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Radar high-resolution range profile (HRRP) is very sensitive to time-shift and target-aspect variation; therefore, HRRP-based radar automatic target recognition (RATR) requires efficient time-shift invariant features and robust feature templates. Although higher order spectra are a set of well-known time-shift invariant features, direct use of them (except for power spectrum) is impractical due to their complexity. A method for calculating the Euclidean distance in higher order spectra feature space is proposed in this paper, which avoids calculating the higher order spectra, effectively reducing the computation complexity and storage requirement. Moreover, according to the widely used scattering center model, theoretical analysis and experimental results in this paper show that the feature vector extracted from the average profile in a small target-aspect sector has better generalization performance than the average feature vector in the same sector when both of them are used as feature templates in HRRP-based RATR. The proposed Euclidean distance calculation method and average profile-based template database are applied to two classification algorithms [the template matching method (TMM) and the radial basis function network (RBFN)] to evaluate the recognition performances of higher order spectra features. Experimental results for measured data show that the power spectrum has the best recognition performance among higher order spectra.