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In comparison with radars, that have a single receiving channel, monopulse systems with their sum and difference channels can accurately estimate not only the signal power and angular position of a target but its angular extent as well. This virtue can be used to facilitate target recognition, classification, and tracking. When an extended target is observed with a monopulse radar and the mutual position of the radar antenna and the target does not significantly change in time, the maximum-likelihood (ML)-estimates of the aforementioned parameters were derived by L. B. Milstein in . If the target moves and the monopulse radar runs in the tracking (continuous or track-while-scan) mode these estimates become inaccurate because amplitudes of signals from the scatterers composing an extended target vary due to the antenna boresight deviations in the vicinity of the target angular position. The presented article is devoted to the synthesis and analysis of algorithms of the joint estimation of the target signal power, angular position and extent in a monopulse radar run in the tracking mode and it is impossible to neglect the antenna boresight deviations. The ML estimates are derived here under the assumption that the sum and difference antenna patterns can be approximated within the antenna beamwidth with the trigonometric functions. Statistical analysis of the estimates is performed and the probability distributions, mean values, and variances are determined.