Cramér-Rao Bound for Estimation After Model Selection and Its Application to Sparse Vector Estimation

Meir, Elad; Routtenberg, Tirza

doi:10.1109/tsp.2021.3068356

Cited by 10 publications

(11 citation statements)

References 62 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Cramer Rao Lower Bound (CRLB) on the mean square error of unbiased estimator is a frequently used metric for determining the correctness of parameter estimate based on a set of data [50]. The CRLB of the algorithm provides the criterion to know the minimum value of error, that can be achieved by the algorithm.…”

Section: B Cramer Rao Lower Boundmentioning

confidence: 99%

Sequential Fusion Based Approach for Estimating Range Gate Pull-Off Parameter in a Networked Radar System: An ECCM Algorithm

2022

View full text Add to dashboard Cite

Networked radar is an emerging and effective alternative to traditional radar systems to provide improved performance by fusing information from multiple radars. Further, networked radar systems (NRS) have found numerous deployments in military and civilian infrastructures in recent years. Electronic countermeasures (ECM) like jamming, Range Gate Pull-Off (RGPO), and Velocity Gate Pull-Off (VGPO) generally pose a high risk to the radar systems by injecting intentional interference. This paper proposes networked radar to detect the RGPO ECM attack and estimate the range gate deception parameter of the deceived local track in an NRS. Each radar comprises a local tracker to provide the local estimates (updated state and updated covariance), and these estimates are then sent to the fusion node. Thereafter, a track-to-track association (T2TA) is formulated at the fusion node to detect the deceived tracks using all the available local tracks. For the deceived track, the pseudo-measurements are created using the inverse Kalman filter-based tracklets. All the local tracks except deceived track are compensated and sequentially fused to create a reference measurement. After that, the deception parameter of the deceived track is estimated by using pseudo-measurement and the reference measurement by employing the recursive least square estimator (RLSE). In addition, the proposed algorithm is analyzed for single and multiple RGPO based ECM scenarios. Further, the Cramer Rao Lower Bound (CRLB) for the proposed methodology is derived. The results are quantified with a Position Root Mean Square Error (PRMSE), CRLB, innovation test, normalized estimation error squared (NEES) test, and confidence interval. The simulation results demonstrate that the proposed estimation technique provides good performance in the presence of all the local tracks are being attacked by RGPO ECM. Besides, it is evident from the results that estimator efficiency is falling below the 5% tail probability of the chi-square distribution.INDEX TERMS Cramer-Rao lower bound, electronic counter countermeasure, networked radar, range gate pull-off, sequential fusion, tracklets

show abstract

Section: B Cramer Rao Lower Boundmentioning

confidence: 99%

Sequential Fusion Based Approach for Estimating Range Gate Pull-Off Parameter in a Networked Radar System: An ECCM Algorithm

2022

View full text Add to dashboard Cite

show abstract

“…In particular, the CCRB [26][27][28][29], which is associated with the CML estimator, is unsuited as a bound on the performance of Good-Turing estimators outside the asymptotic region, while it provides a lower bound on the MSE of any χ-unbiased estimator [28][29][30]. Our recent works on non-Bayesian estimation after selection [31][32][33] suggest that conditional schemes, in which the performance criterion depends on the observed data, require different CRB-type bounds.…”

Section: B Related Workmentioning

confidence: 99%

“…The measure of closeness is determined by the considered cost function, C( θ, θ). Examples for Lehmann unbiasedness with different cost functions and under parametric constraints can be found in [28,29,[31][32][33][34]43].…”

Section: A Lehmann Unbiasednessmentioning

confidence: 99%

“…It should be noted that the condition in (31) requires a uniform unbiasedness, for any θ ∈ Ω θ , while the conditions in (32) and (33) are local conditions that are required to be satisfied only at the specific θ, denoted here by θ, for which the bound is developed. Both the local and uniform missingmass unbiasedness definitions restrict only the values that belong to the set of unseen symbols, i.e.…”

Section: A Lehmann Unbiasednessmentioning

confidence: 99%

See 1 more Smart Citation

Non-Bayesian Parametric Missing-Mass Estimation

Cohen,

Routtenberg,

Tong

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider the classical problem of missing-mass estimation, which deals with estimating the total probability of unseen elements in a sample. The missing-mass estimation problem has various applications in machine learning, statistics, language processing, ecology, sensor networks, and others. The naive, constrained maximum likelihood (CML) estimator is inappropriate for this problem since it tends to overestimate the probability of the observed elements. Similarly, the conventional constrained Cramér-Rao bound (CCRB), which is a lower bound on the mean-squared-error (MSE) of unbiased estimators, does not provide a relevant bound on the performance for this problem. In this paper, we introduce a frequentist, non-Bayesian parametric model of the problem of missing-mass estimation. We introduce the concept of missing-mass unbiasedness by using the Lehmann unbiasedness definition. We derive a non-Bayesian CCRB-type lower bound on the missing-mass MSE (mmMSE), named the missing-mass CCRB (mmCCRB), based on the missing-mass unbiasedness. The missing-mass unbiasedness and the proposed mmCCRB can be used to evaluate the performance of existing estimators. Based on the new mmCCRB, we propose a new method to improve existing estimators by an iterative missing-mass Fisher scoring method. Finally, we demonstrate via numerical simulations that the proposed mmCCRB is a valid and informative lower bound on the mmMSE of state-of-the-art estimators for this problem: the CML, the Good-Turing, and Laplace estimators. We also show that the performance of the Laplace estimator is improved by using the new Fisher-scoring method.

show abstract

“…Lehmann [31] proposed a generalization of the unbiasedness concept based on the chosen cost function for each scenario, which can be used for various cost functions (see, e.g. [14], [14], [34], [36], [37]). The following proposition defines the graph unbiasedness property of estimators w.r.t.…”

Section: A Graph Unbiasednessmentioning

confidence: 99%

Non-Bayesian Estimation Framework for Signal Recovery on Graphs

Routtenberg

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Graph signals arise from physical networks, such as power and communication systems, or as a result of a convenient representation of data with complex structure, such as social networks. We consider the problem of general graph signal recovery from noisy, corrupted, or incomplete measurements and under structural parametric constraints, such as smoothness in the graph frequency domain. In this paper, we formulate the graph signal recovery as a non-Bayesian estimation problem under a weighted mean-squared-error (WMSE) criterion, which is based on a quadratic form of the Laplacian matrix of the graph and its trace WMSE is the Dirichlet energy of the estimation error w.r.t. the graph. The Laplacian-based WMSE penalizes estimation errors according to their graph spectral content and is a difference-based cost function which accounts for the fact that in many cases signal recovery on graphs can only be achieved up to a constant addend. We develop a new Cramér-Rao bound (CRB) on the Laplacian-based WMSE and present the associated Lehmann unbiasedness condition w.r.t. the graph. We discuss the graph CRB and estimation methods for the fundamental problems of 1) A linear Gaussian model with relative measurements; and 2) Bandlimited graph signal recovery. We develop sampling allocation policies that optimize sensor locations in a network for these problems based on the proposed graph CRB. Numerical simulations on random graphs and on electrical network data are used to validate the performance of the graph CRB and sampling policies.

show abstract

Cramér-Rao Bound for Estimation After Model Selection and Its Application to Sparse Vector Estimation

Cited by 10 publications

References 62 publications

Sequential Fusion Based Approach for Estimating Range Gate Pull-Off Parameter in a Networked Radar System: An ECCM Algorithm

Sequential Fusion Based Approach for Estimating Range Gate Pull-Off Parameter in a Networked Radar System: An ECCM Algorithm

Non-Bayesian Parametric Missing-Mass Estimation

Non-Bayesian Estimation Framework for Signal Recovery on Graphs

Contact Info

Product

Resources

About