Precision and Error Propagation in Static MEMS-IMU Inertial Navigation: A Stochastic Time-Series Analysis

This paper investigates the precision and stochastic error propagation of navigation solutions obtained from a low-cost microelectromechanical system inertial measurement unit (MEMS-IMU) under static conditions. A modern smartphone equipped with an MEMS-IMU was rigidly mounted at a calibrated fixed location to establish a zero-reference scenario, and inertial measurements were collected while the device remained stationary. The dataset was divided into 75 non-overlapping segments, each comprising 30 s of data sampled at 10 Hz, to enable statistically robust analysis. For each segment, velocity and position, which are theoretically zero under static conditions, were computed using strapdown inertial mechanization. A comprehensive statistical framework was then applied to characterize the stochastic behavior of both the raw inertial measurements and the derived navigation states. The methodology first assessed data normality, stationarity using the Augmented Dickey-Fuller (ADF) test, and variance homogeneity using Bartlett's test. Subsequently, ARIMA models were identified and validated using the Ljung-Box (LB) test, while power spectral density (PSD) analysis provided complementary frequency-domain characterization. In addition, a multivariate, non-negative least squares variance component estimation (NNLS-VCE) method was employed to jointly estimate the variance components of multiple navigation state variables. The results demonstrate that the accelerometer and gyroscope measurements along all three axes are well characterized as stationary white-noise processes, with standard deviations in the order of 10-2 m/s2 and 10-4 rad/s, respectively. The estimated velocity random walk (VRW) coefficients are 0.197,0.201,0.160 m/s/h, while the corresponding angular random walk (ARW) coefficients are 0.009,0.012,0.008 rad/h. In contrast, the derived velocity and position estimates exhibit random walk behavior caused by error accumulation in the inertial mechanization process and are best represented by ARIMA(0,1,0) and ARIMA(0,2,0) models, respectively, consistent with the corresponding Allan variance analysis. After 30 s of static navigation, the average standard deviations of the ENU velocity estimates are σv=[0.77,0.44,0.29] m/s, while the corresponding position standard deviations are σp=[1.30,0.69,0.46] m. The proposed framework provides a comprehensive approach for the stochastic modeling, precision assessment, and error characterization of low-cost MEMS-IMU navigation systems.