Analysis of a correlation filter for thermal noise reduction in a MEMS gyroscope

This paper analyzes the behavior of a DSP-based correlation filter used to mitigate the effects of thermal noise in a low-cost microelectromechanical system (MEMS) gyroscope. The gyroscope is driven by a 10 kHz sinusoidal signal and outputs a quadrature sinusoid whose amplitude is proportional to the Coriolis acceleration, thereby providing information concerning directional change. Due to the size and configuration of the MEMS gyroscope, the output signal is quite small and is therefore susceptible to both electrical and mechanical thermal noise. This paper employs an optimization theory to analytically establish that the correlation filter is the optimum choice for reducing the effects of thermal noise in the output signal. DSP-based implementation of the filter is then discussed, followed by derivation of an analytic expression for signal-to-noise ratio of the output signal, with independent variables representing noise power spectral density, sampling rate, and integration period of the filter. Practical limitations concerning sampling rate are discussed, as is the relationship between integration period and response time for the gyroscope. Simulation results are also provided, showing agreement with the analytic expressions.