Bandlimited field estimation from samples recorded by a location-unaware mobile sensor

Sampling of physical fields has been a topic that been studied extensively in literature but has been restricted to a small class of fields like temperature or pollution which are essentially modelled by the standard second order partial differential equation for diffusion. Furthermore, a large number of sampling techniques have been studied from sensor networks to mobile sampling under a variety of conditions like known and unknown locations of the sensors or sampling locations and with samples affected by measurement and/or quantization noise. Also, certain works have also addressed time varying fields incorporating the difference in known timestamps of the obtained signals.It would be of great interest to explore fields which are modelled by more general constant coefficient linear partial differential equations to address a larger class of fields that have a more complex evolution. Additionally, this works address an extremely general and challenging problem, in which such a field is sampled using an inexpensive mobile sensor such that both, the locations of the samples and the timestamps of the samples are unknown. Moreover, the locations and timestamps of the samples are assumed to be realizations of two independent unknown renewal processes. Furthermore, the samples have been corrupted by measurement noise. In such a challenging setup, the mean squared error between the original and the estimated signal is shown to decreasing as O(1/n), where n is the average sampling density of the mobile sensor.

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“…The sampling model is in this case a renewal process based sampling model, similar to the one in [27]. Let X 1 , X 2 , .…”

Section: B Distortion Criteriamentioning

confidence: 99%

Bandlimited Spatiotemporal Field Sampling with Location and Time Unaware Mobile Sensors

Salgia

Kumar

2018

2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…from asynchronous sample-trains of length one. However, it is possible only if the locations of the samples are known exactly [9], or at least the order of the samples modulo the period of the signal is given [10], [11]. Signal reconstruction from asynchronous trains of samples for non-bandlimited periodic signals of unknown period is considered in our previous papers [12] and [13].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Periodic Signals From Asynchronous Trains of Samples

Rupniewski

2021

IEEE Signal Process. Lett.

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A short train of equidistant samples rarely suffices to compute a reasonable approximation to a continuous-time signal. Hence, there arises a need for signal reconstruction methods that exploit multiple trains of samples. If the starting times of the trains are known, then stroboscopic techniques can be used for signal reconstruction. If these times are not given, i.e., in the case of asynchronous trains of samples, it is still possible to profit from multiple trains provided that the starting times are uniformly random when considered modulo the period of the signal. For such a scenario, it is known that an infinite set of sample trains allows for reconstruction of the signal up to a time shift provided that the sampling period is small enough and that the derivative of the signal satisfies some regularity conditions. In this paper, we generalize that discovery by showing that the regularity conditions concerning the derivative of the signal can be dropped. The reconstruction of the signal is still possible even if the derivative of the signal does not exist. We also show how to estimate the signal from a finite set of asynchronous trains of samples. Eventually, we prove that the proposed signal estimator is consistent.

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“…Classical sampling and interpolation assumes that the sampling locations are (approximately) known [1], [2]. Of late, it has also been shown that a location-unaware mobile sensor can be used to estimate (reconstruct) a one-dimensional spatially bandlimited field [6].…”

Section: Introductionmentioning

confidence: 99%

“…1(a). Location unawareness is introduced in mobile sensing and distributed sensing for one dimensional field by Kumar [6], [7]. Observing a spatial field at a random location is akin to random sensing studied in compressed sensing [8].…”

Section: Introductionmentioning

confidence: 99%

Mobile Sensing of Two-Dimensional Bandlimited Fields on Random Paths

Rastogi¹,

Kumar²

2017

Preprint

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Mobile sensing has been recently proposed for sampling spatial fields, where mobile sensors record the field along various paths for reconstruction. Classical and contemporary sampling typically assumes that the sampling locations are approximately known. This work explores multiple sampling strategies along random paths to sample and reconstruct a two dimensional bandlimited field. Extensive simulations are carried out, with insights from sensing matrices and their properties, to evaluate the sampling strategies. Their performance is measured by evaluating the stability of field reconstruction from field samples. The effect of location unawareness on some sampling strategies is also evaluated by simulations.

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Bandlimited field estimation from samples recorded by a location-unaware mobile sensor

Cited by 7 publications

References 17 publications

Bandlimited Spatiotemporal Field Sampling with Location and Time Unaware Mobile Sensors

Bandlimited Spatiotemporal Field Sampling with Location and Time Unaware Mobile Sensors

Reconstruction of Periodic Signals From Asynchronous Trains of Samples

Mobile Sensing of Two-Dimensional Bandlimited Fields on Random Paths

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