Estimation of Measurement Errors in Radar Trajectories Using the Least Squares Method

Abstract Radar systems are widely used for the detection and tracking of moving objects such as aircraft, missiles, and other airborne targets. Accurate determination of object coordinates is a key task in radar tracking systems, since the reliability of trajectory analysis and further decision-making depends on the precision of these measurements. However, radar measurements are affected by random errors caused by noise, signal fluctuations, propagation conditions, and system limitations. Therefore, the statistical estimation of measurement errors is an important problem in radar data processing. The purpose of this study is to estimate the root mean square errors of radar coordinate measurements using statistical processing of trajectory data. The research focuses on the analysis of measurement deviations obtained from radar observations and on the application of mathematical methods for improving the accuracy of trajectory representation. The proposed approach is based on the approximation of measured radar trajectories using the least squares method. Polynomial functions are used to approximate the observed trajectory of a moving object, allowing the deterministic component of motion to be separated from random measurement deviations. The coefficients of the approximating polynomial are determined using the least squares technique, and the residual deviations between the measured data and the approximated trajectory are analyzed as random errors. Statistical methods are then applied to estimate the mean values, variances, and confidence intervals of these errors. The obtained results show that trajectory approximation allows effective smoothing of measurement noise and provides reliable estimates of coordinate measurement errors. The proposed method can be used for statistical analysis of radar tracking data and for evaluating the accuracy of radar measurement systems.