Farmers must continuously improve their livestock production systems to remain competitive in the growing dairy market. Precision livestock farming technologies provide individualized monitoring of animals on commercial farms, optimizing livestock production. Continuous acoustic monitoring is a widely accepted sensing technique used to estimate the daily rumination and grazing time budget of free-ranging cattle. However, typical environmental and natural noises on pastures noticeably affect the performance limiting the practical application of current acoustic methods. In this study, we present the operating principle and generalization capability of an acoustic method called Noise-Robust Foraging Activity Recognizer (NRFAR). The proposed method determines foraging activity bouts by analyzing fixed-length segments of identified jaw movement events produced during grazing and rumination. The additive noise robustness of the NRFAR was evaluated for several signal-to-noise ratios using stationary Gaussian white noise and four different nonstationary natural noise sources. In noiseless conditions, NRFAR reached an average balanced accuracy of 86.4%, outperforming two previous acoustic methods by more than 7.5%. Furthermore, NRFAR performed better than previous acoustic methods in 77 of 80 evaluated noisy scenarios (53 cases with p<0.05). NRFAR has been shown to be effective in harsh free-ranging environments and could be used as a reliable solution to improve pasture management and monitor the health and welfare of dairy cows. The instrumentation and computational algorithms presented in this publication are protected by a pending patent application: AR P20220100910. Web demo available at: https://sinc.unl.edu.ar/web-demo/nrfar.