A Barankin-type lower bound on the estimation error of a hybrid parameter vector

Some results on the Weiss–Weinstein bound for conditional and unconditional signal models in array processing

“…So, it only remains the calculation of functions ζ θ (µ, ρ) from Eqn. (18). Since R n = σ 2 n I, one obtains…”

“…(18). In this analysis, the vector µ takes the value µ i at the i th row and zero elsewhere and the vector ρ takes the value ρ j at the j th row and zero elsewhere (of course, one can has i = j).…”

“…(44) and after an optimization over the test points. The optimization over the test points can be done over a search grid or by using the ambiguity diagram of the array in order to reduce significantly the computational cost (see [18], [27], [34], [45], [46]). …”

Methods and Performances for Multi-Pass SAR Interferometry

“…The role of the variance of the APSs in the estimation process may be described through a threshold like behavior. The fact that this aspect is not handled by the HCRB is an intrinsic limitation of the method, whereas other bounds have been proposed in literature that account properly for threshold effects (27). Practical conditions for retaining the validity of the results will be provided in the following.…”

“…The HCRB (26), (27), (28) applies in the case where some of the unknowns are deterministic and others are random; it unifies the deterministic and Bayesian CRB in such a way as to simultaneously bound the covariance matrix of the unbiased estimates of the deterministic parameters and the mean square errors on the estimates of the random variables (26), (27). Let θ be an unbiased estimator of the deterministic parameters θ, and denote α an estimator of the random variables α.…”