensors. We analytically quantify the advantage of using such a sampling scheme over a static sampling scheme by computing the reduction in sampling noise due to the filter. We also analyze the effects of nonuniform sensor speeds on the reconstruction accuracy. Using simulation examples, we demonstrate the advantages of mobile sampling over static sampling in practical problems. We extend our analysis to sampling and reconstruction schemes for monitoring time-varying bandlimited fields using mobile sensors. We demonstrate that in some situations we require a lower density of sensors when using a mobile sensing scheme instead of the conventional static sensing scheme. The exact advantage is quantified for a problem of sampling and reconstructing an audio field.Index Terms-Mobile sensors, spatial anti-aliasing, spatial field sampling and reconstruction.

“…The advantages of mobile sensing over static sensing have been noted in room impulse response measurement for communication systems [4] and in suppressing spatial aliasing in audio source localization [5]. In a different context, moving antennae have been shown to provide advantages over static antennae in synthetic aperture radar [6].…”

Section: Introductionmentioning

confidence: 99%

Sampling and reconstructing spatial fields using mobile sensors

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

2012

The classical approach to sampling time-invariant spatial fields uses static sensors distributed over space. We study a new approach involving mobile sensors that move through space measuring the field values along their paths. A single moving sensor can take measurements over a wide spatial area thus acting as a substitute for a potentially large number of static sensors. A moving sensor encounters the spatial field in its path in the form of a time-domain signal. Hence a time-domain anti-aliasing filter can be employed at the mobile sensor to limit the amount of out-of-band noise prior to sampling. We analytically quantify the advantage of mobile sensing over static sensing in rejecting out-of-band noise. We also demonstrate via simulations the improvement in reconstruction accuracy that can be obtained using mobile sensors and filtering in a temperature measurement problem.