On Visualisation of Linear Estimation and Fusion: From Equations to Ellipses

Visualisation of mathematical objects often leads to faster and easier comprehension of theories. On the other hand, deriving conclusions exclusively from a graphical interpretation can be misleading. A typical case in estimation is an ellipse, which corresponds to contour lines of a bivariate Gaussian density. This paper combines insights from various areas. Algebraic relations are presented first, geometric objects are shown subsequently. Constructions of ellipses by determining radii and positions of tangent lines are discussed. The stress is laid on exposition of linear estimation with a focus on methodology of fusion of estimates, especially in the case when cross-correlations of estimation errors are not fully known. The exposition also covers multidimensional variables, where the ellipses become ellipsoids.