Table 3 Some notations defined in the proposed FOSB-based tracking scheme

○

Variable node

■

Factor node

${\mathbf{x}}_{k+1|k}{}^{\underset{¯}{\underset{¯}{△}}}{\tilde{\mathbf{x}}}_{k+1}$

One-step prediction

${\mathbf{x}}_{k|k}{}^{\underset{¯}{\underset{¯}{△}}}{\widehat{\mathbf{x}}}_k$

Best estimation

${\mathbf{x}}_{k|k+1}{}^{\underset{¯}{\underset{¯}{△}}}{\stackrel{⌣}{\mathbf{x}}}_k$

One-step fixed-lag smoothing

s _k

Speed estimation

x _k

Location estimation

z _k

Location observation

f

Speed transition PDF

f _k

Local speed transition PDF

g

Location transition PDF

g _k

Local location transition PDF

h

Location observation PDF

h _k

Local location observation PDF

l

Refined speed observation PDF

l _k

Local refined speed observation PDF

μ _x→f (x)

Message from variable node x to factor node f

μ _f→x (x)

Message from factor node f to variable node x

The mean of ${\mu }_{s_k\to f_{k+1}}\left(s_k\right)$

Result of speed estimation at the k^th state

The mean of ${\mu }_{x_k\to g_{k+1}}\left(x_k\right)$

Result of location estimation at the k^th state