An attitude and heading reference system, AHRS, for a vehicle, the AHRS comprising: an inertial measurement unit, IMU, configured to generate inertial measurements comprising angular rate and acceleration measurements of the vehicle from at least one accelerometer and at least one gyroscope; a heading source configured to generate heading measurements of the vehicle; and a processor including an adaptive statistical filter, the processor being configured to receive input from the IMU and the heading source, wherein during operation of the vehicle the processor is configured to utilize the adaptive statistical filter to: estimate an attitude and heading of the vehicle; model and estimate IMU errors and heading source errors; and model, adapt, and estimate vehicle acceleration, wherein the modeled vehicle acceleration is adapted using an adaptation algorithm configured to: detect acceleration of the vehicle; compute a synthetic acceleration, which is a combination of the detected and the estimated acceleration quantities; compute a vehicle acceleration upper boundary based on the synthetic acceleration; and transform the vehicle acceleration upper boundary onto parameters for the modeled vehicle acceleration; and wherein the adaptive statistical filter is configured to mitigate the impact of vehicle acceleration effects on the attitude and heading estimate by use of the vehicle acceleration upper boundary. an inertial measurement unit, IMU, configured to generate inertial measurements comprising angular rate and acceleration measurements of the vehicle from at least one accelerometer and at least one gyroscope; a heading source configured to generate heading measurements of the vehicle; and a processor including an adaptive statistical filter, the processor being configured to receive input from the IMU and the heading source, wherein during operation of the vehicle the processor is configured to utilize the adaptive statistical filter to: estimate an attitude and heading of the vehicle; model and estimate IMU errors and heading source errors; and model, adapt, and estimate vehicle acceleration, wherein the modeled vehicle acceleration is adapted using an adaptation algorithm estimate an attitude and heading of the vehicle; model and estimate IMU errors and heading source errors; and model, adapt, and estimate vehicle acceleration, wherein the modeled vehicle acceleration is adapted using an adaptation algorithm configured to: detect acceleration of the vehicle; compute a synthetic acceleration, which is a combination of the detected and the estimated acceleration quantities; compute a vehicle acceleration upper boundary based on the synthetic acceleration; and transform the vehicle acceleration upper boundary onto parameters for the modeled vehicle acceleration; and wherein the adaptive statistical filter is detect acceleration of the vehicle; compute a synthetic acceleration, which is a combination of the detected and the estimated acceleration quantities; compute a vehicle acceleration upper boundary based on the synthetic acceleration; and transform the vehicle acceleration upper boundary onto parameters for the modeled vehicle acceleration; and wherein the adaptive statistical filter is configured to mitigate the impact of vehicle acceleration effects on the attitude and heading estimate by use of the vehicle acceleration upper boundary.