State estimation is a pre-requisite for advanced control applications such as optimization based nonlinear model predictive control since the latter needs to know the current state vector. Thus, any decrease in computation time for the state estimation module can lead to significant benefits in the overall closed loop implementation by reducing the overall computational delay in implementing the control move. The current work contributes to this area by proposing a novel variant of the widely used Extended Kalman Filter (EKF) for nonlinear state estimation. The proposed variant has significantly reduced computation time requirement compared to its traditional implementation. This reduction is obtained by using Broyden’s rank-one update procedure for approximating the time varying process and measurement Jacobian matrices which are needed in EKF at each time instant. Broyden’s update of Jacobian matrix is widely used in numerical techniques literature but its use in estimation literature has hitherto not been reported. In the current work, we map the iterative procedure of Broyden’s update to the time and measurement update steps of EKF to approximate the process and measurement Jacobian matrices needed in EKF using rank-one updates. The proposed approach neither requires any analytical derivative nor additional evaluation of the process and measurement functions. It only utilizes the predicted and filtered states, and predicted measurements as available in EKF. It thus leads to significant reduction in computation time. Comparison of the theoretical Floating Point Operations (FLOPs) requirements, actual computation times, and the estimation performances of the proposed approach with traditional EKF on two case studies including the Tennessee Eastman challenge problem demonstrates the efficacy of the proposed approach.

状态估计是高级控制应用（例如基于优化的非线性模型预测控制）的先决条件，因为后者需要知道当前状态向量。因此，状态估计模块的计算时间的任何减少都可以通过减少实现控制移动的总体计算延迟而导致总体闭环实现中的显着益处。当前的工作通过提出广泛使用的用于非线性状态估计的扩展卡尔曼滤波器 (EKF) 的新变体来为该领域做出贡献。与其传统实现相比，所提出的变体显着减少了计算时间要求。这种减少是通过使用 Broyden 的一级更新程序来获得的，用于逼近 EKF 中每个时刻所需的时变过程和测量雅可比矩阵。Broyden 对雅可比矩阵的更新广泛用于数值技术文献中，但迄今为止尚未报道其在估计文献中的使用。在当前的工作中，我们将 Broyden 更新的迭代过程映射到 EKF 的时间和测量更新步骤，以使用一级更新来近似 EKF 中所需的过程和测量雅可比矩阵。所提出的方法既不需要任何分析导数，也不需要对过程和测量功能进行额外的评估。它仅利用预测和过滤状态，以及 EKF 中可用的预测测量。因此，它导致计算时间的显着减少。在包括田纳西伊士曼挑战问题在内的两个案例研究中，理论浮点运算 (FLOP) 要求、实际计算时间以及所提出方法与传统 EKF 的估计性能的比较证明了所提出方法的有效性。