Inertial Navigation System Modeling

Abstract

Modeling requires representing real world phenomena by mathematical language. To keep the problem tractable the goal is not to produce the most comprehensive descriptive model but to produce the simplest possible model which incorporates the major features of the phenomena of interest. The model is also restricted by the ability of mathematics to describe a phenomenon. This book deals with models which describe the motion of an object on or near the surface of the Earth. This kind of motion is greatly influenced by the geometry of the Earth. There are two broad categories for modeling motion: dynamic and kinematic.

Appendix A

Solving the equation of the form $\dot{y} = yx$

$$ \begin{aligned} & \dot{y} = yx \\ & \frac{dy}{dt} = yx \\ & \frac{dy}{y} = xdt \\ & \left. {\ln (y)} \right|_{{y_{k} }}^{{y_{k + 1} }} = \int {xdt} \\ & \ln (y_{k + 1} ) - \ln (y_{k} ) = \int {xdt} \\ & \ln \left( {\frac{{y_{k + 1} }}{{y_{k} }}} \right) = \int {xdt} \\ & \frac{{y_{k + 1} }}{{y_{k} }} = e^{{\int {xdt} }} \\ & y_{k + 1} = y_{k} e^{{\int {xdt} }} \\ \end{aligned} $$