Sensor Fusion and Pontryagin Duality

Abstract

Boltzmann Machine (BM) and Brooks–Iyengar (BI) algorithm are solving similar problems in sensor fusion. Relationships between these two are established in detail. During 1984, BM was used as a toolset to solve posterior probability finding problems by Hinton (https://youtu.be/kytxEr0KK7Q, [10]). During 1996, Brooks–Iyengar algorithm was published (Brooks and Iyengar in Computer, [8]) and it was trying to have robust and yet precise computation of a parameter in a sensor network, where sensor network might include some faulty sensors as well. In this work, it has shown interesting results on BM and BI, when temperature is zero in BM. Dual space of sensor network is used as a space for sensor classification and also to find computability of measurement. Pontryagin duality (Dikranjan and Stoyanov in An elementary approach to Haar integration and Pontryagin duality in locally compact abelian groups 2011 [14]; Woronowicz in QuantumE(2) group and its Pontryagin dual 2000 [15]) is used to construct dual space for a given sensor network. For example, the Fourier transform can be considered as a dual space of the given sensor network. Kolmogorov complexity is used to model measurement problems into a problem of computability of elements in dual space. Sensor fusion problem is formulated as a problem of finding one program “p” which results in many strings as output. It appears that there is no known necessary sufficient condition on group (formed by using non-faulty sensors) for “p” to exist. And also, it is shown that quantum computing is a natural choice to find such a program “p” which produces many strings as output.