How Not to Make the Joint Extended Kalman Filter Fail with Unstructured Mechanistic Models

Area of Science:

• Biotechnology
• Process Engineering
• Control Systems

Background:

• Unstructured mechanistic models (UMMs) are crucial for biomanufacturing, enabling process monitoring even without known mechanisms.
• Joint estimation of states and parameters using an extended Kalman filter (JEKF) is vital for real-time bioprocess monitoring.

Purpose of the Study:

• To formally describe and prove the failure case of JEKF when applied to UMMs with unshared parameters and limited measurements.
• To propose a novel approach, SANTO, to overcome this JEKF failure and enable simultaneous estimation.

Main Methods:

• Formal description and mathematical proof of JEKF failure in specific UMM configurations.
• Development of the SANTO approach, modifying the initial state error covariance matrix P(t=0).
• Empirical evaluation using synthetic and real biomanufacturing datasets.

Main Results:

• Demonstrated JEKF failure due to constant zero Kalman gain for unshared parameters.
• SANTO successfully prevents Kalman gain from becoming zero by adjusting P(t=0).
• Achieved up to a 17% reduction in root-mean-square percentage error (RMSPE) compared to classical JEKF.

Conclusions:

• The SANTO approach effectively addresses the JEKF failure in UMMs with unshared parameters.
• SANTO significantly enhances the accuracy of real-time bioprocess monitoring.
• This work provides a robust solution for estimating states and parameters in complex biomanufacturing systems.