###### Abstract  
MEMS (micro-electro-mechanical system) gyroscopes and accelerometers are used in several applications. They are very popular due to their small size, low price, and accessibility. The design of MEMS accelerometers enables the measurement of vibrations, with frequencies from tenths of hertz to even \(1\) kHz. MEMS gyroscopes can be applied to measure angular rates, and indirectly also angular oscillations with frequencies similar to accelerometers. Despite significant stochastic errors, MEMS sensors are used not only in popular domestic appliances (e.g., smartphones) but also in safety-critical units, such as aeronautical attitude and heading reference systems (AHRSs). In engineering, methods of stochastic properties analysis are important tools for sensor selection, verification, and the design of measurement algorithms. In this article, three methods used for the analysis of stochastic properties of sensors are presented and comparative analyses are shown. The applied measurement frequencies (\(1\) kHz) were much higher than those typically found in MEMS sensor applications. Additionally, an exemplary analysis of temperature drift frequency, as well as the possibility for the synthesis of complementary filter parameters with the use of the described methods, is shown. Assessment of the stochastic properties of MEMS accelerometers and gyroscopes was performed under both constant and variable temperature conditions (during warm-up after switching on) with the use of classic methods, such as power spectral density (PSD) and Allan variance (AV), as well as the less known but very promising generalized method of wavelet moments (GMWM). accelerometers; gyroscopes; MEMS; stochastic; PSD; Allan variance; GMWM; temperature drift; airplane; aircraft; UAV +
Footnote †: journal: Applied  
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