We make modifications to the unscented Kalman filter (UKF) which bestow almost complete practical identifiability upon a lumped-parameter cardiovascular model with 10 parameters and 4 output observables - a highly non-linear, stiff problem of clinical significance. The modifications overcome the challenging problems of rank deficiency when applying the UKF to parameter estimation. Rank deficiency usually means only a small subset of parameters can be estimated. Traditionally, pragmatic compromises are made, such as selecting an optimal subset of parameters for estimation and fixing non-influential parameters. Kalman filters are typically used for dynamical state tracking, to facilitate the control u at every time step. However, for the purpose of parameter estimation, this constraint no longer applies. Our modification has transformed the utility of UKF for the parameter estimation purpose, including minimally influential parameters, with excellent robustness (i.e., under severe noise corruption, challenging patho-physiology, and no prior knowledge of parameter distributions). The modified UKF algorithm is robust in recovering almost all parameters to over 98% accuracy, over 90% of the time, with a challenging target data set of 50, 10-parameter samples. We compare this to the original implementation of the UKF algorithm for parameter estimation and demonstrate a significant improvement.

翻译：我们对无迹卡尔曼滤波器（UKF）进行了改进，使其能够对一个具有10个参数和4个输出观测量的集总参数心血管模型实现近乎完全的实用可辨识性——这是一个具有临床意义的高度非线性、刚性难题。这些改进克服了将UKF应用于参数估计时面临的秩亏缺挑战。秩亏缺通常意味着只能估计一小部分参数。传统上，研究者会采取务实的折衷方案，例如选择最优参数子集进行估计，并固定那些无影响的参数。卡尔曼滤波器通常用于动态状态跟踪，以便在每个时间步长实现控制输入u。然而，对于参数估计的目的，这一约束不再适用。我们的改进彻底改变了UKF在参数估计中的效用，使其能够估计包括影响极小的参数在内的所有参数，并展现出卓越的鲁棒性（即在严重噪声干扰、具有挑战性的病理生理条件以及缺乏参数分布先验知识的情况下）。改进后的UKF算法在恢复几乎所有参数时表现出色，在超过90%的情况下，对具有挑战性的目标数据集（包含50个10参数样本）的参数恢复准确率超过98%。我们将其与原始UKF算法在参数估计上的实现进行了比较，并证明了显著的性能提升。