Improved nonlinear observable degree analysis using data fusion

For nonlinear Kalman filtering, process noise and observation noise affect the accuracy of system filtering, and filtering accuracy is related to observable degree. That is, the calculation of observable degree will be affected by process noise and observation noise. Traditional solutions for observable degree of nonlinear systems do not take noise into account. In this paper, the observable degree theory is solved by using the Cramer-Rao Lower Bound and the Lie derivative in differential geometry theory. The process noise and the observation noise are taken into account in the calculation matrix of the nonlinear observable degree. The paper proposes a new method based on condition number fusion. The iterative algorithm is used to make the condition number of the fused matrix reach the minimum value. In the result, the error of observable degree calculation can be reduced. The validity of the proposed method is verified by simulation, and the calculation theory of nonlinear observable degree is improved.