Recursive parameter estimation of exhaust gas oxygen sensors with input-dependent time delay and linear parameters

• An estimation approach for wide-range oxygen sensors in diesel engines is proposed.
• These sensors are characterized by input-dependent time delays and linear parameters.
• The proposed algorithm extends an existing recursive gradient-based least-squares algorithm.
• The algorithm requires minimal computational and memory resources.
• Accurate estimates for the oxygen sensor are achieved in simulation and experiment.

Exhaust gas oxygen sensors are widely used for emission control in internal combustion engine systems. Due to their working principle and their positioning, these sensors are subject to input-dependent time delays and input-dependent linear parameters. Consequently, the corresponding time delays and linear parameters can vary fast, i.e. at the same rate as the respective input signals. This paper presents an extension of an existing gradient-based least-squares algorithm and its application to recursively estimate the input-dependent time delays and linear parameters of wide-range oxygen sensors in diesel engines. The extended algorithm is applied in a detailed simulation and experimental study involving real wide-range oxygen sensors that are affected by drift, aging, clogging and manipulation. The input-dependent time delay and linear parameter estimates obtained with the proposed recursive algorithm accurately reproduce the estimates obtained with a numerical offline optimization procedure.