A Real-time Ballistics Fusion Method Based on Tracking the Global Maximum Point of Kernel Density Estimation Function

Abstract

To overcome the weak robustness,hypersensitive to initial values and dependence on theory ballistics equation of existing ballistics fusion algorithms,it was proved that the global maximum point of Gaussian kernel density estimation (KDE) function constructed on limited samples is an unbiased estimator of expected value(EV)of Gaussian distribution which above samples obeys,and a method based on tracking the global maximum point of KDE function was proposed by researching the probability distribution of measurement error. The Gaussian KDE function was built on all measurement data,and thus the essence of ballistics fusion was turned into calculating the global maximum point of Gaussian KDE function. To avoid the time-consuming process in classic iterative method,a tracking algorithm was proposed,which samples many neighbors of the global maximum point through shifting previous result, employs Taylor estimation method to obtain many potential results and selects the result corresponding to the global maxima of Gaussian KDE function. The theoretical analysis and calculation indicate that the tracking algorithm is effective and can be implemented with lower time-consuming by comparing with classic iterative method. The method was compared with optimization method, spline restraint and unscented Kalman filter by experiment.The experimental results show that this method performs higher accuracy,stronger robustness,easier extensibility and higher smoothness in noise-tolerate capability test, sensitivity test for initial values,flexibility test and stability test,and it can be implemented in real-time application.