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[
obj] = ckbs_sumsq_obj(
x,
z,
g,
h,
dg,
dh,
qinv,
rinv)
\[
\begin{array}{rcl}
S ( x_1 , \ldots , x_N ) & = & \sum_{k=1}^N S_k ( x_k , x_{k-1} ) \\
S_k ( x_k , x_{k-1} ) & = &
\frac{1}{2}
( z_k - h_k - H_k * x_k )^\T * R_k^{-1} * ( z_k - h_k - H_k * x_k )
\\
& + &
\frac{1}{2}
( x_k - g_k - G_k * x_{k-1} )^\T * Q_k^{-1} * ( x_k - g_k - G_k * x_{k-1} )
\\
\end{array}
\]
where the matrices
R_k
and
Q_k
are
symmetric positive definite and
x_0
is the constant zero.
k = 1 , \ldots , N
\[
x_k = x(:, k)
\]
and x has size
n \times N
.
k = 1 , \ldots , N
\[
z_k = z(:, k)
\]
and z has size
m \times N
.
k = 1 , \ldots , N
\[
g_k = g(:, k)
\]
and g has size
n \times N
.
k = 1 , \ldots , N
\[
h_k = h(:, k)
\]
and h has size
m \times N
.
k = 1 , \ldots , N
\[
G_k = dg(:,:,k)
\]
and dg has size
n \times n \times N
.
k = 1 , \ldots , N
\[
H_k = dh(:,:,k)
\]
and dh has size
m \times n \times N
.
k = 1 , \ldots , N
\[
Q_k^{-1} = qinv(:,:, k)
\]
and qinv has size
n \times n \times N
.
k = 1 , \ldots , N
\[
R_k^{-1} = rinv(:,:, k)
\]
and rinv has size
m \times m \times N
.
\[
obj = S ( x_1 , \ldots , x_N )
\]
ckbs_sumsq_obj
.
It returns true if ckbs_sumsq_obj
passes the test
and false otherwise.