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Matched field processing (MFP) is an important technique for source localization in shallow water waveguides. To obtain high resolution, some adaptive methods are frequently used, for example, the minimum variance distortionless response (MVDR) MFP. It is well-known that MVDR is quite sensitive to model mismatch, which can hardly be avoided in practical applications. In this paper a robust MVDR method, previously developed for beamforming applications, is generalized to MFP. It is implemented using convex optimization and second order cone (SOC) programming. Simulations show that in the presence of environment mismatch, the developed algorithm performs at least equally well compared to the diagonal loading technique. Besides, the diagonal loading technique performs very poor if with improper loading factor. On the contrary, by choosing the uncertainty factor accordingly, different robustness levels can always be achieved using the developed approach.