I also get the occasional "double" alert. I'd always put this down to an aircraft just entering my range, then just leaving my range, before entering it again.
To be honest, I now make much more use of the Fleet Watch feature to keep an eye on my "interesting" aircraft, these being - G-SAR*, G-CG*, G-CROY, G-VLCN, G-FR*, G-SAS*, X*, Z*