Outlier-robust calibration method for sensor networks

Abstract

Abstract-In this paper, we aim to blindly calibrate the responses of a sensor network whose outputs are possibly corrupted by outliers. In particular, we extend some well-known nullspacebased blind calibration approaches, proposed for fixed sensors with affine responses-i.e., with unknown gain and offset for each sensor-to that difficult case. These state-of-the-art approaches assume that the true data lie in a known lower dimensional subspace, so that in practice sensors can be calibrated by projection of the uncalibrated observations to this subspace. A robust extension was recently proposed in order to provide less sensitivity to noise. In this paper, we show that such methods (including the robust extensions) are very sensitive to outliers and we propose new extensions able to deal with such issues. For that purpose, we assume the outliers to be rare events, which can be modeled as a sparse contribution to the low-rank observed data. Using such an assumption, we separate sparse outliers from the low-rank data, so that we can perform calibration. We show that the proposed approach is able to handle up to 10% of outliers in the data without major impact on the calibration accuracy while state-of-the-art methods are already sensitive to the presence of one unique outlier.

In Situ Calibration Algorithms for Environmental Sensor Networks: A Review

“…Considering the prior choice of the subspace, the parameters of the calibration relationships for all nodes are then estimated using singular value decomposition (SVD) or by solving a system of equations using a least square estimator. This method was extended later in [71] to provide a total least square formulation and also in [72] to take into account outliers and separate them from the measurement matrix.…”

“…Unlike the common practice in the field of machine learning [101] and even if datasets are disclosed or simulation protocols are presented in detail, there is no report of a test case widely used across the literature. The comparison between methods is also limited by code availability: while a few authors [71] [72] have shared their code, in most cases existing strategies must be fully reimplemented for comparison purposes, as in [21]. This is time-consuming and drives the authors to only focus on comparisons between strategies with very specific characteristics, for instance those which use machine learning techniques [102] [103] [104].…”

Informed Nonnegative Matrix Factorization Methods for Mobile Sensor Network Calibration

“…On the one hand, macro-calibration methods aim to calibrate the whole sensor network in order to provide consistent sensor readings [13]- [15], [19]- [22]. They usually require strong assumptions such as the knowledge of the signal subspace [14], [15], [19], [21], sparse assumptions [13], or a long integration time [20], [22]. On the other hand, microcalibration methods aim to iteratively calibrate one unique sensor from the network at a given time [6], [16], [28].…”

Reference-Free Calibration in Sensor Networks

“…Traditional on-field calibration of inaccurate sensors using reference equipment, or lab-based characterization of the sensor (e.g., sensor modelling), is a cumbersome and expensive process, particularly for a large number of sensors [2]. Therefore, state of the art calibration techniques employ network-wide calibration (also known as in-place calibration [3], on-the-fly calibration [4] or macro-calibration [5]), to estimate the calibration parameters of the network using on-field measurements. Here, the calibration parameters typically refer to the sensor gains (or sensitivity), sensor offsets (or bias) and/or sensor drift (i.e., time-varying offset).…”

“…When a reference is unavailable, typically blind calibration algorithms are enforced (e.g., [5], [6]). In the blind calibration framework, the sensed physical phenomenon is assumed to lie in a known lower dimensional subspace.…”