This paper presents the maximum‐likelihood signal processor for steering a vertical array in the vertical direction. The major application is to the estimation of the depth of a distant narrow‐band continuous point source in the waveguide. The eigenfunctions of the guide are used to match the array to the received signal The error of the depth estimate is derived as a function of the aperture and geometry of the array, the covariance function of the ambient noise received by the array, and the observation period; assuming that the source and medium are stationary during that period. The processing technique can be applied to any perfect waveguide in which a signal source is detected by an array of sensors.