# An Interactive Transient Model Correction Active Sonar Target Tracking Method
## 1 Introduction
For nonlinear systems, the main filtering methods include the classical extended Kalman filtering (EKF) based on nonlinear approximation [16; 17], unscented Kalman filtering (UKF) [18], cubature Kalman filtering (CKF) [19], and particle filtering (PF) proposed by [PERSON] et al. [20]. Many researchers have also optimized and improved these filtering methods. Subsequently, the emergence of improved algorithms such as the error-minimizing squared sum filter, the kernel correlation filter [21], and convolutional neural networks have made significant contributions to more precise target tracking. For specific tracking applications, the choice of filtering algorithm should be based on the availability of prior knowledge about system dynamic noise, sensor measurement error statistics, as well as constraints such as tracking accuracy and computational requirements. A comprehensive trade-off selection should be made. At the beginning of each scanning period, the active sonar sends a pulse signal and then receives the target echo. By processing and analyzing the echo, the target information is obtained. By measuring and analyzing the time difference between pulse signal transmitting time and echo receiving time, combined with underwater sound propagation speed, the distance value of the target can be obtained directly. By using spatial directivity and multi-beam direction finding processing of the receiving transducer array, the azimuth of the echo can be determined, and the azimuth information of the target can be obtained. When the transmitting pulse signal is a CW signal, if there is relative motion between the target and the sonar, there will be a frequency offset between the transmitted CW signal and the received echo signal. Through spectrum analysis of the echo signal, the radial velocity of the target relative to the sonar can be calculated. Of course, other pulse signals will also have Doppler shifts, but because they are complex wideband signals, extracting accurate Doppler shifts requires more complex algorithms. The \"velocity\" obtained at this time is only the radial velocity of the target relative to the sonar and not the true speed of the target in the Earth coordinate system. At present, no active sonar can directly measure the acceleration of target motion. Therefore, the tracking of underwater targets by active sonar has the following characteristics: Firstly, it typically adopts the track while scan (TWS) approach, which involves simultaneously searching, measuring, and tracking target information in a periodic manner. This requires high real-time tracking performance. Secondly, the target measurement information has low dimensionality and a slow update rate. Typically, only azimuth and range information in a two-dimensional plane are available, and direct measurements of target depth, velocity, and other information are generally not possible. Additionally, due to the slow propagation speed of sound waves in water compared to electromagnetic waves, the update rate of measurement information is slow, typically taking tens to hundreds of seconds to obtain the next batch of measurements. Thirdly, the target's motion state is highly variable and subject to high process noise. Fourthly, the target may easily \"lose\" due to the influence of the ocean environment and countermeasures, resulting in the inability to acquire target measurement information continuously and stably over multiple scanning cycles. This leads to an increase in tracking output errors, instability, or even filter divergence. Due to the unique application scenarios, there are relatively few reports in the research of active sonar for tracking underwater maneuvering targets. The Ocean Systems Laboratory in the UK has studied the technology of forward-looking sonar for tracking and localizing underwater targets based on particle filtering [22]; The Florida Atlantic University in the United States has applied the KF algorithm to the forward-looking sonar target tracking processing of remotely operated vehicles (ROVs) [23].