Hybrid CRB for Initial and Current States of Discrete-Time Markovian Dynamic Systems

This communication addresses the problem of computing the Hybrid Cramér-Rao Bound (HCRB) in the context of discrete-time Markovian Dynamic Systems (MDS) for both initial and current states, with unknown deterministic parameters. The challenging derivation of HCRBs in this context has previously led to the release of computationally tractable HCRB versions that have the merit of being computed recursively. Expanding upon these prior endeavors, we introduce a unified formalism to compute the fixed-point smoothing and filtering HCRBs for discrete-time MDS depending on unknown deterministic parameters. We consider two configurations for the initial state vector: either assumed unknown deterministic or random with a known covariance matrix. The proposed expressions are applied to tracking a moving target, including its initial state (launch coordinate), its current kinematic state, and the unknown proportionality constant between the air resistance force and velocity.