Probability and Expectancy
Mohinder S. Grewal, Angus P. Andrews · 2014
There are useful properties of certain statistical parameters of probability distributions that are the same for all probability distributions. One does not need to assume that the probability distribution is Gaussian or any other specific distribution. These properties are very useful in Kalman filtering, and this is the essential focus of this chapter. The purpose of the chapter is to develop the essential notation and theory behind probability distributions as needed for defining and understanding Kalman filtering, which uses probability distributions defined on n-dimensional real linear spaces or manifolds. The mathematical principles involved are generally applicable to more abstract settings. The chapter finally discusses the mathematical foundations, probability density functions, expectancy, moments, and optimal estimates, and the nonlinear effects, in detail.