To address the challenges of high costs pertaining to physical sensors and the necessity for manual calibration of tire pressure reference values in indirect tire pressure monitoring systems (iTPMS), this paper proposes a hybrid tire pressure monitoring system (hTPMS) based on the degeneration gated recurrent unit (DGRU) network. First, this study conducts a theoretical analysis of the tire torsional vibration model, which serves as the fundamental basis for tire pressure identification. A simplified filtering algorithm is devised to compensate for ring gear errors, and in conjunction with the Ackermann steering model, the wheel speed discrepancy between the inner and outer tires under small-steering conditions is eliminated, thereby extending the effective operating envelope of the radius iteration method. By fusing the signals from a single physical tire pressure sensor and antilock braking system (ABS) sensors, DGRU neural network estimators are established independently in both the time and frequency domains, enabling real-time and high-precision estimation of tire pressure values. Results of real-vehicle road tests demonstrate that when the tire pressure experiences a sudden drop from 2.6 bar to 1.9 bar, the frequency-domain feature input mode achieves a minimum response time of 73.6 s, with the tire pressure estimation error confined within the tolerance range specified by national standards. Compared with sequence-based input, the time-domain feature input mode enhances the response speed by up to 62.66%, and the algorithm operates on the Aurix TC397 chip with an average CPU utilization rate of merely 0.464%.This system reduces the cost of physical sensors by 75% relative to conventional direct tire pressure monitoring systems (dTPMS), and its accuracy and stability across diverse operating conditions fully comply with the requirements of the national standard GB 26149-2017, offering an innovative approach that integrates mechanical modeling and intelligent algorithms for tire pressure monitoring technology.