# Tracking Extended Targets: Novel TPMB Filter Driven by Model and Data Collaboration
###### Abstract  
In most filtering algorithms involving measurement data association, handling the complex computations due to multiple hypotheses is necessary. This paper introduces a novel Trajectory Poisson Multi-Bernoulli (TPMB) filter for tracking extended targets, facilitated by a synergy between the model and the data. This filter can track extended targets under unknown process and measurement noise. Initially, on the model-driven side, we compute multi-model transition probabilities using the posterior probabilities from models at two consecutive time points with the targets in high maneuverability state. The accuracy of the tracking algorithm is improved by calculating the improved Interacting Multiple Model (IMM) transition probability at each time step. For the data-driven aspect, the Gate-control Belief Propagation (GBP) is set in the message- passing algorithm to reduce the running time of false hypothesis associations. Thus, it is unnecessary to consider all message information when computing the likelihood matrix for target-measurement associations. Subsequently, the posterior density function of the Adaptive Square Root Cubature Kalman Filter (ASCKF) is constructed to adaptively estimate unknown process and measurement noises, while importance sampling in the current particle filter further mitigates particle degradation. Experiments demonstrate that our algorithm reduces the running time of data associations, alleviates particle degradation, and more accurately tracks maneuvering targets under nonlinear conditions and estimates their states. extended target tracking; TPMB filter; IMM; ASCKF; data association +
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model [9], and Poisson space models [10]. Among these, the Poisson space model is the most widely used. In this model, target detection is modeled by a non-homogeneous Poisson Point Process (PPP). The PPP measurement likelihood has a simple factorization that avoids the explicit representation of assumptions about the association between measurements and targets [11]. At each time step, a Poisson distribution of random measurements is generated, spatially distributed around the measurements of the target. To address the issue of tracking multiple targets, the RFS framework is used for modeling. The RFS framework offers a systematic approach to Multi-Target Tracking (MTT) by accommodating changes in the number and state of targets over time. Both targets and measurements are modeled as random finite sets, and the PPP extended target model has been utilized in several computable complex models. The ensemble approach within this framework allows for an optimal Bayesian representation of the birth and death of targets. According to the literature, the state-of-the-art algorithm for tracking an unknown number of elliptical targets is the Poisson Multi-Bernoulli Mixture (PMBM) filter. This method acknowledges that the number, size, shape, and kinematic states of targets are interrelated and influence each other. However, due to the numerous prior conditions and associations that need to be considered, such associations present computational challenges. According to [12; 13], the most advanced algorithm for tracking an unknown number of extended targets is the PMBM filter. For estimating target trajectories, MTT methods based on random vectors link the current state estimates of an object with its past states, or represent the emergence of new targets. In the RFS-based MTT methods, one effective approach is to assign a unique label to each trajectory, allowing each object to be identified as it changes over time [14]. Another effective method is to calculate the multi-target posterior probability over the set of trajectories, which contains all information about multiple trajectories and does not require the use of labels [15]. In multi-target tracking scenarios, the Trajectory Probability Poisson Multi-Bernoulli Mixture (TPMBM) filter and its approximate filter [16], the Trajectory Probability Poisson Multi-Bernoulli (TPMB) filter, have emerged [17].