After further reflection, I realized that the poor performance of the adaptive Kalman filter based on maximum likelihood estimation (MLE) is fundamentally due to two key reasons:

Window Length Issue:

1.If the window length is too small, it becomes impossible to estimate the covariance matrices accurately.

2.Even with a large window length, the algorithm is prone to divergence.

3.In the early stages, when data is insufficient, once the algorithm starts diverging, it becomes irrecoverable later on, even with a large window length.

Observation Data Fluctuation:

The inherent fluctuations in the observation data can significantly affect the estimation of the noise covariance matrices, leading to instability.

Proposed Solution A better approach would be to:

1.Set a larger window length to improve the accuracy of covariance estimation.

2.In the early stages, when data is limited, set the noise covariance matrices as constants based on empirical knowledge.

3.However, this solution increases computational overhead.

This is my understanding and proposed solution to the issue I previously encountered.