Improved Square-Root UKF Algorithm for State Estimation of Nonlinear Systems

The square-root unscented Kalman filter （SR- UKF） for state estimation probably encounters the problem that Cholesky factor update of the covariance matrices can＇t be implemented when the zero＇th weight of sigma points is negative or the mnnerical computation error becomes large during the faltering procedure. Consequently the filter becomes invalid. An improved SR-UKF algorithm （ISR- UKF） is presented for state estimation of arbitrary nonlinear systems with linear measurements. It adopts a modified form of predicted covariance matrices, and modifies the Cholesky factor calculation of the updated covariance matrix originating from the square-root covariance filtering method. Discussions have been given on how to avoid the filter invalidation and further error accumulation. The comparison between the ISR-UKF and the SR-UKF by simulation also shows both have the same accuracy for state estimation. Finally the performance of the improved filter is evaluated under the impact of model mismatch. The error behavior shows that the ISR-UKF can overcome the impact of model mismatch to a certain extent and has excellent trace capability.

A CLASS OF FACTORIZATION UPDATE ALGORITHM FOR SOLVING SYSTEMS OF SPARSE NONLINEAR EQUATIONS

In this paper, we establish a class of sparse update algorithm based on matrix triangular factorizations for solving a system of sparse equations. The local Q-superlinear convergence of the algorithm is proved without introducing an m-step refactorization. We compare the numerical results of the new algorithm with those of the known algorithms, The comparison implies that the new algorithm is satisfactory.

Improved Harris Hawks Algorithm and Its Application in Feature Selection

This research focuses on improving the Harris’Hawks Optimization algorithm(HHO)by tackling several of its shortcomings,including insufficient population diversity,an imbalance in exploration vs.exploitation,and a lack of thorough exploitation depth.To tackle these shortcomings,it proposes enhancements from three distinct perspectives:an initialization technique for populations grounded in opposition-based learning,a strategy for updating escape energy factors to improve the equilibrium between exploitation and exploration,and a comprehensive exploitation approach that utilizes variable neighborhood search along with mutation operators.The effectiveness of the Improved Harris Hawks Optimization algorithm(IHHO)is assessed by comparing it to five leading algorithms across 23 benchmark test functions.Experimental findings indicate that the IHHO surpasses several contemporary algorithms its problem-solving capabilities.Additionally,this paper introduces a feature selection method leveraging the IHHO algorithm(IHHO-FS)to address challenges such as low efficiency in feature selection and high computational costs(time to find the optimal feature combination and model response time)associated with high-dimensional datasets.Comparative analyses between IHHO-FS and six other advanced feature selection methods are conducted across eight datasets.The results demonstrate that IHHO-FS significantly reduces the computational costs associated with classification models by lowering data dimensionality,while also enhancing the efficiency of feature selection.Furthermore,IHHO-FS shows strong competitiveness relative to numerous algorithms.