Determining travel distance with an accelerometer

[DSG]

I would like to accurately determine an absolute travel distance (forward and reverse) from a starting point using a 3-axis accelerometer (less than 1 km total linear distance). I have tried web searches and can find lots of devices and descriptions on how the devices work but very little on the actual algorithms. I know how to use vectors to calculate a distance from the x & y axis as well as calculating velocity from acceleration, but I can find nothing that describes how to correct for tilt.

Is there a resource somewhere where I can read up on this?

Note that I am not interested in GPS; I would like something more accurate without having to hassle with DGPS.

 

[Leftyretro]

I would like to accurately determine an absolute travel distance (forward and reverse) from a starting point using a 3-axis accelerometer (less than 1 km total linear distance). I have tried web searches and can find lots of devices and descriptions on how the devices work but very little on the actual algorithms. I know how to use vectors to calculate a distance from the x & y axis as well as calculating velocity from acceleration, but I can find nothing that describes how to correct for tilt.

Is there a resource somewhere where I can read up on this?

Note that I am not interested in GPS; I would like something more accurate without having to hassle with DGPS.

I believe you are dealing with the basics of inertial navigation. I seem to recall a double integration is required from the basic accelerometer sensors. Anyway try googling on inertial navigation and see if you can come up with some fundamental algorithms or explanations.

Many years ago I read a book about the development of gyros and inertial navigation developed at MIT for the cold war missile programs. It was quite a good read and did go into some detail, but I can't for the life of me recall the title or author.

Lefty

 

[Papabravo]

How exactly do you think that rotation about any of the three axes (pitch, roll or yaw) is going to affect distance in either a relative sense or an absolute sense. Any rotation about a body axis has no effect on the center of mass unless the center of rotation is in a different place than the center of mass. Is that the case?

Are you asking how one could derive angular accelerations, velocities, and displacements from the 3-axis outputs? The answer starts with knowing the relationship between the center of rotation and the center of mass.

Here's a clue:
Linear accelerations change rapidly in magnitude and slowly in direction.
Angular accelerations have two components, radial and tangential. They change rapidly in direction and slowly in magnitude.

 

[DSG]

Lefty,
I did a search as you suggested and found lots of information, but it described absolute positioning and included lots of complex math using pitch, roll, and yaw. This is not what I was needing. I only need a linear travel distance.

I wanted to use the x and y axis to determine travel distance (use of the y-axis is in case the unit was not perfectly square with the x-axis and so I can use vector calculations). This, I think I can handle. I also understand if the device were not level, it would induce a fair amount of error in the x and y acceleration measurement. This is where I need some help with the corrections.

 

[Boncuk]

Hi DGS,

using X and Y values and thereby ignoring the z value will cause fairly great errors.

The inertial navagation platforms use a gyro controlled full kardanic suspension system to align the platform always parallel with the horizon, which takes care of tilt.

This is especially important in air navigation because airplanes never fly at a constant altitude, but at a constant barometric pressure level which changes in true altitude continously thereby changing the pitch angle and hence tilt about all three axis.

For zero error construct such a platform with two gyros. Cage the gyros during spin-up and release them for navigation. (Lots of mechanical works though) Salvaged parts of a HDD drive make good gyros. The platform should be mounted in the center of gravity.

The rest is just a matter of triangulation for which I suggest an artificial grid system.

Boncuk

P.S. May be you can get an LN3-platform from the outdated McDonnell-Douglas F4 (Phantom), a phantastic device. Maximum error from Hannover (Germany) to Goose Bay (New Foundland) 2NM!