[ENH] Use valid covariance matrices in Kalman filter unit tests #8029
Conversation
Using unsymmetric or indefinite matrices break Kalman filter math and may result to random "division by zero" -type errors inside the libraries.
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In practice, it's pretty bad luck if the matrices randomly end up singular, and the Kalman filter equations are also well-defined for non-symmetric matrices. However, they just don't make sense if the matrix is not symmetric PSD, so whatever is happening inside the implementations with such matrices is, from the math point of view, undefined behavior. It's also hard to say if the algorithms (including EM) should be numerically stable with such data. I would not be suprised if this resulted in random occasional test failures but cannot really describe the exact mechanism why that would happen. It would also be legal for a Kalman Filter library to implement the matrix inversion step inside the KF equations by a few different ways, e.g., Cholesky decomposition, LU etc., and these may give different results if the matrix is assumed to be symmetric, but is actually not. |
Using unsymmetric or indefinite matrices break Kalman filter math and may result to random "division by zero" -type errors inside the libraries.
@NoaWegerhoff