Computationally Efficient Adaptive Spline Filters for Nonlinear State Estimation

非线性/非高斯滤波的问题已经产生了显着的兴趣，在文献中，由于在大多数实际系统中的固有的非线性。状态估计问题中的非线性可能由于其存在于状态-测量方程中或状态本身的演化中而出现。多个对象的存在通过将数据关联添加到混合中而使问题进一步复杂化。最优非线性状态估计器由给定到当前时间的所有测量的多目标状态的条件（后验）PDF的计算组成。最佳多目标非线性滤波一般是一个不容易处理的问题，不仅是因为计算的复杂性，但也由于多目标PDF的多模态性质。

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.