Computationally Efficient Adaptive Spline Filters for Nonlinear State Estimation

非线性/非高斯滤波问题由于在大多数实际系统中固有的非线性而引起了文献的极大兴趣。状态估计问题中的非线性可能是由于状态-测量方程或状态本身的演化而产生的。多个对象的存在通过添加数据关联使问题进一步复杂化。最优非线性状态估计包括给定当前所有可用测量值的多目标状态的条件（后验）pdf的计算。最优多目标非线性滤波通常是一个难以处理的问题，这不仅是因为计算的复杂性，而且还因为多目标非线性滤波的多模态特性。

The problem of nonlinear/non-Gaussian filtering has generated significant interest in the literature due to the inherent nonlinearity in most practical systems. The nonlinearity in state estimation problems may arise due to its presence in the state-to-measurement equation or in the evolution of the state itself. The presence of multiple objects further complicates the problem by adding data association to the mix. The optimal nonlinear state estimator consists of the computation of the conditional (posterior) pdf of the multitarget state given all the measurements available up to the current time. Optimal multitarget nonlinear filtering is in general a non-tractable problem, not just because of computational complexity but also due to the multimodal nature of multitarget pdf.