The a posteriori source position probability density function for a narrowband source in an uncertain acoustic environment is derived. The implementation of this probability density function (pdf) is termed the optimum uncertain field processor (OUFP). It is shown that the OUFP is a generalization of matched-field processing to situations in which there is uncertainty about the environment. The robustness of the OUFP is illustrated through performance comparisons to a matched-field algorithm. © 1991, Acoustical Society of America. All rights reserved.