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

Figure 8

Histogram of distribution of deduced from the EnKF (and valid here for PF due to the equivalence in the Gaussian setting) (i.e., ) compared to the one of for an ensemble size of samples. The maximum expected distance of is the vertical segment in solid line. The minimum expected distance of is the vertical segment in dashed line. The results are represented for the different length-scale values: (a)  km, (b)  km, (c)  km, and (d)  km, for the dimension set to .

(a)

(b)

(c)

(d)