On the identifiability problem in the presence of random nuisance parameters

Least squares estimation and hybrid Cramér-Rao lower bound for absolute sensor registration

“…It can be proved [13] that, without loss of generality, if the rotation around z is applied first, the azimuth measurement bias dθ i and the attitude bias dξ i are not identifiable and have to be merged into a single bias. Because of this geometrical coupling, we can define a single bias error as dζ i =dξ i +dθ i .…”

“…h v v n (13) with l=1,...,N t where the registration errors appear explicitly. From the alignment equation in (13) one can infer that the two position error vectors, dt 1 and dt 2 , cannot be estimated separately but only their linear combination can be estimated.…”

“…From the alignment equation in (13) one can infer that the two position error vectors, dt 1 and dt 2 , cannot be estimated separately but only their linear combination can be estimated. It is important to note however, that, as shown in [13], the position error vectors are generally identifiable, i.e. there exists an estimator that is able to estimate them separately from the radar measurements.…”

“…The goal here is to estimate the two unknown parameter vectors Φ 1 and Φ 2 , defined in (14) and (5) respectively, based on K observations relative to each target considered in the scenario. From (13), and taking into account the unbiased property of coordinate transformation (11), we have that: (16) where γ represents the un-modeled zero-mean error and where, as discussed before, dt 1 is assumed to be equal to 0. The nonlinear least squares (NLLS) estimate of the unknown parameter vector …”

An identifying function approach for determining parameter structure of statistical learning machines

“…Typically, if an SLM has hierarchial structures [17,18], latent variables [1,16], state variables [13], nuisance parameters [19] or coupled submodels [11,12], the model may be unidentifiable. Due to the universal existence of nonidentifiability, Watanabe pointed out that "almost all learning machines are singular" [18].…”