I would like to find the distance that a vehicle travels using a Kalman filter. The vehicle is a car that travels the road between two positions. The vehicle has a GPS/barometer/accelerometer device that collects position data, which I converted from a longitude and latitude to a North, East, Down position in metres (This is a position coordinate of the starting coordinate is always 0,0,0). The velocity of the car is measured by this device in North, East, Down coordinates (m/s) (components of the velocity vector). I can access accelerometer measurements but this is in the device frame, not the North East Down frame. The device gives magnetic heading and euler angles roll pitch and yaw. The accelerometer has a problem with drift and the magnetic heading is not always accurate so I think that using the accelerometer for observations is not that important. Can anyone suggest a state matrix that helps me get a distance state? Thanks.