## 1 Introduction
These manufacturing technologies have created inertial sensors that are smaller, low-cost and consume less power, but, at the same time, exhibit much larger errors than their higher-priced counterparts. As a consequence, the reduction in size of the detection units in INSs generates new challenges related to the improvement of their performance. Currently, the miniaturized IMUs performances are limited by the quality of gyro sensors related to the bias stability. Another major requirement for this kind of detection unit is low noise, the achievement of which is still an important issue [53; 54]. Categorized as stochastic errors, the noises in inertial sensors support two distinct components, known in the literature as long-term noise (low-frequency noise) and short-term noise (high-frequency noise) [55; 56; 57; 58; 1]. Additionally, some deterministic errors affect the miniaturized inertial sensors, but the research in the field provided various calibration methods that help to estimate and compensate for it [1; 2; 59; 60; 61; 62; 63]. For short-term noise filtering, the researchers tested various methods based on the wavelet transform [1; 55; 56; 64; 65; 66; 67]. A research team from the University of Putra in Malaysia used a Wavelet Multi-Resolution Algorithm (WMRA) to increase the performance of the low-cost inertial sensors in a MEMS IMU eliminating the short-term noise that parasitizes them. During the experimental tests, with an INS system including the MEMS IMU, different levels of decomposition and thresholding filters were evaluated; the final results provided a more accurate solution of navigation as a consequence of wavelet filtering [55]. In order to increase the accuracy of MEMS gyros, a de-noising mechanism using the second-generation wavelet transform was studied at Harbin Engineering University in China. Using the lifting scheme wavelet transform, the method proved an experimental reduction in the random drift error of a triaxial gyro MEMS [56]. A method to reduce the noise in MEMS gyros was proposed and experimentally demonstrated at the Chongqing University of Posts and Telecommunications, China. It was conceived as a combination between the FFT (fast Fourier transformation) noise reduction mechanism and the mechanism used in the simple wavelet noise reduction. The experimental tests proved an important noise reduction in the gyro data comparatively with the FFT noise reduction method [64]. Researchers from the University of California, Berkeley, proposed a multiple-model adaptive estimation to evaluate the magnitudes of noise variances in a gyro model, using the obtained values in an extended Kalman filter for a micro-satellite attitude estimation [27]. The numerical simulation and experimental data proved that the adaptive estimation of noise parameters improved the attitude estimation performance. In a collaborative research, a Brazilian team from Instituto de Aeronautica e Espaco and from Instituto Nacional de Pesquisa Espacial developed a calibration procedure for an IMU including four gyros in a tetrahedral configuration [65]. The wavelet analysis considered eight levels of decomposition, the filtering aiming at the removal of undesirable high-frequency noise components from the gyro signals; the procedure was experimentally tested and validated. At the Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology from Southeast University in Nanjing, a method using Kalman filtering was proposed for the online de-noising of the sensors data, while the results of the wavelet filtering were used as reference; the level of decomposition used for the Matlab wavelet function was 5 [66]. The conclusions underlined that the IMU measurement noise can be suppressed by the proposed Kalman filter and by the wavelet, while the filtering result obtained with the low-pass equiripple finite impulse response (FIR) filter was worse and there was a noticeable time delay when the tested IMU rotated [66].