Quotestate matrix (\Phi ) has complex eigenvaluesAll my experience with physics-based models. I am sure the eigenvalues related to the stability of the system, but I do not know how.QuoteAlso the model does not work so well with high dimensions (22) but better with lower dimensions (7)In my experience, Kalman filters converge more slowly with higher dimensions. A statistically correct initialization can speed convergence, but unless all the state variables are observable, convergence will be slowed.Another important question: Is system model (Phi) and measurement model (H) linear? If one or both are non-linear, then the filter is no longer guaranteed to converge, and you can experience instabilities. Inflating Q can help combat this, but these types of filters may need more sophisticated equations (such as an Unscented Kalman filter or an Iterated Extended Kalman filter).Since you are working with matrices, there are some numerical methods that will help with stability.The first "trick is to use the Joseph form for updating the corrected covariance. This method ensures that the corrected covariance retains its symmetric positive-definite properties. The equations are:The next item is to use the Cholesky decomposition to factorize . Then use a linear system solver to compute the gain. This method should be more numerically stable than using the inverse and more computationally efficient.