dbfusinglop

In this paper, the authors assume that the time-varing communication network topology is peridically strongly connected and each agent can only communicate once with its neighboring agents during each time instant. The fusion rule for combining arbitrary probability distributions relies on the LogOP scheme and dyanamic average consensus algorithm.

Logarithmic Opinion Pool and Convergence Results

Let the pdf (mathcal{P}_k^i) denote the (i)th agent’s pdf at the (k) time instant. The LinOP and LogOP schemes for combining the pdfs are given by

[mathcal{P}k^{text{LinOP}}(x) = sum{i=1}^N alpha_i mathcal{P}_k^i]

[mathcal{P}k^{text{LogOP}}(x) = frac{prod{i=1}^N(mathcal{P}_k^i)^{alphai}}{int prod{i=1}^N(mathcal{P}_k^i(x))^{alpha_i} dx}]

The combined pdf obtained using LinOP and LogOP gives the weighted algebraic and geometric averages of the individual pdfs respectively.

Another reason for using the LogOP scheme is that it minimizes the information lost during the combination process, where the information loss is measured using the KL divergence.