We extend the model of Karlof and Wagner for modelling side channel attacks via Input Driven Hidden Markov Models (IDHMM) to the case where not every state corresponds to a single observable symbol. This allows us to examine algorithms where errors in measurements can occur between sub-operations, e.g. there may be an error probability of distinguishing an add (A) versus a double (D) for an elliptic curve system. The prior work of Karlof and Wagner would assume the error was between distinguishing an add-double (AD) versus a double (D). Our model also allows the modelling of unknown values, where one is unable to determine whether a given observable is add or double, and is the first model to allow one to analyse incomplete traces. Hence, our extension allows a more realistic modelling of real side channel attacks. In addition we look at additional heuristic approaches to combine multiple traces together so as to deduce further information.