## 1 Introduction  
Synthetic aperture radar (SAR) has the advantage of all-day, all-weather, high-resolution and large-scale observation. These characteristics have made SAR become an important means of battlefield surveillance and reconnaissance [1, 2, 3, 4]. In various military applications, SAR automatic target recognition (ATR) has attracted more and more attention from scholars. With the development of machine learning, various SAR ATR methods have been proposed, including traditional methods [5, 6] and deep-learning-based methods [7, 8]. There methods generally use a batch training strategy to learn all training data. After obtaining the feature extractors and classifiers, the performances of these methods are verified on the test data. Experimental results show that they have high recognition accuracy; for example, the accuracy on MSTAR dataset can easily exceed 99% [9, 10]. Nevertheless, the aforementioned methods suffer from substantial limitations. Specifically, the batch learning strategy is only applicable to situations where the training dataset remains constant. In real-world battlefield settings, acquiring all training data simultaneously is often unfeasible. Upon the acquisition of new training data, it becomes necessary to merge the existing and new training samples and then retrain the SAR ATR model using the combined dataset. This process demands a significant amount of time and computational resources, imposing a heavy burden on the update of the SAR ATR system. Consequently, substituting the batch learning strategy with incremental learning is imperative for the swift updating of the SAR ATR system. Incremental learning, also referred to as continuous or lifelong learning, was initially introduced by [PERSON] et al. in 1962 [11]. It enables a system to continuously assimilate new knowledge from incoming data while retaining the majority of previously acquired knowledge. The significance of incremental learning is manifested in two key aspects [12; 13; 14]:  
(1) In real-world applications, data is typically acquired incrementally; thus, upon encountering novel data, a pre-trained system must undergo adjustments to incorporate the knowledge embedded within the new data. (2) Modifying an existing trained system generally incurs lower time and computational costs compared to retraining the system from scratch. Evidently, incremental learning represents a progressive process of accumulation and updating, closely resembling the human learning paradigm. Evidently, incremental learning constitutes a process of progressive accumulation and iterative refinement, closely mirroring the cognitive learning mechanism inherent in human beings. As shown in Figure 1, incremental learning can update the SAR ATR system at a very low cost. As far as we know, many scholars have carried out works on incremental SAR ATR. For instance, [PERSON] et al. introduced the class boundary selection-based incremental learning (CBsIL). This method preserves prior recognition capabilities by selectively safeguarding class boundary exemplars as new classes are incrementally added [15]. Subsequently, [PERSON] et al. enhanced the incremental nonnegative matrix factorization (INMF) by incorporating sparse constraints, resulting in a modified version denoted as \(L_{p}-INMF\). Compared to the original INMF, \(L_{p}-INMF\), an improved variant, exhibits superior recognition performance [16]. [PERSON] et al. developed the high plastic error correction incremental learning (HPecIL), leveraging models trained on previous tasks to rectify cumulative errors and mitigate model degradation [17]. Meanwhile, [PERSON] et al. proposed a class-incremental synthetic aperture radar (SAR) automatic target recognition (ATR) method. Grounded in a continuous teacher-student learning framework, this deep learning approach effectively alleviates catastrophic forgetting [18] in neural networks [19]. [PERSON] et al. presented POSELM, an optimized version of the extreme learning machine (ELM).