Abstract
<jats:p>The article proposes an integrated approach to modeling the initial stage of tracking air targets in radar systems based on a combination of a probabilistic-temporal model of the GERT type and a recursive state estimation procedure using the Kalman filter. At the macro level, the process of interaction "radar-tracked object" is described by an exponential GERT network using moment generating functions, which allows analytically forming an equivalent W-function, determining the distribution and probability density functions of the interaction time, as well as taking into account multivariate transition trajectories, returns to previous states, and detection confirmation delays. It is shown that the GERT model effectively reproduces global temporal-probabilistic regularities of the process, but does not provide recursive correction of coordinates and velocities estimates in real time and minimization of the mean square error. To overcome these limitations, it is proposed to integrate the Kalman filter as a micro-level tool for trajectory estimation. A discrete linear stochastic model in the state space is formulated, a two-step recursion "prediction-correction", principles of selection of motion models (CV, CA, CT), structures of noise covariance matrices and tuning procedures based on RMSE and NEES criteria are presented. It is shown that the time characteristics obtained from GERT can be used to initialize the initial state and covariances, as well as for adaptive tuning of the sampling step and process noise parameters. The modeling results demonstrate the complementarity of the approaches: GERT forms a structural-probabilistic framework of the tracking process, while the Kalman filter provides smoothing of measurements, reduction of the spread of estimates and a significant reduction of RMSE compared to the macro-level estimate. The proposed integration framework "GERT → Kalman" creates a methodological basis for building a comprehensive model of goal tracking in a cluttered environment, combining the analysis of the temporal-probabilistic structure of the process with highly accurate recursive real-time state estimation.</jats:p>