Robust state estimation of NOx storage amount in NSR catalysts using a pseudomeasurement-based unscented Kalman filter

Accurate estimation of the NOx storage amount is essential for optimizing rich-spike control and improving fuel consumption in NOx storage-reduction (NSR) catalysts. In practical applications, however, the estimation accuracy is often degraded by uncertainties in the state estimation model’s input variables. To address this issue, this study proposes a pseudomeasurement-based unscented Kalman filter (UKF) framework that accurately estimates the NOx storage amount regardless of the presence of input variable errors. Among the model input variables, errors in inlet NOx have the greatest impact on the estimated NOx storage amount; therefore, the inlet NOx error is treated as an unknown parameter and is estimated together with the NOx storage amount. Building on our previous conference work presented at COMODIA 2025, which demonstrated the effectiveness of the proposed method under inlet NOx error conditions, the present study extends the validation to a broader range of practical scenarios. Specifically, the proposed method is evaluated under ideal conditions without input variable errors, with state initialization errors in the NOx storage amount but with error-free inlet NOx, and with both inlet NOx errors and state initialization errors to clarify the effects of their interaction. The state initialization errors are introduced as initial estimated NOx storage amounts corresponding to 5% and 10% of the maximum NOx storage amount, reflecting residual overestimation carried over from preceding operating cycles as well as the estimation uncertainty associated with model mismatch during rich-spike operation. Results obtained using actual engine test data show that the proposed method significantly improves estimation accuracy when inlet NOx errors are present, while exhibiting non-intrusive and fail-safe behavior under ideal conditions and with state initialization errors alone. Furthermore, the proposed method maintains stable estimation performance even under combined uncertainty conditions. These results demonstrate the robustness and practical applicability of the proposed method for NSR catalyst control.