Nonlinear multi-object state estimation algorithms for target tracking, communications and biomedical engineering in the presence of model uncertainties

多传感器-多目标跟踪问题涉及利用传感器检测来估计未知数量的可能具有不同动力学的移动或静止物体（目标）的状态（例如位置和速度）。多目标跟踪在国防（例如，防空）、通信（例如，移动用户跟踪）、信号处理（例如，信号源分离）和生物医学工程（例如，脑电图信号分析）中都有应用。状态估计的标准技术假定线性状态演化和状态-测量方程。它们还假定测量过程和状态动力学中存在高斯噪声。在非线性和非高斯噪声存在的情况下，经典方法的性能下降，往往达到完全崩溃的地步。非线性算法是经典卡尔曼滤波及其线性化变体的替代方案，用于处理非线性状态/测量模型和/或非高斯噪声。特别是基于蒙特卡罗（随机）抽样的方法，如粒子滤波、有限集统计跟踪和联合多目标概率密度跟踪已经成为逼近非线性滤波的一些可能方法，其最优形式在计算上是不可实现的。

The problem of multisensor-multitarget tracking involves the utilization of sensor detections to estimate the state (e.g., position and velocity) of an unknown number of mobile or stationary objects (the targets) with possibly different dynamics. Multi-object tracking has applications in defence (e.g., air defence), communications (e.g., mobile user tracking), signal processing (e.g., signal source separation) and biomedical engineering (e.g., EEG signal analysis). Standard techniques for state estimation assume linear state evolution and state-to-measurement equations. They also assume Gaussian noise in the measurement process and state dynamics. In the presence of nonlinearities and non-Gaussian noise, the performance of classical methods degrades, often to the point of complete breakdown. Nonlinear algorithms are the alternative to the classical Kalman filter and its linearized variants for handling nonlinear state/measurement models and/or non-Gaussian noise. In particular, Monte Carlo (random) sampling based methods like particle filtering, finite set statistics tracking and joint multitarget probability density tracking have become some of the possible ways to approximate nonlinear filtering, the optimal form of which is computationally infeasible.