what are the state of the art techniques to take into account the quality of previous position estimates?
The Kalman filter and extended Kalman filter use the measurement and model covariances to balance the "quality" of estimated (model-based) and measured (feedback-based) position estimates.
From the Wikipedia entry on Kalman filters:
$w_k$ is ...
It is always guaranteed to be positive semi definite.
That being said you have to somewhat deliberately set up your system to be that way. So essentially yes it is always positive definite.
Covariance matrix by definition is always positive semidefinite.
$A^TA$ is always positive semidefinite (Takes care of the propagation matrix and the ...