A Study on a Low-Cost IMU/Doppler Integrated Velocity Estimation Method Under Insufficient GNSS Observation Conditions

The Global Navigation Satellite System (GNSS)/Inertial Measurement Unit (IMU) Loosely Coupled (LC) integration framework has been widely adopted due to its simple structure, but it relies on complete GNSS position and velocity solutions, and the rapid accumulation of IMU errors can easily lead to navigation failure when fewer than four satellites are visible. In this paper, GNSS Doppler observations are fused with IMU attitude information within an LC framework. An inter-satellite differential Doppler model is introduced, and the velocity obtained from the differential Doppler solution is transformed into the navigation frame using the IMU-derived attitude, enabling three-dimensional velocity estimation in the navigation frame even when only two satellites are available. Analysis of real vehicle data collected by the GREAT team at Wuhan University shows that the Signal-to-Noise Ratio (SNR) and the geometric relationship between the Satellite Difference Vector (SDV) and the Receiver Motion Direction (RMD) are the dominant factors affecting velocity accuracy. A multi-factor threshold screening strategy further indicates that when SNR> 40 and ∣SDV·RMD∣ >0.2, the Root Mean Square (RMS) of the velocity error is approximately 0.3 m/s and the data retention rate exceeds 44%, achieving a good balance between accuracy and availability. The results indicate that, while maintaining a simple system structure, the proposed Doppler-IMU fusion method can significantly enhance velocity robustness and positioning continuity within an LC architecture under weak GNSS conditions (when more than two satellites are visible but standalone GNSS positioning is still unavailable), and is suitable for constructing low-cost, highly reliable integrated navigation systems.