Nonlinear process representation using ARMAX models with time dependent coefficients

Motivated by the need to improve the estimation of mass air flow going into an automobile engine, an approach that models a nonlinear process operating over a large dynamic range is developed. This approach is based on stochastic time-varying autoregressive moving average with exogeneous inputs (TARMAX) models. The TARMAX model coefficients are explicit functions of time and vary in a deterministically organized fashion. These TARMAX models are shown to apply to an important class of nonlinear processes and a novel model parameter estimation method fully based on linear operations is presented. The estimation approach is characterized by a low computational complexity and requires no initial guess of the parameter values. The developed approach is used to address problems dealing with improving the operation of a vehicle engine. First, a TARMAX model is used to provide an accurate estimate of the air flow that would have been determined by a laboratory grade sensor if it were installed on the car simply by using engine variables already available in the engine electronic controller (EEC). Second, TARMAX models are used to anticipate the future response of a mass air flow sensor (MAF) in order to obtain an accurate estimate of the cylinders air charge. The estimated TARMAX models prove to have good simulation and prediction capabilities. All models are estimated using actual production vehicle data.