I want to estimate the position on a 3D environment by introducing only acceleration estimates. Is that possible? If I use the extended Kalman Filter and introduce these estimates will I have the appropriate results? Thank you in advance!

  • $\begingroup$ A Kalman filter is pretty meaningless unless you have multiple redundant inputs. Otherwise it's just a fancy excuse for doing the obvious. Could you describe your proposed system, or at least describe what you propose to use for inputs and what you want to get as outputs? $\endgroup$ – TimWescott Sep 27 at 23:29

If the acceleration readings are performed in an inertial (non rotating in particular) frame then yes it's sufficient to use the accelerations, but if the acceleration measurements are performed on the moving craft then no it's not possible alone by accelerometer readings.

Eventhough it's sufficient to use those accelerations $a_x$, $a_y$, and $a_z$ on a cartesian coordinate system to compute the displacement associated with the center of mass of the craft that's moving in 3D, nevertheless you will also need to know the orientation of the craft (hence the accelerometer) so that you can transform its acc measurement vectors into the navigation frame correctly.

Therefore, you also need to consider (at least) the gyroscopic readings to determine the craft orientation wrt your navigation frame. Once you determine the orienation of the craft, then you convert its current acceleration measurements into the non-rotating intertial frame in which you compute the track of the craft by integrating the accelerometer readings.

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  • $\begingroup$ You could indeed use the accelerometer in the cases you mentioned. However, due to noise such double integration will always drift away from the true position. Or more in mathematical terms, just using acceleration measurements gives a system that is not fully observable. $\endgroup$ – fibonatic Jan 1 at 23:30
  • $\begingroup$ Yes you are right of course, besides, despite how it seems contrary to my idealistic statements, I actually didn't mean to say naked integration of acc, rather tried to refer to the general philosophy of getting position from its second derivative ;-). I hope the OP won't write down double sums based on my suggestion :-)) $\endgroup$ – Fat32 Jan 2 at 0:19
  • $\begingroup$ Thank you so much for your suggestion. I am quite confused on this issue, I have a lot of ideas in order to come to my point, but I think that a lot of them are false.I have found an accelometer application that writes the estimates ax,ay,az per microseconds while I walk on a place and after that I can save these data as text. My wonder is about making them as vectors for each cartesian coordinate in order to introduce them on a extended Kalman filter Javascript and find the vectors x and P. $\endgroup$ – Maria D. Jan 2 at 16:11
  • $\begingroup$ Or even transforming these acc data to position according to kinematic equations, and after that introducing them on Javascript. $\endgroup$ – Maria D. Jan 2 at 16:53
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    $\begingroup$ Thank you so much for your help. I will read books on inertial navigation systems in order to understand this subject deeply . $\endgroup$ – Maria D. Jan 2 at 18:01

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