TABLE OF CONTENTS In this section we design a Kalman filter for a short-range air defense radar. The radar tracks a hostile fighter-bomber on a ground attack mission. The trajectory is a typical "turn-dive-and-turn-climb" maneuver (Figure 8.17). The tracking radar is located at the origin of the Cartesian coordinate system.
We write the state equation (aircraft position and motion) in CCS coordinates (x,y,z) as follows.
The above three simultaneous linear equations can be written in a vector-matrix form where n ax, n ay, and n az are the random acceleration noise in x, y, and z axes.
A more compact form is
The random acceleration noise covariance matrix Q k is given by
The random acceleration noise is assumed equal for three axes: n ax = n ay = n az, uncorrelated and uniformly distributed over 3.0 g.
The variance 
. The measurement equation in LOS coordinates system is
The measurement equation in a compact matrix form is
The measurement error covariance matrix R k in LOS is given by
On the other hand, the error covariance matrix R k in CCS is given by
Since the state equation is written in CCS coordinates and the measurement equation in LOS coordinates, we need a conversion formula between the two coordinates.
Figure 8.18 helps us to formulate the conversion between the Cartesian coordinates and...
