Methods and systems are provided reusing processed sensor data to identify multiple types of sensor degradation. In one example, a central peak of a distribution, such as a generalized extreme value distribution, of sensor readings is re-used to identify asymmetric sensor degradation and stuck in-range sensor degradation.

The objective of the present invention is to provide an exhaust purification system that is capable of purifying exhaust gas during both lean and stoichiometric driving. The exhaust purification system is equipped with: a feedback-use identifier, which identifies parameter values such that the error between the output value from a LAF sensor and the estimated value for the LAF sensor output as obtained from a model equation is minimized; and a stoichiometric driving mode controller. The controller performs feedback control and thereby determines the fuel injection amount such that in the stoichiometric driving mode the equivalence ratio value as calculated from the parameters reaches a target value which is set such that a three-way purification reaction occurs in an under-engine catalyst. The identifier identifies the model parameters before feedback control is initiated by the controller.

An estimation device includes: a memory and a processor, wherein the processor is configured to execute a process including: determining a point of a burning having a higher peak in a predetermined range of a heat release rate based on a peak of a burning having a smaller peak, in a heat release rate waveform in an internal combustion engine that performs a multiple-stage fuel injection; calculating a tangential line of the heat release rate waveform at the point; setting a predetermined point on the tangential line as an initial value for identifying a model parameter of a heat release rate model; identifying the model parameter so that a difference between a calculation value of the heat release rate model and the heat release rate waveform is reduced with use of the initial value; and estimating a heat release rate with a result of an identification of the identifying.

Implementations described herein relate to utilizing discrete transient local state space models to modify an output from a steady state NO.sub.x estimation model to provide a final estimated NO.sub.x value. An engine operating space, defined by a speed and injection quantity map, is subdivided into several discrete local state spaces and a transient model is developed for each discrete state space to output a NO.sub.x estimation correction value. The transient models may be a regression model or the transient model may be an empirical map of data values. The NO.sub.x estimation correction value modifies a steady state NO.sub.x value to calculate the final NO.sub.x estimated value. The final NO.sub.x estimated value is then output to another component, such as a controller as an input for controlling one or more components of an engine, an aftertreatment system, and/or a diagnostic system.

Disclosed herein are devices, systems, and methods relating to balancing engine performance and engine emissions of an engine in a vehicle in real time. In an example, a method can include sensing operation data indicative of an engine response during a current engine operation. The current ending operation can include a supervisory control of engine emissions. The method can include evaluating a response model to determine engine performance deviation data corresponding to an expected baseline engine performance and an expected current engine performance at the current engine operation. This evaluation can be performed via controller. This evaluation can be based on the operation data. The method can include generating and setting a performance constraint in response to evaluating the response model. The performance constraint can be set such that the engine performance deviation data is maintained at a controls objective that inhibits deterioration of the engine performance over time.