Temperature-dependent Optimized Calibration of a MEMS Inertial Measurement Unit

This paper is concerned with the temperature-dependent calibration of MEMS inertial measurement units (IMU). Calibration is the process of estimating time-invariant parameters that characterize the IMU output errors. These errors depend on the angular rates, the linear accelerations, and the temperature experienced by the device. Previous works emphasized the development of estimators for given inputs, from least-squares batch estimators to Kalman filters or artificial neural networks. Our work focus on optimizing the time profiles of these inputs. Several maximization problems of the observability Gramian determinant or trace are proposed with constraints that are derived from operational limitations. Three approaches are deterministic. The first two are parametric where the input profiles are low-order time polynomials, or step and ramp functions with optimized switching times. A third approach is nonparametric and relies on time discretization of the input functions. A fourth approach is probabilistic and seeks the best joint distributions of the temperature and rates, which are modeled as random variables. The design approaches are first verified on a single gyro model before being applied to the three-axes gyroscope case. The design model includes biases, scale factors non-linearity of order 4 in the angular rate, and misalignment parameters. All parameters are expressed as third-order temperature polynomials. Profiles of the input temperature and of the angular rates are obtained by merging the randomized approach and the deterministic nonparametric approach. The sensitivity of the optimized cost is investigated by changing key parameters: the total calibration time, the initial temperature, the sequence of the angular rates, and the time spent at each rate. The method is verified via a simulated calibration with the “best” profiles of the rate and temperature. The method is then validated via an experimental calibration using an approximation of the “best” profiles. For the calibration of the accelerometers the input temperature profile is identical to that of the gyroscopes. The performances are compared with calibration results based on standard profiles of the angular rates and temperature. The proposed approach outperforms the standard one by up to one order of magnitude in the gyroscopes angular rate prediction error. The residual errors are not temperature dependent. A breakdown of the error shows that biases, scale factors, and misalignment contribute evenly.