This paper proposes a new and efficient approach where a nature-inspired optimisation technique has abetted the Kalman filter (KF) for accurately solving the parametric estimation problem of highly complex non-linear systems. The KF is the best optimal state estimator in terms of normalised mean squared error (NMSE) for linear Gaussian state-space models. However, the use of mismatched noise statistics in KF might result in performance degradation. To address this issue, three steps are proposed in this work for the accurate estimation of the unknown non-linear system parameters by using the Volterra model. The first step is to reformulate the Volterra model into a measurement form. Secondly, the KF parameters are optimised by using an evolutionary algorithm with an efficient objective function. The third step is to estimate the coefficients of the unknown system by using the KF technique with the help of optimally tuned KF parameters achieved in the second step. In simulations, three distinct higher memory size second-order Volterra models, two non-linear benchmark systems and the primary path of active-noise control (ANC) system based on real data sets are identified by using the basic KF, genetic algorithm (GA) assisted KF (GA-KF), particle swarm optimisation (PSO) assisted KF (PSO-KF), firefly algorithm (FA) assisted KF (FA-KF) and ant lion optimisation (ALO) assisted KF (ALO-KF) techniques. The experimental results illustrate that the ALO-KF approach leads to better coefficient estimation compared to FA-KF, PSO-KF, GA-KF, and basic KF methods.

本文提出了一种新的有效方法，其中一种受自然启发的优化技术支持卡尔曼滤波器 (KF)，用于准确解决高度复杂的非线性系统的参数估计问题。KF 是线性高斯状态空间模型在归一化均方误差 (NMSE) 方面的最佳最佳状态估计器。但是，在 KF 中使用不匹配的噪声统计可能会导致性能下降。为了解决这个问题，在这项工作中提出了三个步骤，以使用 Volterra 模型准确估计未知的非线性系统参数。第一步是将 Volterra 模型重新表述为测量形式。其次，通过使用具有高效目标函数的进化算法来优化 KF 参数。第三步是利用 KF 技术，借助在第二步中获得的最佳调谐 KF 参数来估计未知系统的系数。在模拟中，使用基本的 KF、遗传算法 (GA) 识别三个不同的更高内存大小的二阶 Volterra 模型、两个非线性基准系统和基于真实数据集的主动噪声控制 (ANC) 系统的主要路径）辅助KF（GA-KF）、粒子群优化（PSO）辅助KF（PSO-KF）、萤火虫算法（FA）辅助KF（FA-KF）和蚁狮优化（ALO）辅助KF（ALO-KF）技术. 实验结果表明，与 FA-KF、PSO-KF、GA-KF 和基本 KF 方法相比，ALO-KF 方法导致更好的系数估计。