Purpose
This routine computes the value of the
Student's t objective function.
Notation
The affine Kalman-Bucy smoother residual sum of squares is defined by
\[
\begin{array}{rcl}
S ( x_1 , \ldots , x_N ) & = & \sum_{k=1}^N S_k ( x_k , x_{k-1} ) \\
S_k ( x_k , x_{k-1} ) & = &
\frac{1}{2}
( z_k - h_k - H_k * x_k )^\R{T} * R_k^{-1} * ( z_k - h_k - H_k * x_k )
\\
& + &
\frac{1}{2}
( x_k - g_k - G_k * x_{k-1} )^\R{T} * Q_k^{-1} * ( x_k - g_k - G_k * x_{k-1} )
\\
\end{array}
\]
where the matrices R_k
and Q_k
are
symmetric positive definite and
x_0
is the constant zero.
x
The argument
x
is a two dimensional array,
for k = 1 , \ldots , N \[
x_k = x(:, k)
\]
and
x
has size n \times N
.
z
The argument
z
is a two dimensional array,
for k = 1 , \ldots , N \[
z_k = z(:, k)
\]
and
z
has size m \times N
.
g_fun
The argument
g_fun
is a function handle to the process model.
h_fun
The argument
h_fun
is a function handle to the measurement
model.
qinv
The argument
qinv
is a three dimensional array,
for k = 1 , \ldots , N \[
Q_k^{-1} = qinv(:,:, k)
\]
and
qinv
has size n \times n \times N
.
rinv
The argument
rinv
is a three dimensional array,
for k = 1 , \ldots , N \[
R_k^{-1} = rinv(:,:, k)
\]
and
rinv
has size m \times m \times N
.
obj
The result
obj
is a scalar given by
\[
obj = S ( x_1 , \ldots , x_N )
\]
Example
The file t_obj_ok.m
contains an example and test of
ckbs_t_obj.
It returns true if ckbs_t_obj passes the test
and false otherwise.
Input File: src/ckbs_t_obj.m
