Simultaneous Perturbation Stochastic Approximation-Based Consensus for Tracking Under Unknown-But-Bounded Disturbances

Abstract

We consider a setup where a distributed set of sensors working cooperatively can estimate an unknown signal of interest, whereas any individual sensor cannot fulfil the task due to lack of necessary information diversity. This paper deals with these kinds of estimation and tracking problems and focuses on a class of simultaneous perturbation stochastic approximation (SPSA)-based consensus algorithms for the cases when the corrupted observations of sensors are transmitted between sensors with communication noise and the communication protocol has to satisfy a prespecified cost constraints on the network topology. Sufficient conditions are introduced to guarantee the stability of estimates obtained in this way, without resorting to commonly used but stringent conventional statistical assumptions about the observation noise such as randomness, independence, and zero mean. We derive an upper bound of the mean-square error of the estimates in the problem of unknown time-varying parameters tracking under unknown-but-bounded observation errors and noisy communication channels. The result is illustrated by a practical application to the multi-sensor multi-target tracking problem.

Emergent Intelligence and Distributed Stochastic Optimization

“…A similar idea of solving the practical problem of multi-agent technologies with unknown-butbounded perturbations is discussed in the article [13]. A new distributed algorithm based on stochastic approximation of simultaneous disturbances (SPSA) is proposed.…”

A new method of adaptive mesoscale control in complex multiagent networked dynamical systems

“…, the maximum in-degree among all nodes contained in the graph G C as deg + max (C). The above-mentioned unreliability factor related to limited bandwidth can be associated with the cost of data transmission in the network and characterized by matrix C. As in [Granichin et al, 2020a], we represent cost constraints of agent i ∈ N as a predefined upper bound Q: deg + i (C) ≤ Q. Thus, the total bandwidth of the network is adaptively adjusted in terms of the total cost of communication with neighbors of agent i.…”

“…Next, we consider a data aggregation protocol satisfying the predefined averaged cost constraints: Definition. [Granichin et al, 2020a] Random subgraph G Bt satisfies the averaged cost constraints with level Q if…”

Calibration of Aperture Arrays in Time Domain Using the Simultaneous Perturbation Algorithm

“…However, in the optimization process for some applications, gradient is not available or is difficult to compute, such as for array calibration. In [13], [14], a new simultaneous perturbation stochastic approximation (SPSA) consensus algorithm for distributed tracking under unknown-but-bounded disturbances is proposed, it is suitable for distributed problems to estimate time-varying parameters and compensate them.…”