Digital Signal Processing Reference
In-Depth Information
−0.4
80
70
−0.3
−0.2
60
−0.1
50
0
40
0.1
30
0.2
20
0.3
10
0.4
0
0.5
14
28
42
56
70
84
98
112
126
140
distance/km
Fig. 8.9
Median spectra of real radar data
Fig. 8.10
Real detection by
16
median
Target 1
Target 3
14
Target 4
Target 2
12
10
8
6
4
2
10
36
62
88
114
140
distance/km
8.7 Conclusions
In this article, we considered the medians of a probability measure in a Riemannian
manifold. Firstly, the existence and uniqueness results of local medians are given. In
order to compute medians in practical cases, we also proposed a subgradient algo-
rithm with convergence result. After that, Fréchet medians are considered. We gave
their statistical consistency and some quantitative estimations of their robustness.
Moreover, we showed that in compact Riemannian manifolds the Fréchet medians of
generic data points are always unique. Some stochastic and deterministic algorithms
are proposed for computing Riemannian
p
-means, simulations of these algorithms
are also given. Finally, by using Riemannian median and the information geome-
try of covariance matrices, we developed a new geometric method for radar target
