Yang Wang In strong tracking extended Kalman filter, the fading factor is added in order to give more weight to the most recent measurements and minimize the impact of earlier measurements on the estimated state. The goal is to improve the filter's sensitivity to shifts in system behavior.

Before the update phase, the projected state covariance matrix is multiplied by the fading factor to incorporate it into the method. This can be accomplished as follows:

1. At the present time phase, compute the expected state covariance matrix P-.

2. Compute the fading factor lambda. This can be a fixed number or one that is calculated dynamically based on some parameters.

3. P-_w = lambda * P- is the weighted projected state correlation matrix.

4. Based on the weighted projected state correlation matrix, compute the Kalman gain K.

5. Update the expected state and correlation matrix using the Kalman gain and the observation.

It should be noted that the fading factor lambda selection is essential and can have a substantial effect on filter performance. When lambda becomes too high, the filter becomes excessively sensitive to noise and measurement mistakes, resulting in divergence. If lambda is too tiny, the filter may be unable to track changes in the system dynamics efficiently.

To select a suitable value of lambda, some simulations and sensitivity analysis may be required to assess the filter effectiveness under various circumstances.

Overall, using a strong tracking extended Kalman filter with fading factors can enhance the filter's responsiveness to changes in system dynamics, especially when the system is extremely nonlinear or has substantial measurement noise. However, in order to prevent instability and guarantee excellent filter performance, the fading factor must be cautiously chosen.

Without looking at your equations I cannot be sure. But I have the feeling that it should be that lambda