LV2 Inertial Navigation Numerical Integration Methods

Numerical integration methods are used to approximate the definite integral of a function. Various methods exist such as the Midpoint, Trapezoidal and Simpson Rules. The different methods that exist tend to offer a tradeoff between simplicity and accuracy. Simpson’s method is the most accurate of the aforementioned methods and is used in the LV2 INS calculations. Simpson’s method is one that assumes that the samples used in the calculation are evenly spaced over the desired interval. More complicated methods exist, that offer greater accuracy I might add, that allow for unequally spaced samples over the desired interval. Using A/D converters for sampling continuous signals usually implies evenly spaced samples and so most numerical integration methods used in an engineering application, such as inertial navigation, will employ a fixed step size as opposed to a variable step size. The methods used approximate the values of velocity and position by integrating over sets of intervals. For example, the present time velocity can be approximated using the summation of the results of integration.