Arrays of seismometers, hydrophones, and electromagnetic receivers have several signal processing problems in common. This paper is concerned primarily with source location and secondarily with signal extraction. The basic problem can be described as follows: A transient signal from an event is detected in the outputs of the sensor array. We determine the location of the source from the temporal positions of the signal in the array outputs. Further, if the signal is unknown, we estimate it. The approach taken here differs from previous investigations in three ways: (i) a Bayes estimation approach is used, (ii) the estimates are evaluated recursively with respect to channels, and (iii) a time-domain approach is used, as opposed to a frequency-domain approach. The proposed estimation technique is optimum with respect to a large class of loss functions, since it is based on the expectation of the posterior distribution. Recursive evaluation of the posterior expectation has several advantages. At each step we have the optimum estimate of the unknown parameters and the corresponding covariance matrix. A channel selection rule and stopping rule are defined in terms of the covariance matrix. Further, having an optimum estimate at each step permits simplification of the processing; e.g., the search interval may be limited to the most probable region of the parameter space. Such techniques significantly decrease the processing time and increase the rate of convergence. Equations are developed for the known-signal case with planar and spherical wavefronts, and results are presented from a computer simulation. Subsequently, equations for the unknown-signal case are presented with simulation results.