A heteroskedasticity and autocorrelation consistent test for process noise calibration of Kalman filters in multi-sensor orbit determination

Process noise calibration is a central problem in sequential orbit determination. If the process noise covariance is too small the filter is overconfident, and if it is too large it is overconservative. In both cases the estimation error grows and the reported covariance stops describing it, which affects downstream products such as conjunction assessment or re-entry prediction. No widely adopted method diagnoses the calibration in multi-sensor settings, where measurements of different type and dimension must enter a single consistency metric. This work presents the Heteroskedasticity and Autocorrelation Consistent Dimensionless Averaged Normalised Innovation Squared (HAC-DANIS) test, which evaluates process noise calibration from the innovation sequence of the filter, without ground truth. The normalised innovation squared (NIS) of each measurement is divided by its dimension, which puts sensors of any dimension on a common scale, and the standard error of the averaged sequence is obtained with the heteroskedasticity and autocorrelation consistent (HAC) Newey--West estimator, which accounts for the sensor-dependent variance of the sequence and for the serial correlation left by a miscalibrated filter or an imperfect dynamical model. Under mixing and moment conditions the statistic is asymptotically standard normal for a calibrated filter, and for a miscalibrated one its sign indicates the direction of the miscalibration. The autocorrelation function of the normalised sequence complements the test with a characterisation of the mistuning regime. Applied to an unscented Kalman filter processing simulated laser, telescope and radar observations of four satellites in low Earth orbit, the test rejects the eight miscalibrated process noise configurations with the sign of their miscalibration and does not reject the four calibrated with it.