This paper proposes a marginal multi-object Bayesian filter with multiple hypotheses to track multiple objects in the presence of object appearing and object disappearing, missed detection and clutter. This filter delivers the probability of existence and probability density function of each object. A mathematical model for searching K-best hypotheses is set up by the maximization of the generalized joint likelihood ratios of hypotheses, which results in a 2-dimensional assignment problem. The K-best hypotheses can be acquired by using the Murty algorithm to solve the 2-dimensional assignment problem. According to the K-best hypotheses, the existence probabilities and probability density functions of objects are formed. Furthermore, an implementation of this filter for a linear Gaussian system is developed and is extended to nonlinear observations. Experimental result demonstrates that the proposed filter outperforms other available filters at various numbers of clutter and different detecting probabilities.

本文提出了一种具有多个假设的边缘多目标贝叶斯滤波器，以在存在对象出现和对象消失、漏检和杂波的情况下跟踪多个对象。该过滤器提供每个对象的存在概率和概率密度函数。通过最大化假设的广义联合似然比来建立搜索K-best假设的数学模型，这导致了二维分配问题。使用Murty算法解决二维分配问题，可以得到K-best假设。根据K-best假设，形成物体的存在概率和概率密度函数。此外，开发了用于线性高斯系统的此滤波器的实现，并将其扩展到非线性观测。