Tactical Inertial Measurement Unit Thermal Bias Modeling Fundamentals
Tactical IMU thermal bias modeling requires combining static higher-order polynomials with real-time temperature derivative terms to eliminate dynamic lag errors.
Static Polynomial Model
Numerical Approximation
Representing the relationship between an input stimulus and a sensor output through a series of power terms provides a mathematical framework for linearization. A static polynomial model converts raw digital counts into engineering units by applying coefficients derived from a regression analysis of calibration data. This approach assumes that the sensor response depends only on the current input value and ignores any time dependent or hysteretic effects.
Coefficient Determination
Least squares algorithms typically calculate the optimal values for each term to minimize the residual error across the specified measurement range. Third or fourth order equations are common for bridge-based sensors where nonlinearity is a known physical property of the strain element. Higher order models may improve the fit on the training data but often introduce oscillations between the points, a phenomenon known as Runge’s effect.
Accuracy Boundary
Extrapolation beyond the calibrated range leads to rapid divergence from the physical reality of the sensing element. Because a static polynomial model is purely empirical, it carries no physical insight into why the sensor behaves in a certain way. Designers must define the valid domain of the model to prevent the software from generating nonsensical values during over-range conditions.
Computational Implementation
Logic efficiency dictates the choice of the polynomial degree in embedded systems where floating point operations are expensive. Recursive algorithms like Horner’s method reduce the number of multiplications required to evaluate the static polynomial model in real time.