Well, ‘pole’ is new to me, and apparently also to The Dictionary of Circadian Physiology. A PubMed search for it points me to circadian rhythm studies in the high Arctic. Probably not the sort of ‘pole’ you’re interested in.
My guess is that ‘pole’ refers to the centre of the plot. If that’s correct, it would mean the same as the confidence limits including zero, therefore the estimated parameters are not significant, and no circadian rhythm exists for the variable you’re studying.
You might want to email the author of those functions to clarify this.
My only other suggestion is to see if you can fit your data using Curve fitting to a sinusoidal function, but using the Statistics (and Machine Learning) Toolbox function nlinfit and nlparci in addition to (that is, after) the fminsearch call I used. Use the parameter estimates from fminsearch as the initial parameter estimates for nlinfit.
I don’t have your data to experiment with, but it’s worth a go to see if you can get an acceptable fit and parameter estimates. You can then use the cart2pol function to plot it as a characteristic polar plot.
