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In current matched field processing (MFP) methods all the algorithms concentrate on generating a single high fidelity replica for matching the received signals. Several well known sources of mismatch limit this, so one must accept some degree of signal gain degradation in most experiments. Generally, less than 5 dB is acceptable, but beyond this the power leaks into too many other resolution cells and MFP usually does not "focus" on the target even when the "in bin" signal to noise ratio at a single sensor is large. Here we accept that the ocean is an uncertain environment and use a stochastic representation for the signal which spans more than one spatial dimension. We first examine the covariance structure of signals propagating In a random medium. This can be done both analytically using results in the acoustics literature or by simulations which incorporate the ocean physics of random fluctuations. Next, we consider a generalization of MFP, which we term stochastic matched field processing (SMFP) which attempts to focus the power from all the signal dimensions. Finally, we consider the deeper question of when does an uncertain ocean medium randomize the spatial structure so much that localization cannot be done. Probably a more important application of stochastic signal models is for robust nulling techniques. Many existing arrays do not achieve their full potential for nulling because the environment is not stationary over the time scales required for adaptive methods, commonly termed the "snap-shot deficient" situation. If one attempts parametric methods, the spatial signals leading to the array manifold do not span the space of the interfering signals because the ocean has randomized them. Higher dimensional nulling such as adjacent resolution cells has been done, but it is not clear if this is the appropriate physical model for spanning the interference. Here we use acoustic propagation models for this and examine nulling techniques which are robust to the - ncertain ocean environment.