Estimation methods and filtering techniques are nowadays an integral part of any computer-based navigation system. The purpose of these techniques is to provide an estimate of required variables which is sufficiently accurate for real-time command and control purposes. Repeatability, which is important for so many applications, is deemed to be a by-product of the estimation process. For this requirement it is not strictly necessary for the process to be accurate, it is sufficient if it is only consistent; these are closely linked but one does not imply the other. The modern approach is to minimize the variance of the noisy observations or the sum of the squares of the residuals, and the methods available for doing this are increasingly refined. The impression given in the literature (and it is extensive) is that data processing can somehow compensate for the shortcomings of the basic sensors with respect to the operation being considered. Within certain limits this is true, but the real reason for the sudden surge of Kalman filtering for real-time on-line applications was the relative simplicity of the computational process. In a way, Kalman filtering has done for estimation theory what the Fast Fourier Transform has done for spectral analysis.

The concept is simple enough to state. It consists of combining two independent estimates of a variable to form a weighted mean. One of these estimates is a forecast and the other is the current measurement.