# An Interactive Transient Model Correction Active Sonar Target Tracking Method
## 2 Description of the TMC Tracking Method  
Based on the following two points of analysis, the overall design approach of the algorithm and the overall schematic diagram as shown in Figure 1 are presented:  
1. Due to the characteristics of submarine targets and water media, when a submarine target is moving underwater, sudden changes in maneuvering state generally do not occur. In combination with the long measurement acquisition period of active sonar for underwater submarine targets, it can be assumed that within two sampling intervals, the change in target motion state is uniform, and the motion state changes that occur within a number of consecutive sampling periods can be considered a transient process. By correcting this transient process, the tracking instability or decreased accuracy caused by changes in motion mode can be solved.
2. In general, after given design requirements, the precision of active sonar target measurement data is stable. Therefore, the deviation between target measurement values and state estimation values can be considered to be caused by changes in their motion state. According to the changes in the variance of measurement values or state estimation values, it can be judged whether the target's motion state has changed, and the motion state parameters can be corrected to make the motion model closer to the true motion state of the target.  
As shown in Figure 1, the system state model is first established, including the displacements (\(r_{x}\), \(r_{y}\)) and velocity components (\(v_{x}\), \(v_{y}\)) on the X-axis and Y-axis. Then, the state model is initialized and assigned values. Subsequently, KF processing is performed according to the flow of one-step advance prediction, filtering gain matrix calculation, and filtering estimation update. Additionally, the residual covariance \(\mathbf{S}(k)\) of the current cycle is calculated and analyzed. When \(\mathbf{S}(k)\) is less than the preset decision threshold, the KF result is used as the tracking filter output. When it is greater than the preset decision threshold, it is judged that there is a significant deviation between the current state model and the actual motion of the target, and thus correction is necessary. Using the constant gain filtering method, the current measurement value is filtered, and the KF gain matrix is adjusted based on the filtering result. Additionally, the motion velocity, position, and process noise of the state model are corrected. With the corrected state model parameters and filter gain matrix, the KF process is re-performed. Under normal circumstances, the active sonar receives the echo signals reflected by the target and processes the echo signals to obtain direct measurement information such as radial distance and azimuth information. For the KF algorithm that models and processes tracking in a Cartesian coordinate system, it is necessary to perform coordinate system transformation and deflection removal processing on the measurement data to obtain the displacement information (\(d_{x}(k)\), \(d_{y}(k)\)) of the target on the X-axis and Y-axis in the Cartesian coordinate system, which is used as the measurement update for tracking filtering.