This work presents an embedded computing framework for the analysis and design of large scale algorithms utilized in the estimation of acoustic doubly dispersive, randomly time-variant, underwater communication channels. Channel estimation results are used, in turn, in the proposed framework for the development of efficient high performance algorithms, based on fast Fourier transformations, for the search, detection, estimation, and tracking (SDET) of underwater moving objects through acoustic wavefront signal analysis techniques associated with real-time electronic surveillance and acoustic monitoring (eSAM) operations. Particular importance is given in this work to the estimation of the range and speed of deep underwater moving objects modeled as point targets. The work demonstrates how to use Kronecker products signal algebra (KSA), a branch of finite-dimensional tensor signal algebra, is used as a mathematical language to assist in the development and implementation of the embedded computing algorithms.