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。提出的工作目标是开发先进的算法来解决存在模型不确定性的非线性状态估计中的一些具体问题，并应用于目标跟踪，通信和生物医学工程。新算法的基本特征将是在有许多目标跟踪的现实问题中的计算效率。除了非线性状态估计算法之外，还将推导出在具有模型不确定性、非高斯噪声和非线性状态模型的特定问题中，量化任何算法可获得的最佳精度的性能界限。将通过理论和实验手段进行性能评估，以验证新算法的有效性。

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.The objective of the proposed work is to develop advanced algorithms to solve a number of specific problems in nonlinear state estimation in the presence of model uncertainties with application to target tracking, communications and biomedical engineering. The fundamental characteristics of the new algorithms will be computational efficiency in realistic problems with many objects to track. In addition to nonlinear state estimation algorithms, performance bounds that quantify the best accuracy obtainable by any algorithm, in specific problems with model uncertainties, non-Gaussian noise and nonlinear state models, will be derived as well. Performance evaluation through theoretical as well as experimental means will be carried out to validate the usefulness of the new algorithms.