I have a question which I can not give an answer even if it is some days I am thinking about that. In general a INS is made by an accelerometer + a gyroscope. Is it possible to obtain the same information using accelerometer + magnetometer? If it is possible what are the pros and cons of this new solution?
In an INS you need to know the orientation and the acceleration. The magnetometer or gyroscope provides the orientation information. (In 2D anyway, in 3D the accelerometer can help with up and down) The main differences are:
A gyroscope tells you your orientation relative to when it was turned on. If you need an absolute orientation (and you may not), you'll need to zero it somehow. For example by putting the INS on a flat table pointing north and pressing a "calibrate" button.
A magnetometer tells you your orientation relative to a magnetic field. Across most of the populated areas of earth the magnetic field is within 20 degrees of true north/south, but it may point up or down by 60 degrees to the horizontal. You might need to calibrate that out, either by programming in the magnetic inclination for the location it's being used, or a process like the point above.
A magnetometer points towards magnets, obviously. You can't rely on one if you have magnets near your INS. Large iron/steel objects, including iron ore deposits, can also cause problems.
A magnetometer is slower than a gyroscope. If your INS is doing acrobatics or rapidly rotating, a gyroscope will give rapid, accurate measurements.
A magnetometer doesn't drift (much). If a gyroscope is used for a long time, the output angle may drift round. If you an recalibrate every so often that's fine, but if you can't then that's a problem. More expensive gyroscopes drift less, and ring laser gyroscopes hardly at all.
There are numerous magnetometers, accelerometers and gyroscopes on the market, each with different performance and price. You'll want to work out what specifications you need for your INS, and translate that into specifications for the sensor. You'll probably find one option cheaper than the other once you've done that.
For best results, you would want to combine an accelerometer, gyroscope, and magnetometer. The gyroscope would provide quick, accurate output and the magnetometer would correct for long-term drift of the gyroscope. If you have a GPS, then you can use that to correct for long term position drift coming from the accelerometer, and, provided you are moving, direction drift from the gyroscope.