## 1 Introduction
The main intuitive motivation for such an approach is the fact that identical readings of all sensors provide the following: (1) uniformly good measurement results in the case of the majority of high-quality sensors; (2) an important possibility of obtaining ideal calibration of the whole network by the preliminary micro-calibration of only one selected sensor--this is taken later as a reference (leader) in an algorithm, ensuring the equality of all the asymptotic corrected sensor gains and offsets to those introduced by the reference node. The mentioned basic algorithms have been modified in such a way as to provide even more flexibility, proposing the separate calibration of sensor gains using sensor output increments; this methodology has its roots in the distributed time-synchronization problem [37; 38; 39; 40; 41; 42; 43]. In the literature, we can find related studies based on an entirely deterministic setting [44], on a stochastic setting (including measurement and communication-noise- and gossip-based asynchronous communications between the sensors [45]), and on nonlinear calibration algorithms aiming to achieve robustification under the influence of outliers in the form of impulsive stochastic disturbances [46]. It is to be noted here that all the algorithms in both sets of papers are essentially based on _affine sensor models_ and _affine calibration functions_. In this paper, we are going to make a step further in the development of the calibration methodology from [34; 35; 36; 44; 45; 46; 47]. We provide a generalization of the existing results by considering _nonlinear sensor models_, aiming to investigate robustness with regard to the influence of unknown nonlinear inputs, representing the difference between the real sensor characteristics and the initially introduced affine model. We adopt a specific strategy for _gain calibration_[44; 45; 46; 47], based on autonomous gain calibration due to its high flexibility in practice. We define the figure of merit of the following: (1) the basic algorithms applying full consensus, including all the network nodes; (2) algorithms obtained by fixing one node to an a priori defined reference value, in order to select algorithms possessing good stability properties and high robustness to noise and parameter changes. In this sense, we propose a number of originally formulated theorems providing the B.I.B.O. (bounded input-bounded output) stability of the algorithms and indicating their capabilities to reach consensus (Sections 3-6). We illustrate the obtained theoretical results by simulation (Section 7) and apply the best algorithm to an ad hoc sensor network, designed and implemented in an originally developed multichannel aerodynamic pressure-sensing instrument (Section 8). To the authors' knowledge, similar or comparable results cannot be found in the literature. The first part of the paper (Sections 2-6) is dominantly theoretical, providing several original contributions concerning the stability properties of the algorithms. In Section 2, we briefly give a new definition of sensor outputs, containing a general static nonlinear term and stochastic disturbances in the form of additive measurement and communication noises. Section 3 is devoted to _offset calibration_. Within two theorems, we derive explicit formulae for the evolution of corrected offsets in the following cases: (1) the generic full-consensus-based calibration algorithm; (2) an algorithm based on pinning the algorithm to a selected reference node (sensor) in such a way as to fix the corrected offset as a reference value. It is proved that, in both cases, we can obtain the B.I.B.O. stability of the algorithms, with one substantial property: in the first case, the expected value at consensus is in the form of a weighted sum of the initial parameter estimates; in the second case, it is directly the predefined reference value (ideally equal to zero). In Section 4, we analyze algorithms for gain calibration based on the approach adopted in [45], using measurements of _sensor output increments_.