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This paper presents a delay-free tracking differentiator based on variational mode decomposition (VMD) for extracting the useful signal from a noisy measurement of gyroscope. Sigmoid function-based tracking differentiator (STD) is a novel tracking differentiator with the advantages of noise-attenuation ability and dynamical performance. However, there is a contradiction in STD; i.e., selecting a larger acceleration factor may cause faster convergence but bad random noise reduction whereas selecting a smaller acceleration factor may lead to signal delay but effective random noise reduction. Here, multiscale transformation is introduced to overcome the contradiction of STD. VMD is selected to decompose the noisy signal into multiscale components, and the correlation coefficients between each component and original signal are calculated, then the component with biggest correlation coefficient is reserved and other components are filtered by the proposed adaptive STD algorithm based on the correlation coefficient of each component, and finally the denoising result is obtained after reconstruction. The prominent advantages of the proposed algorithm are as follows: (i) compared to traditional tracking differentiators, better noise suppression ability can be achieved with suppression of time delay; (ii) compared to other widely used denoising methods, a simpler structure but better denoising ability can be obtained.

Delay-Free Tracking Differentiator Design Based on Variational Mode Decomposition: Application on MEMS Gyroscope Denoising