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The inverse synthetic aperture LiDAR (ISAL) system demonstrates excellent performance in various application scenarios, including long-range target imaging and recognition. However, due to the micrometer scale of the ISAL system carrier, compensating for the motion error of high-speed complex motion targets becomes challenging. Linear frequency modulation (LFM) signals are not enough to describe these targets accurately, as they can be better represented by high-order polynomial phase signals. Nevertheless, the presence of second-order and higher phase components can greatly affect the coherent synthesis between pulses. To tackle this issue, we propose a non-searching fast cubic phase signal estimation algorithm based on the fourth-order instantaneous autocorrelation function. This algorithm aims to estimate the second-order and third-order coefficients of the rotational error signals using the non-uniform Fourier transform. By accounting for advection compensation, we model the phase of the signal of the complex motion target as the third-order form of the slow time. The Fourier transform of the fourth-order instantaneous autocorrelation function presents challenges, such as the nonlinear coupling between the slow time and delay time, as well as the nonuniform sampling of the delay time. We suggest utilizing the nonuniform Fourier transform to complete the two-dimensional transformation and estimate the obtained second-order and third-order coefficients. In comparison to the traditional range doppler (RD) algorithm, our proposed algorithm achieves better image point focusing and enhances the energy aggregation of scattering points by approximately four times. Simulation results validate the effectiveness of this algorithm.
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