Batch Bayesian auto-tuning for nonlinear Kalman estimators

The optimal performance of nonlinear Kalman estimators (NKEs) depends on properly tuning five key components: process noise covariance, measurement noise covariance, initial state noise covariance, initial state conditions, and dynamic model parameters. However, the traditional auto-tuning approaches based on normalized estimation error squared or normalized innovation squared cannot efficiently estimate all NKE components because they rely on ground truth state models (usually unavailable) or on a subset of measured data used to compute the innovation errors. Furthermore, manual tuning is labor-intensive and prone to errors. In this work, we introduce an approach called batch Bayesian auto-tuning (BAT) for NKEs. This novel approach enables using all available measured data (not just those selected for generating innovation errors) during the tuning process of all NKE components. This is done by defining a comprehensive posterior distribution of all NKE components given all available measured data outside of the NKE recursive process based on the equivalence between the posterior distributions used in batch and recursive Bayesian inference. Our empirical validation on a synthetic bioprocess dataset demonstrates that BAT significantly improves the consistency and accuracy of NKE estimations compared to baseline methods. These findings indicate that BAT can effectively optimize NKE tuning, improving performance and reliability in practical applications.