# Tracking Extended Targets: Novel TPMB Filter Driven by Model and Data Collaboration
###### Abstract
For methods based on gating and sampling, the assumption that negligible weights can be truncated avoids the exhaustive data association often required for large datasets [18]. Therefore, in scenarios with high uncertainty in data association, performance degradation can occur due to information loss. To prevent the loss of information associated with explicit enumeration and local association assumptions, the method of computing the multi-target marginal posterior for data association is used, which marginalizes the unknown data association uncertainties [10]. Currently, the best-performing multi-EOT algorithm, as proposed in [19], is the Sum-Product Algorithm (SPA) based on particle Belief Propagation (BP), which is implemented through a factor graph of the joint posterior of multi-target states and measurement association variables. Simulation results in [20] demonstrate that the TPMB filter based on factor graphs outperforms the TPMBM filter that uses gating clustering and truncated sampling in terms of estimation errors and runtime. The BP algorithm recursively iterates to obtain global hypothesis data association information, transmitting this association information between factor nodes and variable nodes via a directed graph. In the process of approximating PMB with PMBM, Kullback-Leibler Divergence (KLD) minimization is used to marginalize the uncertainty of data hypotheses, thereby reducing the amount of data processing. This process has led to the development of a closed-form filter that initiates the recursive process from the joint posterior factor graph model of object sets and association variables, along with the message-passing equations. This paper presents a model-data-driven message-passing algorithm that adaptively adjusts the motion models of targets in different dynamics through an Interactive Multiple Model (IMM) to adapt to the switching motion state at different time steps [21]. In the message-passing process using factor graphs, considering the measurement association factor's message as an approximation of the posterior probability requires computation for each message-passing variable, which is complex. The proposed algorithm reduces the complexity of data association and minimizes message passing by gating hypothetical surviving targets, thereby enhancing algorithm efficiency. In the filter, a new particle filtering method is introduced that constructs the importance density function for each particle's state via the Adaptive Square Root Cubature Kalman Filter (ASCKF), optimizing the covariance matrices of process noise and measurement noise to improve the tracking performance of high-maneuver targets under noise and clutter influences [22; 23]. This paper is an important extension of [19; 22], including the following contributions:  
1. In addressing the complexity of model transition probability calculations in the IMM algorithm, we utilize changes in the posterior probability between two consecutive moments to reflect the transition probabilities between models. On the other hand, the standard IMM algorithm considers process noise as a constant during model switching, affecting the accuracy of the filtering algorithm. The improved IMM algorithm adaptively adjusts the magnitude of process noise, reducing errors in model switching. 2. In addressing the complex message passing between variable nodes and factor nodes in factor graphs, we have improved the posterior association step of the factor graph. The message-passing process is streamlined through adaptive gating, eliminating the need to consider all inter-node relationships when computing association nodes, thereby reducing running time. 3. To address the issue of particle degradation observed in the methods using particles, we employ the SCKF to perform particle importance sampling and use the Gate-control Belief Propagation (GBP) for the improved IMM-TPMB-GBP filter, updating the particle filter based on these sampling results.