considering the error on the cumulation over a whole cycle implies that this sequence that is the cycle is significant for this calculation hence indivisible in fact a zero mean error can be obtained on the whole sequence by underestimating the cumulation over one part of the cycle and by overestimating it on another yet while these parts can be repeated independently the cumulative error will be high for example if the cycle contains city driving at low speed where the model overestimates the emissions and freeway driving for which the model underestimates the emissions a wide difference is accordingly accumulated between the prediction and reality by traveling exclusively in conditions specific to one of the parts if only city driving applies the emissions are always overestimated and never compensated for by a freeway underestimation on the contrary if these two parts were acceleration and deceleration this problem would not arise because the number would not vary despite the driving conditions the cumulation criterion on a sliding window is an intermediate criterion between these two extremes it consists in using the maximum absolute error of the cumulative quantity over a certain distance for example 1 km fig1 shows the general architecture of a system for estimating quantities of pollutant compounds emitted in the exhaust gases of a diesel engine according to the invention the system comprises one or more neural networks 1 receiving input data 2 and supplying the estimated quantities 3 at the output the system further comprises means 4 for cumulating the estimated quantities to give cumulative quantities 5 the system also comprises means 6 for resetting the estimated quantities of pollutant compounds independently of each other these means 6 are.