Basically, a "covered person" is anyone who is covered under PIP. N.Y. Insurance Law § 5102(j) defines a "covered person" as:
Any pedestrian injured through the use or operation of, or any owner, operator or occupant of, a motor vehicle which has in effect the financial security required by article six or eight of the vehicle and traffic law or which is referred to in subdivision two of section three hundred twenty-one of such law; or any other person entitled to first party benefits.
NOTE: The definition of a "motor vehicle," provided in § 5102(f) does not include a motorcycle.
NOTE ALSO: A person is not a "coverd person" if their vehcle is insured by a company not authorized in New York or not meeting New York's required liability coverage. Article Six of New York Vehicle and Traffic Law ("V&T"), § 310 and following, is New York's "Motor Vehicle Financial Security Act" (Article Eight, V&T 370 and 371, discusses vehicles for hire). Section 311(4) defines required coverage. It requires 25/50/10 for automobiles. Automobiles registered in New York must be insured by an "insurer duly authorized to transact business in" New York. Vehicles registered out of New York state must be insured by "an authorized insurer" or by an unauthorized insurer which has filed with the Commisioner of Insurance a letter "consenting to service of process and declaring its policies shall be deemed to be varied to comply with the requirements of this article."
Although it is not perfectly clear, it seems that unauthorized insurers are subject to the requirement of arbitration in section 5105.