Residual Asymmetry Modeling and Joint Time–Frequency Estimation for High-Dynamic Two-Way Microwave Links

High-precision time synchronization among high-dynamic platforms is an important foundation for distributed detection, cooperative sensing, and networked operation of high-speed mobile platforms. In high-dynamic two-way microwave links, rapid variations in propagation geometry, Doppler-related frequency offsets, and link-quality fluctuations can break the approximate symmetry between uplink and downlink propagation. Although geometric and motion compensation can remove the dominant propagation-asymmetry term, residual asymmetric errors caused by propagation modeling errors, compensation mismatch, and link degradation may still remain and couple into clock-offset estimation, thereby reducing synchronization stability and accuracy. To address this problem, this paper proposes a modeling and joint estimation method for residual asymmetric errors in high-dynamic two-way microwave links. The post-compensation residual error is modeled as a recursively estimable dynamic state, and its rate of change is introduced to characterize the short-term evolution of the residual term. Meanwhile, a four-timestamp and frequency-offset joint observation model is constructed, in which frequency-offset information is used as an observation-level auxiliary constraint to enhance local separability among the clock offset, frequency offset, and residual link state. On this basis, a link-state-information-assisted IMM-IEKF is adopted to realize online joint estimation of clock parameters and link residual errors. Under the equivalent stochastic-error simulation setting, the proposed method effectively suppresses post-compensation residual asymmetric errors and achieves sub-nanosecond synchronization accuracy under strong-dynamic and degraded-link conditions.