Identifying high confidence cycles

I now have two data sets that can be classed as possible cycles:

• Each possible interval identified by thresholding
• Every pair of 'on' and 'off' steady states

We know from the analysis of the fridge, the 'on' duration of each cycle has mean = 15 minutes and variance = 2 minutes. If we assume the duration of a cycle is normally distributed about the mean, we can create the following likelihood function:

Now we can filter out possible 'on' cycles below a likelihood threshold, leaving a set of cycles containing possible duplicates. We can remove duplicates by:

• If two 'on' cycles overlap, discard the one with the lower likelihood
• If two 'on' cycles are within the minimum 'off' duration of each other, discard the one with the lower likelihood

This produces a list of high confidence 'on' cycles. The next step is to identify any missing cycles between these, using a combination of:

• Low confidence state-transitions
• Possible intervals for fridge cycles
• Applying the model of typical fridge behaviour using surrounding high confidence cycles