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Bridge weigh-in-motion (BWIM) is a technique for detecting heavy vehicles that may cause serious damage to real bridges. BWIM is realized by analyzing the strain signals observed at places on the bridge in terms of bridge-component responses to the axle loads. In current practice, a BWIM system requires multiple strain sensors to collect vehicle properties including speed and axle positions for accurate load estimation, which may limit the system’s life-span.

In this paper, we consider the problem of jointly localizing a microphone array and identifying the direction of arrival of acoustic events. Under the assumption that the sources are in the far field, this problem can be formulated as a constrained low-rank matrix factorization with an unknown column offset. Our focus is on handling missing entries, particularly when the measurement matrix does not contain a single complete column. This case has not received attention in the literature and is not handled by existing algorithms, however it is prevalent in practice.