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Planetary gearbox faults are the leading causes of downtime in wind turbines (WTs). In recent years, numerous and various vibration-based approaches have been put forward for WT gearbox fault detection. In the vibration-based techniques, order tracking-based methods, which by identifying fault orders in gearbox drivetrains, are regarded as very promising and powerful techniques. In the currently available order tracking methods, auxiliary devices are required to accurately obtain the instantaneous angular speed (IAS) of drivetrain. To tackle this problem, instantaneous angular speed estimation from vibration signals has been studied and some tacho-less order tracking (TLOT) approaches have been developed. However, many vital parameters for IAS estimation in the currently available TLOT algorithms need to be manually selected, which raise the question of user-friendliness, even result in a false diagnosis. As mentioned earlier, aiming at the shortcomings, a novel TLOT method based on adaptive IAS estimation is proposed for WT planetary gearbox fault diagnosis. In the proposed method, the nonlinear mode decomposition (NMD) method is improved, and its computational burden is reduced. And, the tachometer information of the drivetrain is adaptively extracted by the improved NMD method from generator vibration signal for gearbox vibration signal resampling. A field test is conducted, and the vibration signal of WT planetary gearbox with the compound fault is used for further investigation. The experimental validation results demonstrate that the planetary gearbox compound fault can be successfully detected, and the proposed method outperforms the traditional method based on generalized demodulation.