CE750 First Officer described a dual IRS/GPS failure at FL410 and attempted realignment; which is unsuccessful. Flight continues to destination with ATC assistance.

Narrative

Equipment failures resulted in navigation and heading errors that required no-gyro vectors to final approach at planned destination. Weather was clear sky and unlimited visibility for duration of flight and the left seat was the pilot flying. Approximately 15 minutes after level off at FL410; IRS-1 began to drift from the aircraft's blended solution of lateral position. Maximum drift indications from the FMS indicated a drift rate of >10 and a total drift of 71 NM after 30 minutes. Additionally; wind speed and direction from IRS-1 were highly irregular in bearing and strength. We considered re-aligning IRS-1 and reviewed the checklist. Instead; we decided to monitor IRS-1 and utilized PFD SEL-right for the A-Autopilot to follow guidance since IRS-2's navigation was operating normally. One hour and 15 minutes after the first indications; the drift improved from 71 NM to 4.9 NM with drift rate of 1.0. A few minutes later; IRS-1 drifted back out again (ultimately back to 70 nm+). Ten minutes later IRS-2 drifted to 12.0 NM and increasing with subsequent FMS messages saying GPS-1 and GPS-2 FAILED. Max drift indications for IRS-2 reached 49 NM and 25 NM for both GPS-1 and GPS-2. When IRS-2 started to drift; we informed ATC of our predicament and that we were not RVSM capable. Additionally; we requested to join the J10 airway between OBH and DSM VORTAC's in order to follow raw-data (green needles) between the two stations and an altitude block of FL410 to FL430 to begin realignment of both IRS's. We descended about 250 FT when IRS alignment began while flying on standby gauges for 20-30 seconds IAW with the checklist (DUAL IRS FAILURE). We attempted to update the true heading in the FMS (button 3R on the IRS status page) from the magnetic compass but primary headings were about 20-30 degrees off in flight. Neither IRS returned to display lateral (lat-long) position information for the remainder of the flight. We continued to navigate point-point using the green needles; however; due to our lack of confidence in our heading system; we requested no-gyro vectors for a visual approach during arrival to our destination. On final approach and during landing rollout on Runway 31C; the primary headings read 275 degrees (magnetic compass was oscillating +/-10 degrees from 310). We confirmed the Standby-PWR switch was on throughout the flight and there were no off-flags on the PFD's/MPD's. We recommend the following for further investigation: -Review IRS in flight alignment checklist for completeness (DUAL IRS FAILURE and IN FLIGHT ALIGNMENT OF ONE IRS; during an in flight alignment; the current checklist directs to set IRS to ATT position and remain there (not return back to NAV mode). Based on system descriptions in the Cessna Operating Manual (OM) Model 750 and our Initial Pilot Training Manual (IPTM); the IRS will not regain alignment until the IRS rotary knob is placed in the OFF position for at least 3 seconds then NAV (ref: Cessna OM; pg 3-83 and our IPTM). The current checklist may be incomplete.