NOX Sensor NH3 Cross-Sensitivity

Assuming the NOx sensor is only cross-sensitive to ammonia and the Horiba gas analyzer readings are the actual exhaust gas NOx concentrations, based on these data and the NOx sensor ammonia cross-sensitivity model in Eq. (14.31), it can be clearly observed that the cross-sensitivity is different in these tests and also changes with time. By the preliminary examinations of the data, it can be seen that the cross-sensitivity in the test of Fig. 14.2 was about 2, and was decreased to 0.5 in the test of Fig. 14.3. Furthermore, the value in the test of Fig. 14.4 was changing with time. In the light of these observations, it can be concluded that the NOx sensor ammonia cross-sensitivity is dynamic and cannot be simply treated as a constant for estimating the actual NOx concentration in exhaust gas. 

The challenge of estimating the NOx sensor ammonia cross-sensitivity factor lies in the fact that a dynamic model is hard to be developed. For the SCR-out NOx concentration estimation, it is possible to employ an accurate SCR model with a NOx sensor upstream of the SCR catalyst and the amount of AdBlue injection. However, such prediction requires a high-accuracy SCR model, which is 

Kalman filter is well known as an efficient recursive filter that can optimally estimate the states of linear dynamic systems from a series of noisy measurements [20]. For nonlinear systems, extended Kalman filters [21,22] have been developed and validated by many studies to be effective in real applications [17, 23-25]. Unlike model-based estimators which heavily rely upon the plant models, a specific feature of a Kalman filter is that it finds the stochastic relations between model predictions and sensor measurements, and then estimates system states in an optimal approach. By utilizing this feature of the Kalman filter, a slowly time-varying state can be treated as a constant and its variation can be estimated by comparing the model predictions and measurements in a stochastic manner. 

According to the studies in [11] and [26], the cross-sensitivity factor Kcs variation is mainly caused by temperature change. Because engine exhaust temperature dynamics after the SCR catalyst is generally slow, the cross-sensitivity factor K s in Eq. (14.31) is assumed to be a slowly time-varying variable, and it can be modeled by the following equation  

By the above models, the prediction equation in a discrete form is obtained as 

---