The symmetric autocorrelation function (SAF) has a huge computational complexity, which may limit the practical application of SAF-based scaled inverse Fourier transform (SCIFT). Taking the relationship between SAF and summation into consideration, a frequency-domain method is proposed for the fast implementation of the SCIFT, and the energy integration performance remains unchanged. Mathematic analysis and numerical simulations are provided to illustrate the efficiency of this method.

The multivariate range function of the high-speed maneuvering target induces modulations on both the envelop and phase, i.e., the range cell migration (RCM) and Doppler frequency migration (DFM) which degrade the long-time coherent integration used for detection and localization. To solve this problem, many long-time coherent integration methods have been proposed. Based on mechanisms of typical methods, this paper names two signal processing modes, i.e., processing unification (PU) mode and processing separation (PS) mode, and presents their general forms. Thereafter, based on the principle of the PS mode, a novel long-time coherent integration method, known as the generalized dechirp-keystone transform (GDKT), is proposed for radar high-speed maneuvering target detection and localization. The computational cost, energy integration, peak-to-sidelobe level (PSL), resolution, and anti-noise performance of the GDKT are analyzed and compared with those of the maximum likelihood estimation (MLE) method and keystone transform-dechirp (KTD) method. With mathematical analyses and numerical simulations, we validate two main superiorities of the GDKT, including (1) the statistically optimal anti-noise performance, and (2) the low computational cost. The real radar data is also used to validate the GDKT. It is worthwhile noting that, based on closed analytical formulae of the MLE method, KTD method, and GDKT, several doubts in radar high-speed maneuvering target detection and localization are mathematically interpreted, such as the blind speed sidelobe (BSSL) and the relationship between the PU and PS modes.

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High speed of the hypersonic vehicle can cause the noticeable scale effect and intra-pulse Doppler on radar echoes, especially under the large time-bandwidth product transmitting signal. Under this condition, the conventional narrowband matched filter can introduce an obvious output signal-tonoise ratio loss to the radar target detection and big errors to motion parameter estimation. In addition, the long-time integration and high speed can lead to the across range unit, which further deteriorates the detection performance and motion parameter estimation. In order to address these problems, we first mathematically analyze the wideband radar echo model (because the narrowband condition is not met for hypersonic vehicle detection) and obtain the mathematic relationship among the scale effect, speed, and time-bandwidth product. Thereafter, based on this mathematic relationship, we define a generalized matched filter and propose a coherent long-time integration algorithm for the hypersonic vehicle detection. Compared with the full parameter space searching algorithm, this proposed algorithm obtains nearly the same anti-noise performance with a much lower computational complexity. Through mathematical analyses and numerical simulations, we verify the effectiveness of the proposed algorithm. It is worthwhile noting that the aforementioned mathematic relationship provides a theoretical basis for the transformation from the wideband radar echo model to the conventional narrowband radar echo model. On this basis, the hypersonic vehicle detection algorithm can be studied widely. INDEX TERMS Hypersonic vehicle, scale effect, coherent integration, across range unit.

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