Tuesday, February 10, 2015

Kalman-Bucy filtering

A great introduction to the derivation and application:

http://www.academia.edu/1512888/Introduction_to_the_Kalman_Filter_and_its_Derivation

Related Math:

http://math.stackexchange.com/questions/622195/taking-a-derivative-with-respect-to-a-matrix


EMD and Hilbert-Huang Transform

Original Paper:

http://tec.earth.sinica.edu.tw/research/report/paper/20070711HHT.pdf

A related gait study using emd applied to gyroscope data:

"Integration of Human Walking Gyroscopic Data Using Empirical Mode Decomposition" http://www.mdpi.com/1424-8220/14/1/370


A comparison of EMD and Wavelets (and the fusion of both) in data analysis:

http://www.arpapress.com/volumes/vol11issue3/ijrras_11_3_16.pdf


Madgwick and Mahoney Filter

Madgwick Filter

http://www.x-io.co.uk/res/doc/madgwick_internal_report.pdf

Mahoney Filter in the context of modern filtering approaches

http://arxiv.org/pdf/1110.0274.pdf

Mahoney's complete filter:

https://hal-unice.archives-ouvertes.fr/hal-00488376/document


Quaternion (Background) and interpolation

This is a good source on the basics of quaternion math and interpolation:

http://www.geometrictools.com/Documentation/Quaternions.pdf

An interesting paper on "Spherical Averages and Applications to Spherical Splines and Interpolation"

http://www.math.ucsd.edu/~sbuss/ResearchWeb/spheremean/paper.pdf

Wavelets (Background)

Overview and general approach:

http://www.eecis.udel.edu/~amer/CISC651/IEEEwavelet.pdf

For in-depth treatment of wavelets, I have checked out the following book from ksl and have made significant progress:

Computational signal processing with wavelets



ROS and UbuntuARM links

In order to install UbuntuARM on the Beaglebone Black we hope to use for recording, I have found several helpful links to decide: which version of UbuntuARM to use, which versions UbuntuARM are compatible with which versions of ROS, and lastly some already made nodes to record from the MPU 6050.

http://beagleboard.org/getting-started
https://github.com/ggallin08/crwucutter_core_bbb
http://wiki.ros.org/indigo/Installation/UbuntuARM
http://wiki.ros.org/hydro/Installation/UbuntuARM