A Lower Bound for Sequential Estimators

A popular class of parameter estimation method is based on a sequential/iterative scheme. In this framework, each component is estimated one by one and at each iteration the underlying model is based on the estimation of a single component corrupted by a structured interference (the other components) and by an unstructured Gaussian noise. So, in the context of the bearing estimation problem, we derive the deterministic Cramer-Rao Bound, called Interfering CRB (I-CRB), associated with this model. In particular, we show that for low Interference to Noise Ratio (INR), the I-CRB reaches the CRB for a single component (without structured interference). Inversely, for high INR, the I-CRB is equal to the Prior-CRB where we assume the exact knowledge of the structured interference. In addition, we show that in the closely-spaced bearings, the I-CRB has two typical regimes depending of the INR.