How to improve accuracy or extrapolate missing or bad GPS points

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Is there an easy to use freeware tool to postprocess my location data, in order to correct 1) location errors (or improve accuracy not based on differential GPS correction) and 2) deal with missing locations, based on ecological information?

e.g. spikes in the location data are indicative of location errors, as are large angles between 3 fixes at small step sizes

Brown hare location data is based on small GPS collar (U-blox LEA4S), and has been measured every 6 minutes in an open , relatively flat enviroment, including acceleration data every minute for 35 days, 24hr a day



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