The problem of synthesis of optimal and quasi-optimal algorithms for receiving and processing BOC signals intended for use in global navigation satellite systems (GNSSs), such as GPS (USA), Galileo (European Union), GLONASS (Russia), and BeiDou (China), is solved on the basis of the Markov theory of random process estimation by the method of step-by-step solution of the Stratonovich equation. The problem of optimal nonlinear filtering is solved in relation to a vector discrete-continuous Markov random process for the case when its continuous part is a vector diffusion Markov process, and the discrete part is characterized by a simple Markov chain of several positions. It is assumed that useful BOC signals are observed against a background of additive white Gaussian noise. The main analytical relations of optimal and quasi-optimal algorithms for receiving and processing BOC signals are presented, as well as the corresponding block diagram of a quasi-optimal system for receiving and processing GNSS BOC signals. The results of the study are also applicable in cases of noise-like signals of modern GNSSs, for which BOC signals are not used yet.
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