This article proposes a novel outlier-robust localization algorithm that is based on time difference of arrival measurements at an airport for multilateration surveillance. An outlier-robust filtering scheme is derived based on Student's-t-distribution, where the state, a scale matrix, and a degree of freedom parameter are estimated simultaneously using variational Bayesian (VB) inference. An interacting multiple model (IMM) filter with different system models is implemented to handle the multimodal dynamics of the aircraft, yielding the IMM-VB algorithm. Specifically, the likelihood function is newly derived using VB inference for the combination procedure in the proposed IMM-VB algorithm. The experimental results obtained from a flight test using a commercial aircraft at an airport demonstrate that the proposed IMM-VB algorithm has better localization accuracy and robustness to outlier measurements than the existing state-of-the-art approaches.