GLF2 FLT CREW HAS NAV 1 AND 2 FAIL TO CONNECT PROPERLY TO THE HSI; RESULTING IN A FAULTY LOC SIGNAL AND A SUBSEQUENT MISSED APPROACH.

Narrative

IN IMC; WE WERE ASSIGNED TO INTERCEPT AND TRACK INBOUND ON THE ZZZ RWY XXL LOC. AT APPROX 19 DME WE BEGAN TO NOTICE A SWING ON THE LOC NEEDLE ON THE OBS. WE QUESTIONED THE APCH CTLR ON ANY PREVIOUSLY RPTED LOC SWINGS. APCH AND ANOTHER ACFT RPTED THAT THERE WERE NO OBSERVED LOC SWINGS. WE ASKED OUR POS; WERE TOLD THAT WE WERE 2 DEGS OFF RWY XXL LOC. AFTER BEING CLRED FOR THE ILS RWY XXL AND INTERCEPTING THE GS; THE CAPT'S OBS WITH GS AND LOC INFO FAILED. WE NOTIFIED ATC AND INITIATED A MISSED APCH. WE HAD NO GUIDANCE FROM THE NAV #1 AND #2 AND HAD TO FLY RADAR VECTORS TO VMC. NOT KNOWING WHAT HAD CAUSED THE NAV FAILURE; WE CLBED OUT AT 500 FPM. ONCE IN VMC; WE WERE HANDED OFF TO SOCAL FOR VECTORS TO AN ARPT (ZZZ1) IN VMC. DURING THE PROCESS; WE WERE UNABLE TO 'BACK UP THE APCH' WITH THE FMS AS IT DOES NOT HAVE ILS CAPABILITIES (HONEYWELL GNS XLS). IT TOOK SOME TIME IN VMC TO DETERMINE THAT THERE WAS A FAILURE OF THE #1 AND #2 NAV CONNECTION TO THE HSI. ONCE CONNECTED TO THE FMS; WE WERE ABLE TO NAV IN 'VMC ON TOP.' OUTSTANDING HELP FROM ATC!