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Table 1 Huber, Cauchy and OLS loss and weight functions

From: Robust error estimation based on factor-graph models for non-line-of-sight localization

Method

Huber’s t

Cauchy

OLS

Weight

\(\tau _i= \left\{ \begin{array}{cc} 1.0 &{} \text {if } |z_i|\le a_H \\ a_H/|z_i| &{} \text {if } |z_i|> a_H\end{array}\right.\)

\(\tau _i=1/(1+(z_i/a_C)^2)\)

\(\tau _i=1\)

Loss fnc

\(\rho _i= \left\{ \begin{array}{cc} 1/2 z_i^2 &{} \text {if } |z_i|\le a_H \\ |z_i|a_H-1/2a_H^2 &{} \text {if } |z_i|> a_H\end{array}\right.\)

\((a_C^2/2)\log (1+(z_i/a_C)^2)\)

\(1/2 z_i^2\)

Parameter

\(a_H\)

\(a_C\)

NA