Extended target tracking algorithms require the estimation of the target's shape in addition to its kinematic properties. The star-convex model can describe the details of the target's shape compared with the traditional elliptical model. The shape estimation based on the star-convex model is a complex nonlinear problem, which also contains the uncertainty of the measurement distribution on the surface of the target. Therefore, we propose a novel nonlinear measurement transformation (MT) to map measurements into a high dimensional space, so that the transformed measurements have a more linear relationship with the states. The MT also extracts the uncorrelated distance and angle information of the measurement in the local polar coordinates to improve the stability and accuracy of the shape estimation. Then a linear minimum mean square error estimator is constructed using the nonlinear uncorrelated MT, and a Bayesian filter under Gaussian assumptions is derived. Moreover, we also propose a novel mathematical metric based on the star-convex model that measures the distance between the reference shape parameters and their estimated values. Simulation results demonstrate the effectiveness of the proposed algorithm in the case of high sensor noise, low measurement rate, and dense sensor clutter.

扩展的目标跟踪算法除了需要其运动学特性之外，还需要估计目标的形状。与传统的椭圆模型相比，星凸模型可以描述目标形状的细节。基于星形-凸模型的形状估计是一个复杂的非线性问题，其中还包含目标表面测量分布的不确定性。因此，我们提出了一种新颖的非线性测量变换（MT），将测量值映射到高维空间，从而使变换后的测量值与状态之间具有更线性的关系。MT还提取局部极坐标中测量值的不相关距离和角度信息，以提高形状估计的稳定性和准确性。然后，使用非线性不相关MT构造线性最小均方误差估计器，并推导高斯假设下的贝叶斯滤波器。此外，我们还提出了一种基于星形-凸模型的新颖数学度量，该度量可测量参考形状参数与其估计值之间的距离。仿真结果证明了该算法在高传感器噪声，低测量速率和密集传感器杂波情况下的有效性。