Engine exhaust backpressure is a critical parameter in the calculation of the volumetric efficiency and exhaust gas recirculation flow of an internal combustion engine. The backpressure also needs to be controlled to a presetting limit under high speed and load engine operating conditions to avoid damaging a turbocharger. In this paper, a method is developed to estimate exhaust pressure for internal combustion engines equipped with variable geometry turbochargers. The method uses a model-based approach that applies a coordinate transformation to generate a turbine map for the estimation of exhaust pressure. This estimation can substitute for an expensive pressure sensor, thus saving significant cost for production vehicles. On the other hand, for internal combustion engines that have already installed exhaust pressure sensors, this estimation can be used to generate residual signals for model-based diagnostics. Cumulative sum algorithms are applied to residuals based on multiple sensor fusion, and with the help of signal processing, the algorithms are able to detect and isolate critical failure modes of a turbocharger system.