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Abstract
Radars can detect useful and unuseful targets. Targets are usually declared by plots which contain plot positions (R,e) or (x,y), height and other identifiable information. Some of these plots are due to noise or ground clutter, clouds, rain, fog, and other undesired targets. Radar tracker is implemented to track only useful (intended) targets such as aircraft with certain speed and height. Therefore, the tracker usually improves radar picture and eliminates false plots. False plots are characterized by non-correlated parameters from one scan to another, but useful targets do such correlation. The study of hardware and software tracking of radar targets is undertaken. We focus on the monopulse tracking radar which compares the amplitudes and phases of all beam returns to sense the amount of target displacement off the tracking axis. Besides to the phased array antenna and microwave comparator circuitry, it includes three receiver channels declared as the sum channel, elevation angle difference channel, and azimuth angle difference channel. Software Implementation is easier and is popular than the hardware. Specifically, the Kalman filter as a linear estimator that minimizes the mean squared error as long as the target dynamics are modeled accurately. We analyzed other recursive filters such as a~. a~’Y for constant velocity and constant acceleration targets respectively. These filters are considered special cases of the general solution provided by the Kalman filter for the mean squared estimation problem. The position error of critically damped a~ filter for lazy/aggressive maneuvering targets in case of additive white noise is demonstrated to focus on its characteristics relevant to the transient capability and frequency response. Also we investigated the position, velocity, and acceleration errors of such filter for targets moving with non constant acceleration. The Kalman filter parameters are addressed including the gain coefficients and covariance matrix which facilitate its application to the maneuvering targets. The actual position and velocity of two dimensional moving targets are computed and compared with that obtained from the estimated ones in case of Cartesian and polar
coordinates. The measurement noises [v .•. (n1 vy(n)] are assumed to be mutually uncorrelated and zero mean white Gaussian with variances (0-;” 0-;9)’ The extended Kalman filter (EKF) equations using Taylor expansion and linear estimator with minimum mean square error are deduced, and applied to three dimensional target moving with constant velocity. The root mean square error is computed using the EKF algorithm. In addition, we addressed the improved kalman filter using the block, and sequential processes to cope with the problem of nonlinearity associated with the measurement equations. The error in position is demonstrated using the improved, extended, and unscented Kalman filters to benefit from their advantages in minimizing the errors resulting from the nonlinearity. The comparison of actual and predicted trajectories for three dimensional targets using the mentioned filters algorithms have been studied. Symmetrical measurement method (SME) based on proportional integral extended kalman filter algorithm is analyzed and applied to track three different targets using a single sensor. This multi target tracking has evoked great interest in recent years because of its application in both military and civilian areas such as ballistic missile defense, air defense, battlefield surveillance, ocean surveillance, air traffic control.