2526 The GNU Octave and Matlab code used to calculate the noise covariance matrices using the ALS technique is available online using the GNU General Public License. The CPU was built from ICs [. Grewaland A.
As you can see, the estimated value converges toward the true value. the difference between the current a priori prediction and the current observation information, is multiplied by the optimal Kalman gain and combined with the previous state estimate to refine the state estimate. 111 — 123 .
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Zhou, Stochastic Controls, Hamiltonian Systems and HJB Equations, Springer, New York, 1999.
Until now, we’ve dealt with one dimensional processes, like estimating the liquid temperature. Ma , Pathwise stochastic this link problems and stochastic HJB equations , SIAM J. The uncertainties are much more significant for an aircraft due to possible aircraft maneuvers.
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A. R. e. Additionally, the cross covariance matrix is also needed
The Kalman gain is
The updated mean and covariance estimates are
When the observation model
p
(
z
k
x
k
)
{\displaystyle p(\mathbf {z} _{k}\mid \mathbf {x} _{k})}
is highly non-linear and/or non-Gaussian, it may prove advantageous to apply Bayes’ rule and estimate
where
p
(
k
z
k
)
N
(
g
(
z
k
)
,
Q
(
z
k
)
)
{\displaystyle p(\mathbf {x} _{k}\mid \mathbf {z} _{k})\approx {\mathcal {N}}(g(\mathbf {z} _{k}),Q(\mathbf {z} _{k}))}
for nonlinear functions
g
,
Q
{\displaystyle g,Q}
.
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.