ERJ 145 Captain reported failure of the Air/Ground Sensing system caused an Air/Ground Light on Gear retraction. The flight crew continued the flight to destination airport. At gear extension approach; the light remained on and the flight crew continued to landing.

Narrative

During the initial climbout of OKC we got an Air/Ground message on EICAS. We continued our climb and once we were out of sterile and at a safe altitude we ran the QRH; which said that we could possibly not have steering and thrust reversers. We patched through to Dispatch who connected us to a Maintenance Supervisor. The Supervisor informed us that the light would most likely extinguish when we dropped the gear. We continued the flight and decided we would compute the numbers for both scenarios; the light extinguishing; and the light not extinguishing with the unfactored landing distance times 1.7. Working as a crew we decided we would extend the gear early and that if the light did not extinguish we would request priority handling out of an abundance of caution and in case we didn't have reversers or steering.When we got the ATIS at ZZZ they were using the east directional runways and the winds were out of the South; 20 gusting 30. According to the QRH we were supposed to run the unfactored landing distance; flaps 45; times 1.7. Given the winds we did not feel flaps 45 was appropriate so we ran the numbers flaps 22 times 1.7. The number we came up with was about 8;000 ft. and we had about 9;000 feet of available runway. We didn't feel comfortable with that number and decided; as a crew; we would request Runway XXL out of an abundance of caution. From this point we continued the flight and on the arrival extended the gear early; but the light did not extinguish. As previously briefed; we requested priority handling and asked for the longer runway.At some point on the approach; while deviating around a thunderstorm and lightning; we were read new winds which were still out of the south but at just 15 kts. We reran the numbers at flaps 45 times 1.7; per the QRH and had much better numbers; especially now that we had requested 15L. Throughout the whole flight; Name and I communicated with Dispatch; Maintenance; Passengers; our FA; and ATC to the greatest extent possible. Name requested from ATC to have the plane met by emergency vehicles and said that we would need a tow. I was a little confused because the QRH stated that we 'may' not have steering or reversers; but he told me we would not and that he had just done this in the sim the week prior. We continued that approach and had a safe landing; bringing the plane to a stop on the runway and emergency vehicles stated the aircraft seemed fine.Shortly after landing I inquired why we don't just try to taxi to the high speed using rudders or see if the steering worked. Name said he was sure it wouldn't work and was concerned about the possible of uncommanded swerving. We were towed to the gate and the passengers deplaned normally and no one was hurt. I believe we were in a high stress environment trying to accomplish a flight while also communicating with multiple agencies and dealing with bad weather. As the person reading the QRH I think I should've been more assertive with the fact that the QRH said 'may not have...'. I also feel I should've been more assertive once we were on the ground about attempting to taxi; in order to clear the runway. I also think Name may have had some training biases due to a recent similar training event in the sim. Later discussion made me realize that he thought we would have no brakes and no steering; where I was definitely under the impression it was just a possibility of no reversers and no steering. In the end we worked well as a crew; but there were some lapses in communication; but the overall outcome was a safe landing where no one was hurt.