Date: 201206
Local time of day: 0601-1200
Location: LGA.Airport, NY
Flight conditions: Mixed
Weather elements / visibility: 5
Light: Daylight
Aircraft: Large Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Takeoff / Launch
Airspace: Class B LGA
ATC / advisory: Tower LGA
Reporter organization: Air Carrier
Reporter function: Pilot Not Flying; Captain
Human factors: Training / Qualification; Confusion; Distraction; Situational Awareness; Communication Breakdown; Time Pressure
Second reporter function: First Officer; Pilot Flying
Anomaly: Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert
Contributing factors: Human Factors; Environment - Non Weather Related; Airport
Primary problem: Human Factors

Narrative: We took off without a proper takeoff clearance at LGA. LGA was landing 4 (ILS) and departing 13. Taxi times for departure were probably 45 to 50 minutes or so due to the weather and time of departure. Both the Ground and Local Controllers were doing an excellent job of keeping things moving along. It was finally our turn to depart and we were cleared to line up and hold on Runway 13; which we did. The brakes were set and I transferred aircraft control to the First Officer as it was his leg. We were cleared via the TNNIS Departure (an RNAV departure with a track outbound on a 050 course). As a Company flight was landing on Runway 4; we heard the Tower issue a go-around to another flight on the approach; but didn't really catch the call sign. As our company aircraft is turning off the runway onto Taxiway G; we see another flight on the approach a few miles or so out and the Tower cleared them to land; hence we mentioned to one another that the flight which was issued the go-around must be behind them. We are both used to the pace of LGA operations and the next thing we both believed we heard was a clearance for us to takeoff but to maintain runway heading. All of this made sense to us and we figured the runway heading and 3;000 FT clearance was to prevent a conflict with the aircraft going around. I read back the takeoff clearance and we commenced our departure. After we were airborne; the Tower advised that we had departed without a takeoff clearance and to contact Departure Control. Turns out the runway heading and 3;000 FT clearance was for the flight on the go-around; which had a very similar call sign also ending in #. I believe it may have been another carrier's # and we were Company #. Needless to say; neither one of us was too pleased to find this out. I cannot tell you if this was caused by some radio transmissions being incomplete due to the circumstances and frequency congestion; or a possible assumption on our part that the clearance was for us because it was understandable given these circumstances; and furthered by the similar sounding call signs. What I can tell you is if I should ever find us facing a similar scenario (a high volume airport with intersecting operations; combined with some weather and a not necessarily normal event occurring - i.e.; a go-around); I will make absolutely sure that the clearance was for our flight. Nonetheless; there was no conflict with any other aircraft and our flight proceeded uneventfully.


Second narrative: [Narrative #2 contained no additional information.]


Synopsis: An air carrier aircraft departed LGA Runway 13 without takeoff clearance because they became confused about which aircraft ATC was issuing clearances to and thought their callsign was given a takeoff clearance.