Bias

Bias refers to a systematic error in sensor measurements, representing a persistent offset between the sensor output and the true physical quantity. It usually appears in the same units as the sensor’s measurement. Gyroscopes report measurements are in degrees per hour (°/h) or radians per second (rad/s). Accelerometers measurements are presented in meters per second squared (m/s²) or multiples of gravitational acceleration (g).

Gyroscope bias manifests as a constant angular rate offset, resulting in errors in orientation estimates that accumulate over time even when the sensor is stationary. Accelerometer bias, similarly, appears as a constant acceleration offset, which, when integrated over time, generates velocity and position errors.

In many high-precision applications, these measurements vary and do not remain strictly constant. Environmental conditions, such as temperature, can influence their values. Engineers compensate for these variations through calibration or real-time estimation to maintain accurate performance.

Unlike random noise, which fluctuates around zero, bias remains systematic and accumulates continuously over time. This accumulation makes it a critical error source in inertial navigation.

Integrated navigation systems, such as GNSS-aided INS, actively estimate and correct bias using sensor fusion algorithms. Engineers often implement these algorithms with Kalman filters or related techniques to maintain accurate navigation and reliable performance.

Mathematically, a sensor measurement (y_m) can be represented as the sum of the true value (y_t), the bias (b), and random noise (n), where the bias component is the deterministic part that drives long-term drift.

Equation: y_m = y_t + b + n

Engineers must properly identify, calibrate, and compensate to minimize cumulative navigation errors. Proper management ensures accurate positioning and reliable orientation over time. This approach is especially critical in GNSS-denied or high-dynamic environments.

Engineers can measure many different parameters in IMUs and INS. These include in-run bias stability, repeatability, and bias over temperature.