Abstract: To address the limitations of measurement rate modeling for multiple extended targets, this paper proposes a Bayesian multiple extended target tracking (METT) method with flexibility and parameter scalability. The method is based on measurement modeling using a Non-homogeneous Poisson Process (NHPP) and employs the Probability Hypothesis Density (PHD) filter within the random finite set (RFS) framework. For METT, the associations between measurements and targets are unknown and time-varying. To model the Poisson measurement rate of the target more flexibly and ensure the closed implementation method based on the PHD filter, the following modeling approach is adopted: the target's measurement rate is modeled as a Generalized Inverse Gaussian (GIG) distribution, the target's kinematic state is modeled as a Gaussian distribution, and the target's extened state is modeled as an Inverse Wishart (IW) distribution. Specifically, the GIG models for measurement rate of extended targets are divided into Time Independent Poisson Rate (TIPR) types and the Time Dependent Poisson Rate (TDPR) types. For TIPR modeling, an analytical implementation based on a mixture of Generalized Inverse Gaussian-Gaussian Inverse Wishart (GIG-GIW) distributions is derived. For TDPR modeling, additional sampling steps are required to assist in approximately updating the Poisson measurement rate of each extended target. The experimental results demonstrate that the proposed tracking algorithm achieves significant performance improvements across key performance indicators, including kinematic state, extended state, and measurement rate estimation of targets.