# An Interactive Transient Model Correction Active Sonar Target Tracking Method
## 1 Introduction
Canada's [PERSON] has derived a robust EKF algorithm and applied it to underwater moving target tracking [24]. [PERSON] and others have proposed a novel particle filtering algorithm for underwater moving target tracking [25]. References [26, 27] proposed a composite filtering method that combines the robustness of particle filtering with the real-time performance of KF, effectively reducing tracking errors. Reference [28] studied the target localization and tracking method based on azimuth Doppler frequency deviation two-dimensional measurement information, which can achieve faster convergence and higher tracking accuracy compared with one-dimensional azimuth measurement information. [PERSON] et al. [29] discussed the application of the CKF algorithm based on the variance square root in torped target tracking, aiming at the problem that the covariance can become non-positive definite and cause filter instability or even divergence in high-dimensional systems using the UKF algorithm. [PERSON] et al. [30] studied underwater maneuvering target tracking based on the interactive multiple model (IMM). [PERSON] et al. [31] addressed the issue that the single-model KF cannot fully adapt to all motion states of underwater targets. They used the interactive multiple model KF method to process the ultra-short baseline tracking data of autonomous underwater vehicles (AUVs). The motion models enhance motion state adaptability through probability matrix transitions. The experimental results demonstrated that this algorithm has better state adaptability than the single-model KF algorithm when the multi-model set is reasonably constructed. [PERSON] et al. [32] combined EKF and UKF with the IMM algorithm for underwater target tracking. Their research suggests that under high measurement error conditions, the IMM-UKF algorithm has higher tracking accuracy than the IMM-EKF algorithm. In recent years, the algorithm based on depth learning and neural networks has been applied to underwater target tracking to solve model mismatches and other problems and improve tracking stability [33, 34, 35]. Due to the special nature of underwater target detection, such as submarines, there is a scarcity of statistical characteristics from known target data samples. As a result, solving the probability transition matrix poses one of the significant challenges, given that the Markov chain transition probability in the interactive multiple model tracking method relies on statistical analysis of these data. The selection of the set of maneuvering target motion models is another challenge: if the goal is to cover as many target motion modes as possible, the model set can become very large, and the model space approaches continuity, making the model set countably infinite, leading to a drastic increase in computational complexity and potential model competition, which can even worsen tracking performance. On the other hand, if there are fewer motion models in the model set, it can be difficult to cover all possible target motion modes, leading to insufficient tracking accuracy or even tracking divergence. Therefore, using a multi-model set to describe the motion of the target can, to some extent, overcome the limitations of the single model. However, the computational complexity of the multi-model approach is high, requiring a high level of prior information about the target, which leads to an increase in computational resources. This may not be suitable for some engineering applications. Additionally, when active sonar is used to detect underwater submarines that maneuver evasively, changes in target reflectivity and dynamics can cause periodic measurement values to be lost (i.e., periodic measurement information is not continuous), lead to a decrease in tracking performance and even loss of target tracking. To address the problem of active sonar tracking of underwater submarine targets, this study proposes a novel underwater maneuvering target tracking method based on transient correction using random mixing models.