From the Kalman Filter to the Particle Filter: A Geometrical Perspective of the Curse of Dimensionality

Figure 11

Histogram of , the cosine of the angle between the analysis increment and the background samples deduced from the EnKF (and valid here for the PF due to the equivalence in the Gaussian setting), for the various length-scales (a)  km, (b)  km, (c)  km, and (d)  km, for the dimension set to .

(a)

(b)

(c)

(d)