  One of the modern research lines in econometrics studies focuses on
translating a wide variety of structural econometric models into their
state-space form, which allows for efficient unknown dynamic system state and
parameter estimations by the Kalman filtering scheme. The mentioned trend
yields advanced state-space model structures, which demand innovative
estimation techniques driven by application requirements to be devised. This
paper explores both the linear time-invariant multiple-input, multiple-output
system (LTI MIMO) and the pairwise Markov model (PMM) with the related pairwise
Kalman filter (PKF). In particular, we design robust gradient-based adaptive
Kalman-like filtering methods for the simultaneous state and parameter
estimation in the outlined model structures. Our methods are fast and accurate
because their analytically computed gradient is utilized in the calculation
instead of its numerical approximation. Also, these employ the numerically
robust $UDU^\top$-factorization-based Kalman filter implementation, which is
reliable in practice. Our novel techniques are examined on numerical examples
and used for treating one stochastic model in econometrics.
