Matrix analysis
On the time-varying Riccati difference equation of optimal filtering
SIAM Journal on Control and Optimization
Linear System Theory and Design
Linear System Theory and Design
Robust Kalman Filtering for Signals and Systems with Large Uncertainties
Robust Kalman Filtering for Signals and Systems with Large Uncertainties
SIAM Journal on Control and Optimization
Partial Stability for a Class of Nonlinear Systems
SIAM Journal on Control and Optimization
Robust Kalman filters for linear time-varying systems withstochastic parametric uncertainties
IEEE Transactions on Signal Processing
Robust H∞ filter design of uncertain descriptor systems with discrete and distributed delays
IEEE Transactions on Signal Processing
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This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.