As an introduction to the capabilities of the INS Toolbox, consider a simplified three-dimensional INS simulation. The toolbox function PROGEN generates three-dimensional flight profiles in a locally level coordinate system. The toolbox functions GENDV and GENDTHET take the output of PROGEN and generate ideal, error-free delta-V’s and delta-theta’s (note that these are the components due to vehicle motion relative to the local-level coordinate frame only. Earth rotation and Coriolis effects are handled separately. See the sections on sensor error simulations and great circle path simulations: Error-Free and with Sensor Errors).

insdem02bThe inertial processing of the “measurements” first involves initializing position, velocity and attitude. For the moment we will assume that the initialization has been accomplished without error. The next steps (which are performed for each measurement epoch) involve 1) using the toolbox function BODUPDAT to update the body-to-nav direction cosine matrix (attitude representation); 2) using the updated direction cosine matrix to translate the delta-V’s from the body-frame to the local-level frame; 3) accumulating the translated delta-V’s to update velocity and 4) integrating velocity to update position.

A demo program which performs the aforementioned tasks is provided with the toolbox. On a global scale, the result of the inertial processing is virtually identical to the original flight profile. There are errors, however, due to imperfect integration. The errors are small but measurable:

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insdem03It is apparent from the plot that multiple sampling rates were employed. Staight segments do not need to be sampled as often as turns and other dynamics and the toolbox supports multi-rate simulations. Another example given in the toolbox is a repeat of the above example but with time steps cut in half. The results, as expected, are better: