We present a novel filtering algorithm that employs Bayesian transfer learning to address the challenges posed by mismatched intensity of the noise in a pair of sensors, each of which tracks an object using a nonlinear dynamic system model. In this setting, the primary sensor experiences a higher noise intensity in tracking the object than the source sensor. To improve the estimation accuracy of the primary sensor, we propose a framework that integrates Bayesian transfer learning into an Unscented Kalman Filter (UKF) and a Cubature Kalman Filter (CKF). In this approach, the parameters of the predicted observations in the source sensor are transferred to the primary sensor and used as an additional prior in the filtering process. Our simulation results show that the transfer learning approach significantly outperforms the conventional isolated UKF and CKF. Comparisons to a form of measurement vector fusion are also presented.