We present new models relating combustion pressure to crankshaft velocity in an internal combustion engine. There are three aspects to this model. First, by changing the independent variable from time to crankshaft angle, a nonlinear differential equation model becomes a linear first-order differential equation. Second, a new stochastic signal model for combustion pressure uses the sum of a deterministic waveform and a raised cosine window amplitude modulated by a Bernoulli-Gaussian random sequence, parametrizing the pressure by the sample modulating sequence. This results in a state equation for the square of angular velocity sampled once every combustion, with the modulating sequence as input. Third, the inverse problem of reconstructing pressure from noisy angular velocity measurements can now be formulated as a state-space deconvolution problem, and solved using a Kalman-Alter-based deconvolution algorithm. Experimental results are shown supporting theoretical developments.
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