What will be the best approach to get the most localization accuracy out of only an accelerometer and gyroscope?
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$\begingroup$ Some time ago I read a paper on tracking pedestrians using only shoe-mounted inertial sensors. I can't find it right now, but research in that direction might turn up a few sets of results... $\endgroup$ – Andy Jan 20 '16 at 7:21
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$\begingroup$ dont know about localization. but for both sensor accuracy try to implement a filter to the sensor reading. kalman filter/complimentary filter work best i think.. $\endgroup$ – kai1709 Jan 20 '16 at 8:07
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$\begingroup$ This question has been asked many times on Robotics StackExchange. Most recently: robotics.stackexchange.com/questions/8857/… . $\endgroup$ – Gouda Jan 20 '16 at 9:30
I believe internal sensors such as those are impossible for localization. Navigation from a known location is possible with common methods of inertial navigation. These methods are limited by the accuracy of the sensors and external observations.
This is similar to this question: imu position without GPS or camera
The short answer is that what you ask is not possible given realistic constraints.