Model-based estimation of cylinder pressure sensor offset using least-squares methods

Two methods for estimating the sensor offset of a cylinder pressure transducer are developed. Both methods fit the pressure data during pre-combustion compression to a polytropic curve. The first method assumes a known polytropic exponent, and the other estimates the polytropic exponent. The first method results in a linear least-squares problem, and the second method results in a nonlinear least-squares problem. The nonlinear least-squares problem is solved by separating out the nonlinear dependence and solving the single-variable minimization problem. For this, a finite difference Newton method is applied. Using this method, the cost of solving the nonlinear least-squares problem is only slightly higher than solving the linear least-squares problem. Both methods show good statistical behavior. Estimation error variances are inversely proportional to the number of pressure samples used for the estimation. The method is computationally inexpensive, and well suited for real-time control applications