The paper aims to realize a rapid online estimation of the state-of-power (SOP) with multiple constraints of a lithium-ion battery. Firstly, based on the improved first-order resistance-capacitance (RC) model with one-state hysteresis, a linear state-space battery model is built; then, using the dual extended Kalman filtering (DEKF) method, the battery parameters and states, including open-circuit voltage (OCV), are estimated. Secondly, by employing the estimated OCV as the observed value to build the second dual Kalman filters, the battery SOC is estimated. Thirdly, a novel rapid-calculating peak power/SOP method with multiple constraints is proposed in which, according to the bisection judgment method, the battery’s peak state is determined; then, one or two instantaneous peak powers are used to determine the peak power during $T$ seconds. In addition, in the battery operating process, the actual constraint that the battery is under is analyzed specifically. Finally, three simplified versions of the Federal Urban Driving Schedule (SFUDS) with inserted pulse experiments are conducted to verify the effectiveness and accuracy of the proposed online SOP estimation method.

In order to estimate the diesel particulate filter (DPF) soot load and improve the accuracy of regeneration timing, a novel method based on an equivalent circuit model is proposed based on the electric-fluid analogy. This proposed method can reduce the impact of the engine transient operation on the soot load, accurately calculate the flow resistance, and improve the estimation accuracy of the soot load. Firstly, the least square method is used to identify the flow resistance based on the World Harmonized Transient Cycle (WHTC) test data, and the relationship between flow resistance, exhaust temperature and soot load is established. Secondly, the online estimation of the soot load is achieved by using the dual extended Kalman filter (DEKF). The results show that this method has good convergence and robustness with the maximal absolute error of 0.2 g/L at regeneration timing, which can meet engineering requirements. Additionally, this method can estimate the soot load under engine transient operating conditions and avoids a large number of experimental tests, extensive calibration and the analysis of complex chemical reactions required in traditional methods.