The J-Orthogonal Square-Root NIRK-Based Extended-Unscented Kalman Filter for Nonlinear Continuous-Discrete Stochastic Systems

Abstract

The paper presents a novel state estimation algorithm of the extended-unscented Kalman-like sort. In particular, this mixed-type filter employs the adaptive Nested Implicit Runge-Kutta (NIRK) method of order 6 and with an embedded automatic control of the numerical integration accuracy, which is used for prediction of the mean and covariance in its time-update step. Then, the filter's measurement update is grounded in the Unscented Transform (UT), i.e. it employs the measurement-update step of the famous Unscented Kalman Filter (UKF). Here, the principal novelty is the square-root fashion of the Accurate Continuous-Discrete Extended-Unscented Kalman Filter (ACD-EUKF) devised. Moreover, taking into account the negativity of some UT weights in continuous-discrete stochastic scenarios of large size we utilize the hyperbolic Householder transforms for designing the J-orthogonal square-root filtering algorithm, which is examined numerically in severe conditions of tackling the challenging radar tracking problem of size 7, where an aircraft executes a coordinated turn. It is also compared to the original non-square-root ACD-EUKF method within our stochastic target tracking scenario with ill-conditioned measurements.