Hi Jonas,
I understand from your query that you are interested in finding out why the covariance matrix might become non-positive definite and whether tunable parameters affect it.
A covariance matrix becoming non-positive definite can be caused by several factors:
- Numerical Instabilities: When the UKF equations are solved using finite-precision arithmetic (as is the case in computer implementations), small numerical errors can accumulate and lead to a loss of positive definiteness.
- Improper Tuning Parameters: The UKF has several parameters, such as alpha, beta, and kappa (or ki), which control the spread of the sigma points around the mean state estimate and the confidence in the process and measurement noise covariance matrices. If these are not chosen correctly, they can lead to an ill-conditioned covariance matrix.
- Model Mismatch: If the process model or the measurement model used in the UKF does not accurately represent the true system dynamics or measurement process, it can lead to incorrect covariance updates.
- Poor Observability: If the system or the measurements do not provide enough information to fully observe the state of the system, it can make the covariance matrix estimation unreliable.
Regarding the tunable parameters, when the system response to a varying parameter is slow, a larger value for alpha might be required to maintain stability. If you are encountering stability issues, you may consider working with the Square Root UKF, which is computationally more stable.
Hope this helps.
