1. Sensor Error Characteristics By: Hector Rotstein

2. Introduction Inertial sensors exhibit constant and variable errors Some of these errors can be calibrated at production. Calibration procedure is a complex procedure that can take more than one day of work Still the first statement holds It is important to analyze the impact of the errors in navigation performance Do that by modeling and error analysis

3. Main Characteristics Each basic sensor error has four components: fixed contribution, temperature-dependent variation, run-to-run variation and in-run variation In addition, errors vary according to environmental conditions: vibration, pressure, acceleration and rate Some critical errors: – Bias and bias instability – Scale factor and non-linearity – Noise

4. Biases Bias is a constant error present in all sensors In many cases, it is the main error source In an IMU, biases are denoted b x, b y and b z while drifts are denoted d x, d y and d z. Errors are always expressed in body axes. Biases are usually split into fixed (or turn-on, or repeatability) and in-run (or bias instability). fixed in-run

5. Biases (cont’d) Accelerometer biases are usually measured in mili-g’s or micro-g’s Gyro biases are measured in degrees per hour Typical accelerometer biases vary from a few micro-g’s to a few tens of mili-g’s Typical gyro drifts vary from 1/1000 to 100 deg/h In many applications turn-on biases are compensated for by averaging measurements Short term behavior is modeled for error analysis

6. Scale Factor and Misalignment Errors due to scale factor are proportional to measured signal Denoted s gx, s gx, s gx and s ax, s ax, s ax Usually measured in parts per million (ppm) or % Misalignment results from the lack of alignment between the sensitivity and the IMU axes Input = output actual output

7. Scale Factor and Misalignment (cont’d) Misalignment errors are also proportional to the true inputs Scale Factor and misalignment errors can be modeled using a pair of matrices:

8. Random Noise All physical sensors exhibit random noise Typical sources are electrical noise, pick-off limitations, vibration, output quantization, etc. Random noise can be denoted by vectors  a,  g Since actual measurements are increments, noise appears as a random walk: integral of a random process. Units are deg/sqrt-h and m/sec/sqrt-h or micro-g/sqrt-Hz Inexpensive sensors (e.g., MEMS) can exhibit significant high-frequency and correlated noise

9. Other Error Sources 1.Scale factor non-linearity. Errors are correlated with higher powers of the input 2.Vibration sensitivity. Vibration induced errors that looked like biases (VRE). Units: deg/h/g-rms 2 3.Gyros g-sensitivity. Units: deg/h/g 4.…

10. Modeling Errors From the above, one can model the sensor errors using Biases are sometimes further measured using: Here  is called the correlation time

11. Calibration Calibration is the science (and art!) of estimating and compensating for constant sensor errors and assembly misalignments Due to temperature variation, calibration is done as a function of temperature A function (or look-up table) is computed and stored in the sensor. Measurements are compensated for on-line