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I have values for the variables (C, v, g, w at all sample points) but I do not know how to evaluate the integral. This equation is supposed to be implemented on a computer as part of a larger algorithm for navigation purposes. I have a feeling that the gyroscope sensor reading and or the accelerometer reading may be required to evaluate the integral but I am uncertain.

C is a 3x3 rotation matrix from subscript frame to superscript frame. Subscript and superscript n means the east north up frame.

m is the discrete point in time at the start of the data and k is the current discrete point in time.

v is a 1x3 vector of velocity, g is a 1x3 vector of gravity, w_ie_n is the 1x3 vector of Earth rate. X means the cross product. t refers to time.

The equation comes from the journal article:

A New Fast In-motion Coarse Alignment Method for GPS-aided Low-cost SINS (Yulong Huang, Yonggang Zhang)

How would I evaluate that integral?