Core Concepts of Random Walk
Random Walk refers to the process in which minute erroneous measurements by IMU add up over time. Such errors cannot be observed over short periods but add together in the integration process leading to large drift in position and orientation estimates.
It is like walking in any direction you please: the longer you walk, the more distant you will become from where you started even though you take small steps.
Angle Random Walk (ARW): Influences gyroscopes and they are expressed in °/√hr. It brings about orientation errors which increase as time goes by.
Velocity Random Walk (VRW): This is a process that influences how accelerometers are measured and it is in the ratio m/s/√h. It generates errors of position that increase as the time squared.
The two types essentially restrict the time period that an IMU can deliver proper navigation without external correction.
With A Random walk on IMU Performance
IMUs sense acceleration and angular velocity, but in order to obtain position and orientation, they have to be integrated. Random noise in these signals get amplified in integrating:
Position error ∝ Time²
Orientation error ∝ Time
This implies that the errors of the position increase quadratically, and thus are particularly troublesome to the navigation systems.
The Random Walk characteristics are very temperature dependent. With varying temperature of operation:
- Parameters of noise may vary by 10-20 percent
- There is more bias instability
- Calibration parameters drift
This is because thermal management will be very important in the case of high-precision applications.
IMUs are not all made the same. Random Walks have greatly different features:
- Consumer IMUs: 0.5-2.0°/√hr (gyro)
- Industrial IMUs: 0.1-0.5°/√hr
- Tactical grade: 0.01-0.05°/√hr
- Navigation grade: <0.001°/√hr
Such a disparity of quality is at a cost that exponentially rises.
In inertial navigation systems (INS) Random Walk lead to:
- Position drift: Up to Kilometers per hour in consumers devices
- Attitude errors: These are several degrees after few minutes of operation.
- Velocity errors: Growing linearly with time
Such inaccuracies require other sensors to correct it frequently.
Why √hr in units? The mathematics of random processes gives the √hr unit. In a random walk the error standard deviation increases as the square root of time. So °/√hr or in words, the angular error (in degrees) following time t hours will, approximately, be ARW × √t.
Taming Random Walk Effects
The accuracy is increased greatly by integrating IMU data and other sensors (GPS, magnetometers, vision systems) through the use of technologies such as that offered by the Kalman filter. The IMU supplies high-rate information in between low-rate absolute position reports.
Temperature Sensors and Calibration tables can be implemented so that systems can adapt to thermal influences on parameters of Random Walk. This has the improved potential of eliminating temperature related drift by 50-80 percent.
Complex algorithms such as determination of Allan Variance analysis can achieve characterization and compensation of Random Walk. Noise can be detected and removed using adaptive filtering methods which are real-time methods.
The Random Walk is significantly decreased at the hardware level through new space-age technologies such as MEMS-based gyroscopes with vacuum packaging, quantum sensors and optical gyros.
Applications Affected by Random Walk
Conclusion
There is also an intrinsic fault with IMU technology called Random Walk which leads to increasing errors in inertial navigation systems. It is very important to understand this phenomenon because:
- Choosing right IMU grades to certain applications
- Effective sensor fusion systems Design
- Proper method of calibration and compensation is put into place.
- Establishing proper expectation to the accuracy of navigation