Infrared small target detection is an important and core problem in infrared search and track systems. Many infrared small target detection methods work well under the premise of a static background; however, the detection effect decreases seriously when the background changes dynamically. In addition, the spatiotemporal information of the target and background of the image sequence are not fully developed and utilized, lacking long-term temporal characteristics. To solve these problems, a novel long-term spatial–temporal tensor (LSTT) model is proposed in this paper. The image registration technique is employed to realize the matching between frames. By directly superimposing the aligned images, the spatiotemporal features of the resulting tensor are not damaged or reduced. From the perspective of the horizontal slice of this tensor, it is found that the background component has similarity in the time dimension and correlation in the space dimension, which is more consistent with the prerequisite of low rank, while the target component is sparse. Therefore, we transform the problem of infrared detection of a small moving target into a low-rank sparse decomposition problem of new tensors composed of several continuous horizontal slices of the aligned image tensor. The low rank of the background is constrained by the partial tubal nuclear norm (PTNN), and the tensor decomposition problem is quickly solved using the alternating-direction method of multipliers (ADMM). Our experimental results demonstrate that the proposed LSTT method can effectively detect small moving targets against a dynamic background. Compared with other benchmark methods, the new method has better performance in terms of detection efficiency and accuracy. In particular, the new LSTT method can extract the spatiotemporal information of more frames in a longer time domain and obtain a higher detection rate.

This study focuses on the key challenges in detecting and estimating motion parameters of ground maneuvering targets for airborne radar sensors. The complex unknown motion states of the ground maneuvering target, including velocity, acceleration, and jerk, result in range migrations (RMs) and Doppler frequency migrations (DFMs). These effects severely degrade the long-time coherent accumulation performance of the airborne radar, thereby limiting the reliable detection and precise parameter estimation of maneuvering targets. To address this issue, a new detection and motion parameter estimation method based on the range frequency reversal transform (RFRT) and searching Lv’s distribution (SLVD), i.e., RFRT-SLVD, is proposed. Specifically, the third-order RM (TRM) and quadratic DFM (QDFM) are considered. The proposed method operates as follows: First, RMs are eliminated simultaneously via the RFRT operation, which multiplies the echo by its reversed data in the range frequency and slow-time domains, leveraging the symmetric equal-interval sampling property of the range frequency. Subsequently, a phase compensation function (PCF) related to the jerk is constructed to compensate the QDFM. Finally, the LVD is performed to remove residual DFMs and achieve effective signal energy accumulation. Additionally, the case of a fast-moving target with Doppler ambiguity is analyzed, and a method for estimating three motion parameters is provided. A key advantage of the proposed technique is its ability to directly compensate the RMs without requiring prior knowledge of the maneuvering target, while also avoiding the blind speed sidelobe (BSSL) effect. In comparison with existing algorithms, RFRT-SLVD achieves a balanced trade-off between parameter estimation performance and computational efficiency. Numerical analyses and experiments are conducted to validate the method, assessing its detection capability for ground maneuvering targets, Doppler ambiguity resolution in parameter estimation, computational complexity, and method applicability in multi-target scenarios.