Component-By-Component Construction Kalman Filters

The component-by-component construction Kalman filter (CBCKF) is developed from the lattice rules in quasi-Monte Carlo (QMC) by incorporating the component-by-component (CBC) construction method to deterministically generate uniformly distributed sample points. The CBC construction systematically optimizes QMC points for specific integration dimensions and accuracy requirement to enhance the precision of multidimensional integrals in the Gaussian environment, leading to the improvement of state estimation accuracy. To further enhance the numerical stability of CBCKF, the square-root CBCKF (SCBCKF) is proposed accordingly. Meanwhile, to address the parameter selection issue existing in both CBCKF and SCBCKF, the number of sampling points is optimized through the maximum likelihood estimation method. Additionally, the Cramér-Rao lower bound (CRLB) of the nonlinear system model is introduced as a performance metric, and the detailed discussions on error propagation and computational complexities of the proposed filters are also provided. The performance superiorities of the proposed CBCKF and SCBCKF are verified through the simulations with two nonlinear examples.