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approach was able to identify the pre-mixed and diffusive combustion phases, for different engine loads. Results were compared with a simple inversion procedure, showing a good agreement. The combustion ignition delay was also calculated, showing its variation with the engine load. Keywords Rate of heat release • Inverse problems • Bayesian technique List of symbols A Area A/F Air/fuel ratio B Piston bore CA Crankshaft angle f Linear or non-linear function of the state variables g Linear or non-linear function representing the observation model h Heat transfer coefficient LHV Lower heating value m Mass n Engine speed in Hz n Vector of noise associated with the observation model P Pressure Q Heat t Time T Temperature v Average gas velocity within the cylinder v Vector of noise associated with the evolution model V Volume w Weights of particles W Covariance matrix x Mass fraction of burned fuel y Vector of state variables z Vector of observation variables Abstract The rate of heat released during the combustion in Diesel engines is important for many reasons, including performance evaluation, pollutant formation, and control. Combustion in Diesel engines can be generally divided into three phases: pre-mixed, diffusive or mixed-controlled, and late combustion. The objective of this paper is to estimate the rate of heat released by the fuel in a marine Diesel engine, in order to identify the pre-mixed and diffusive phases, using the Sampling Importance Resampling (SIR) Bayesian Particle Filter. Experimental pressure data obtained from a piezoelectric sensor, installed in a research marine diesel engine (MAN Innovator 4c), was used to feed the observation model in such Bayesian approach. The evolution model for the pressure was formulated in terms of a set of ordinary differential equations, coming from the First Law of Thermodynamics, together with a random walk model for the unknown state variable. The proposed

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