Considering a common case where measurements are obtained from independent sensors, we present a novel outlier-robust filter for nonlinear dynamical systems in this work. The proposed method is devised by modifying the measurement model and subsequently using the theory of Variational Bayes and general Gaussian filtering. We treat the measurement outliers independently for independent observations leading to selective rejection of the corrupted data during inference. By carrying out simulations for variable number of sensors we verify that an implementation of the proposed filter is computationally more efficient as compared to the proposed modifications of similar baseline methods still yielding similar estimation quality. In addition, experimentation results for various real-time indoor localization scenarios using Ultra-wide Band (UWB) sensors demonstrate the practical utility of the proposed method.