The first step in building a model is choosing its State vector.
This vector contains the parameters that you wish to determine.
It should also contain other parameters that control the structure of the system.
To be specific, the non-random part of the measurement values
and the non-random change of the State vector from one time point to the next.
For time indices
k = 1 to
k = nk,
the corresponding state vector value is denoted by
/ x(1) \
| k . |
x = | . |
k | . |
| x(nx) |
\ k /
nx is the number of elements in the state vector.
The filter in EXAMPLE.KBF
determines the position of a ship on the ocean given range measurements
to two shore stations.
The first two elements of the State vector are the east and north position
of the ship relative to a reference point on land.
The State vector also contains the east and north velocities components.
/ x(1) \ /east component of ships location at time index k\
| k | | |
| x(2) | |east component of ships location at time index k|
x = | k | = | |
k | x(3) | |east component of ships location at time index k|
| k | | |
| x(4) | |east component of ships location at time index k|
\ k / \ /