Robust Dynamic Multi-Modal Data Fusion: A Model Uncertainty Perspective

Bin Liu

Abstract: This letter is concerned with multi-modal data fusion (MMDF) under unexpected modality failures in nonlinear non-Gaussian dynamic processes. An efficient framework to tackle this problem is proposed. In particular, a notion termed modality “ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">usefulness</i> ,” which takes a value of 1 or 0, is used for indicating whether the observation of this modality is useful or not. For <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> modalities involved, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^n$</tex-math></inline-formula> combinations of their “ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">usefulness</i> ” values exist. Each combination defines one hypothetical model of the true data generative process. Then the problem of concern is formalized as a task of nonlinear non-Gaussian state filtering under model uncertainty, which is addressed by a dynamic model averaging (DMA) based particle filter (PF) algorithm. This DMA algorithm employs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2^n$</tex-math></inline-formula> models, while all models share the same state-transition function and a unique set of particle values. That makes its computational complexity only slightly larger than a single model based PF algorithm, especially for scenarios in which <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is small. Experimental results show that the proposed solution outperforms remarkably state-of-the-art methods. Code and data are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/robinlau1981/fusion</uri> .