In the IMU Sensor of the Sensor Fusion and Tracking Toolbox where the world frame is NED and the sensor frame is Front-Right-Down it seems the IMU measurements are the opposite of the specific force, which according to [1] (eq. 3.97) is 
where P is a platform frame or body frame. The same definition is given by multiple other well known authors such as [2] 
where i is a space-fixed axis and 
is a the position vector with respect to the origin. Same for [3] in which the specific force is defined as 
where 
is the gravitation force. Following the previous definition, an IMU at rest on a table in a NED world with an FRD coordinate frame should measure the force of the table pushing up on it. Thus the measurement should be 
and I can confirm this with an SBG Ellipse IMU I have at hand. Now suppose the IMU slides forward at 
on the table then the specific force measurement should be 
. It seems mathworks has decided to instead define the specific force as 
and my question here is: Why was this convention chosen and is there some documentation explaning this choice? As an example, here I generate an IMU trajectory with +1.0 acceleration on the x-axis using code modified from the examples page. fs = 100;
nsamples = fs * 1;
traj = kinematicTrajectory('SampleRate',fs);
accBody = zeros(nsamples,3);
accBody(:,1) = 1;
angVelBody = zeros(nsamples,3);
[~,orientationNED,~,accNED,angVelNED] = traj(accBody,angVelBody);
IMU = imuSensor('accel-mag','SampleRate',fs);
[accelReadings,magReadings] = IMU(accNED,angVelNED,orientationNED);
figure(1)
t = (0:(nsamples-1))/fs;
plot(t,accelReadings)
legend('X-axis','Y-axis','Z-axis')
ylabel('Acceleration (m/s^2)')
title('Accelerometer Readings')
Which results in
We can observe that even though I accelerate +1 in x I measure -1 in x.
[1] Jay Farrell. 2008. Aided Navigation: GPS with High Rate Sensors (1 ed.). McGraw-Hill, Inc., New York, NY, USA. page 100
[2] Titterton, David; Weston, John: 'Strapdown Inertial Navigation Technology' (Radar, Sonar & Navigation, 2004). page 24
[3] Groves, Paul D. Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems, 2nd edition. page 67-68
