The traditional processing model of the temperature error for a gyroscope is serial, meaning that de-noising and temperature drift compensation are implemented in a two-step procedure. Hence, the result of the latter depends on the performance of the former; in particular, negative de-noising produces a negative compensation result. To reduce this dependence, we propose a parallel processing algorithm of the temperature error based on variational mode decomposition (VMD) and an augmented nonlinear differentiator (AND). An application to a micro-electro-mechanical system gyroscope is described to demonstrate the effectiveness and applicability of the proposed algorithm. Its major advantages are (i) a combination of VMD, extreme learning machines, and AND is proposed, and an adaptive accelerometer factor determination method for AND is given based on the VMD, both of which improve the effectiveness of the de-noising process; (ii) temperature drift and noise in the temperature error can be extracted and processed synchronously, thereby reducing the dependency of drift compensation on the de-noising result and making the temperature error process more efficient. [ABSTRACT FROM AUTHOR]