Quasi-Consistent Norm-Constrained Extended Kalman Filter for Attitude Estimation

One of the primary applications of the norm-constrained Kalman filter (NCKF) is attitude estimation for spacecraft. However, the extension of NCKF to nonlinear attitude estimation systems is affected by the truncation error generated by linearization. This leads to the filter lacking consistency, which means that filter being unbiased, i.e., the actual mean squared error of the estimation equals to the mean squared error predicted by the filter. To tackle this issue, based on an analysis of the consistency of NCKF, the quasi-Consistent norm-Constrained extended Kalman filter is proposed. The consistency constraint ensures that, when dealing with complex nonlinear systems in attitude estimation, the estimation error remains within an acceptable range, resulting in stable estimation accuracy. This method guarantees that the actual mean squared estimation error does not significantly exceed the mean squared error predicted by the filter. Therefore, it can reliably determine the error bounds of the estimation, thereby improving computational accuracy. Simulation experiments on spacecraft attitude estimation further validate this conclusion.