TY - JOUR

T1 - Information-preserving transformations for signal parameter estimation

AU - Stein, Manuel

AU - Castaneda, Mario

AU - Mezghani, Amine

AU - Nossek, Josef A.

PY - 2014/7

Y1 - 2014/7

N2 - The problem of parameter estimation from large noisy data is considered. If the observation size $N$ is large, the calculation of efficient estimators is computationally expensive. Further, memory can be a limiting factor in technical systems where data is stored for later processing. Here we follow the idea of reducing the size of the observation by projecting the data onto a subspace of smaller dimension $M \ll N$ , but with the highest possible informative value regarding the estimation problem. Under the assumption that a prior distribution of the parameter is available and the output size is fixed to $M$, we derive a characterization of the Pareto-optimal set of linear transformations by using a weighted form of the Bayesian Cramér-Rao lower bound (BCRLB) which stands in relation to the expected value of the Fisher information measure. Satellite-based positioning is discussed as a possible application. Here $N$ must be chosen large in order to compensate for low signal-to-noise ratios (SNR). For different values of $M$ , we visualize the information-loss and show by simulation of the MAP estimator the potential accuracy when operating on the reduced data.

AB - The problem of parameter estimation from large noisy data is considered. If the observation size $N$ is large, the calculation of efficient estimators is computationally expensive. Further, memory can be a limiting factor in technical systems where data is stored for later processing. Here we follow the idea of reducing the size of the observation by projecting the data onto a subspace of smaller dimension $M \ll N$ , but with the highest possible informative value regarding the estimation problem. Under the assumption that a prior distribution of the parameter is available and the output size is fixed to $M$, we derive a characterization of the Pareto-optimal set of linear transformations by using a weighted form of the Bayesian Cramér-Rao lower bound (BCRLB) which stands in relation to the expected value of the Fisher information measure. Satellite-based positioning is discussed as a possible application. Here $N$ must be chosen large in order to compensate for low signal-to-noise ratios (SNR). For different values of $M$ , we visualize the information-loss and show by simulation of the MAP estimator the potential accuracy when operating on the reduced data.

KW - Dimensionality reduction

KW - parameter estimation

UR - http://www.scopus.com/inward/record.url?scp=84900843655&partnerID=8YFLogxK

U2 - 10.1109/LSP.2014.2315537

DO - 10.1109/LSP.2014.2315537

M3 - Article

AN - SCOPUS:84900843655

SN - 1070-9908

VL - 21

SP - 866

EP - 870

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

IS - 7

M1 - 6782658

ER -