## 1 Introduction  
In recent years, we have witnessed increasing interest in the diverse applications of large _sensor networks_, which are composed of a large number of sensors of different kinds. Sensor networks represent important parts of Cyber-Physical Systems (CPSs), the Internet of Things (IoT), large-scale systems, and networked control systems (see, e.g., [1, 2, 3, 4, 5, 6, 7, 8]). In a majority of cases, sensor networks are used for _supervision and monitoring_ purposes, e.g., the monitoring of air characteristics (the concentrations of different gases, particles, etc. ),environment properties (temperature, humidity, and radioactivity), and wind properties; they can also be parts of feedback control for large-scale systems, systems of systems, etc. Important applications of sensor networks can also be found in research and development laboratories to support complex experiments. The calibration of large sensor networks represents a great challenge from the point of view of _concept_, _technology, and organization_, bearing in mind the always-present need for high-precision measurement data in spite of potentially insufficient sensor quality and hostile environments. There are different formal definitions of the _sensor network calibration problem_[9; 10; 11; 12; 13]. Classical calibration procedures are usually performed in controlled environments; when this is not possible, or when sensors are deployed at barely accessible positions, calibration can be performed with respect to (1) pre-calibrated reference node(s), (2) selected sets of calibrated nodes (_distributed calibration_), and (3) non-calibrated nodes (_blind calibration_) [13]. Notice also that a large number of sensors, even those dedicated to important and sensitive functions, are often sold without _individual sensor calibration_ (so-called _micro-calibration_, usually performed under strictly controlled conditions [13]). The calibration of a sensor network as a whole may be necessary for the successful deployment of large CPS and IoT systems, bearing in mind the inherent imperfections of the devices, the time variations of sensor parameters, the noise in acquired data, and random disturbances in the environment. The development of calibration methodologies that are applicable at the level of a _sensor network as a whole_ represents a great theoretical and practical challenge. According to some authors, _macro-calibration_ deals with the calibration problem at the network level, e.g., [13; 14; 15; 16]; meanwhile, macro-calibration, _without known stimuli_, is identified as the problem of _blind macro-calibration_, which is very complex and conceptually related to the problem of blind deconvolution [17; 18; 19; 20; 21]. The existing approaches to macro-calibration start from different a priori assumptions and use different methodologies, but they typically require centralized actions and non-recursive computations, e.g., [13; 14; 15; 22; 23; 24]. Different macro-calibration methodologies can be found in the literature, including signal space projection [22; 25], sparsity and convex optimization [26], consistency maximization [27], Kalman filtering [28], sparse Bayesian learning [29], deep learning [30], autoregressive signal modeling, matrix factorization [31], and consensus-based clustering [32] (additional examples can be found in a short survey within [33]). It is actually even more challenging, both conceptually and practically, to develop efficient _decentralized algorithms for the blind macro-calibration_ of sensor networks. One of the rare methodologically consistent solutions to this problem can be found in [34; 35; 36]. A comprehensive picture of the most important theoretical and practical aspects of the underlying ideas in this approach is presented in [33]. The proposed algorithms are of the _distributed-gradient type_, providing equal corrected sensor outputs by ensuring convergence to the _consensus_ of _all the corrected sensor gains and offsets_, without requiring any type of function centralization.