# An Interactive Transient Model Correction Active Sonar Target Tracking Method
## 1 Introduction  
Active sonar target tracking is based on the discrete point tracks of underwater moving targets detected by sonar. Through track correlation, state estimation and other filtering processing, random errors in the measurement process are suppressed, and the accuracy of target measurements is improved. This makes the target track smoother and allows more state information about the target to be obtained, such as course, speed, acceleration and other parameters. Active sonar target tracking belongs to the category of maneuvering target tracking. For maneuvering target tracking, researchers at home and abroad have mainly conducted a large amount of research work from three directions: maneuvering target motion model, filtering algorithm, and track management. Among them, the motion model and filtering algorithm are the core and key. In the 1970s, [PERSON] et al. [1] proposed the constant velocity (CV) model, and [PERSON] et al. [2] proposed the constant acceleration (CA) model. These two models belong to the most basic linear mathematical models and are mainly suitable for weakly maneuvering targets. In the context of nonlinear motion models, [PERSON] proposed a first-order time-correlated stochastic model with a zero mean of target maneuvering acceleration, known as the Singer model [3], which is suitable for target motion patterns that fall between CV and CA movements. [PERSON] et al. proposed a correlated Gaussian noise model with a random switch mean, known as the semi-Markov model [4; 5]. The main difference between the semi-Markov model and the Singer model is that the semi-Markov model introduces non-zero acceleration. In the early 1980s, [PERSON] proposed the \"current\" statistical model for maneuvering targets [6; 7], which used a more realistic non-zero mean and a modified Rayleigh distribution to characterize the maneuvering acceleration characteristicsof targets. To describe the acceleration distribution of maneuvering targets more accurately, [PERSON] et al. extended the derivative of acceleration to a state variable based on the Singer model, and proposed the Jerk model [8; 9]. Since the Jerk model adds the derivative of acceleration as a state variable, the description of acceleration is more accurate, which also improves tracking accuracy. The motion form of maneuvering targets is usually complex and variable [10]. When the target's motion state undergoes significant changes, the preset single model mismatches with the actual motion state, leading to reduced filtering precision, filter divergence, unstable target tracking, and target loss [11]. To address this issue, [PERSON] et al. proposed the interacting multiple model (IMM) algorithm based on generalized pseudo-Bayesian theory [12]. This algorithm has received extensive research and applications in the tracking of maneuvering targets in the air, ground, and water in recent years. The standard IMM algorithm is a recursive algorithm that assumes the motion state of the tracked target can be described by a finite set of models. Multiple models work simultaneously, and the posterior probabilities of each model are used to weight the filtering inputs and outputs. The transition between models is described by a Markov chain process. The IMM algorithm allows the online model to closely approximate the actual motion state of the target and ensures that the inputs of all filters in the system at each discrete sampling time match the actual system state, avoiding filter divergence. These studies can improve the suitability of the model and the real motion of the target, thereby enhancing tracking accuracy. In terms of tracking filtering algorithms, linear systems often employ two-point extrapolation filtering, Wiener filtering, least squares filtering, \(\alpha\)-\(\beta\)[13], \(\alpha\)-\(\beta\)-\(\gamma\)[14], and the KF [15] method.