This article addresses the problem of constructing an accurate and reliable navigation system for autonomous mobile robots (MR) operating in environments where Global Navigation Satellite System (GNSS) signals are unavailable. A hybrid approach is proposed, combining data from odometry, an electronic compass, and an active ultrasonic beacon system. Based on the technical specification for the development of a heavy mobile robot (mass 200 kg with payload), the selection of sensors and control algorithms is justified. Mathematical modeling includes a trilateration method with temperature compensation of the speed of sound and data filtering based on an Extended Kalman Filter (EKF). Experimental results confirm the possibility of achieving positioning accuracy of ±10 cm in steady-state operation: the coordinate determination error did not exceed 12 cm in dynamic mode and 8 cm in static mode. Initial transient errors during EKF convergence (up to 2 m) are effectively suppressed within 3–5 seconds of system operation.