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This paper presents a diagnostics methodology that has applications to internal combustion engines as well as other dynamic devices. Included is an overview of the theoretical foundation of the approach, discussions on its application to internal combustion engine diagnostics, and experimental engine data showing the application of this methodology. Also included are the recent developments addressing issues of the effect of motoring compression and expansion work on crankshaft speed fluctuations and the resulting torque estimation. The methodology consists of a hard-wired nonlinear to linear transformation of engine variables that allow all subsequent diagnostics and control calculations to use linear mathematics, which significantly simplifies the size and complexity of the engine control and diagnostics strategy and code.