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Precision and Error Propagation in Static MEMS-IMU Inertial Navigation: A Stochastic Time-Series Analysis
Mohammad Mahdi Kariminejad1, Mohammad Ali Sharifi1, Mir Abolfazl Mostafavi2
1School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran 1439957131, Iran.
Sensors (Basel, Switzerland)
|August 13, 2026
Summary
This study analyzes errors in smartphone inertial navigation systems (MEMS-IMU) under static conditions. Results show raw sensor data is white noise, but derived position and velocity exhibit random walk errors.
Area of Science:
- Navigation Systems Engineering
- Sensor Data Analysis
- Robotics and Autonomous Systems
Background:
- Low-cost Microelectromechanical System Inertial Measurement Units (MEMS-IMUs) are increasingly used in navigation.
- Understanding their precision and error propagation under static conditions is crucial for reliable performance.
- Existing methods for error characterization require robust statistical frameworks.
Purpose of the Study:
- To investigate the precision and stochastic error propagation of navigation solutions from a MEMS-IMU using a smartphone.
- To develop and apply a comprehensive statistical framework for characterizing sensor and navigation state errors.
- To quantify the performance limitations of low-cost MEMS-IMUs in static scenarios.
Main Methods:
- Utilized a smartphone with MEMS-IMU rigidly mounted in a zero-reference scenario.
- Collected static inertial measurements, divided into statistically robust segments.
- Applied strapdown inertial mechanization to compute velocity and position.
- Employed statistical tests (ADF, Bartlett's, Ljung-Box) and ARIMA modeling for data analysis.
- Used power spectral density (PSD) and multivariate non-negative least squares variance component estimation (NNLS-VCE).
Main Results:
- Accelerometer and gyroscope data are characterized as stationary white-noise processes.
- Standard deviations for raw sensor data are ~10^-2 m/s^2 (accelerometer) and ~10^-4 rad/s (gyroscope).
- Derived velocity and position estimates exhibit random walk behavior, modeled by ARIMA(0,1,0) and ARIMA(0,2,0) respectively.
- After 30s, average standard deviations for ENU velocity and position estimates are σv=[0.77,0.44,0.29] m/s and σp=[1.30,0.69,0.46] m.
Conclusions:
- The proposed framework effectively models stochastic behavior and characterizes errors in low-cost MEMS-IMU navigation.
- Raw MEMS-IMU data behaves as white noise, but integration leads to significant random walk errors in velocity and position.
- This research provides a comprehensive approach for assessing the precision and performance of MEMS-IMU-based navigation systems.
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