TABLE OF CONTENTS In this section we track the same fighter-bomber on a ground-strafing mission. In the previous section we wrote the state equation in CCS coordinates. For the present demonstration we write the state equation in LOS coordinates.
The state equations are
The state equation in a vector-matrix form is
where n ar, n a?, and n a? are random acceleration noise in range, azimuth, and elevation angle, respectively. The state equation in a more compact vector-matrix form is
and the corresponding measurement equation is
where n r, n ?, and n ? are the measurement errors in range, azimuth, and elevation angle respectively. The measurement error covariance matrix R k is given by
where E {n i n j} = 0, when i ? j, uncorrelated noise.
The variance in range, azimuth, and elevation angle are taken to be identical to those in the previous program, KAL_MIG.CPP. They are
We note that matrix R k is time-invariant. The elements of the corresponding matrix in CCS coordinates are lengthy trigonometric expressions through a Jaco-bian transform. We have lightened the computation loads in the present example. (Trigonometric computation is a lengthy sum of power series expansions.)
The state error covariance matrix Q k is given by
where E{n 2 ar} = ? 2 ar, E{n 2 a?} = ? 2 a?, E{n 2 2?} = ? 2 a ?
In...
