Notes on the Tightness of the Hybrid CramÉr–Rao Lower Bound

Noam, Yair; Messer, H.

doi:10.1109/tsp.2009.2015113

Cited by 101 publications

(82 citation statements)

References 33 publications

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“…The MCRLB was derived in [Gin98] and its relation to the CRLB investigated e.g. in [Gin98], [Gin00] and [Noa09], and it was found that the MCRLB is looser than the CRLB. The MCRLB was applied in radar e.g.…”

Section: J Vt J V H V H T H T E Dt Ft H T H T H V H V Ementioning

confidence: 99%

Waveform Diversity and Design for Interoperating Radar Systems

Greco¹

2013

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY)15 January 2013 (From -To) REPORT TYPE Final Report DATES COVERED SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)EOARD Unit 4515 BOX 14 APO AE 09421 SPONSOR/MONITOR'S ACRONYM(S)AFRL/AFOSR/IOE (EOARD) SPONSOR/MONITOR'S REPORT NUMBER(S) AFRL-AFOSR-UK-TR-2013-0003 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTESGovernment Purpose Rights -University Di Pisa ABSTRACTFor many years, conventional radars transmitted, received, and processed the same waveform on every pulse or burst within a coherent processing interval (CPI), independently of the environment. Now, modern radar systems have considerable flexibility in their modes of operation, both on receive and transmit. In particular, it is possible to modify the waveform on a pulse to pulse basis, and electronically steered phased arrays can quickly point the radar beam in any feasible direction. In the course of this research project, we introduced the Ambiguity Function, an analytical tool for waveform design and analysis that is useful for examining resolution, sidelobe behavior, and ambiguity in range and Doppler of a given signal waveform. Some techniques to design multiple access frequency hop codes with good auto and cross-ambiguity functions are characterized, focusing on the frequency hop patterns. We have shown that the performance of each channel of the multistatic system heavily depends on the transmitted waveform and on the geometry of the scenario, that is, the position of receivers and transmitters with respect to the position of the target. In particular, both geometry factors and transmitted waveforms play an important role in the shape of the Ambiguity Function and hence in the value of the Cramer-Rao Lower Bound (CRLB). We have calculated the bistatic CRLBs of target range and velocity of each transmit-receive pair as a function of the target kinematic parameters and to provide a local measure of the estimation accuracy of these parameters. Finally, in this work we have analyzed the problem of the optimum sensor selection along the trajectory of a tracked ta...

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Section: J Vt J V H V H T H T E Dt Ft H T H T H V H V Ementioning

confidence: 99%

Waveform Diversity and Design for Interoperating Radar Systems

Greco¹

2013

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“…Signal processing community generally use the Hybrid Cramér-Rao Bound (HCRB) [1] for which some asymptotic achievability results [2] are known. The HCRB, as well as the classical CRB, is known to be simple to obtain for various problems (see Part III of [3]) but suffers from some drawbacks.…”

Section: Introductionmentioning

confidence: 99%

A Ziv-Zakaï type bound for hybrid parameter estimation

Ren¹,

Galy²,

Chaumette³

et al. 2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. In this communication, we propose a new hybrid lower bound which, for the first time, includes the Ziv-Zakaï bound well known for its tightness in the Bayesian context (random parameters only). For the general case of parameterized mean model with Gaussian noise, closed-form expressions of the proposed bound are provided.

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“…The problem of non-Bayesian parameter estimation in the presence of random nuisance parameters was investigated in [6][7][8][9][10]. On the other hand, Bayesian estimation based on a family of prior distributions indexed by a set of parameters known as hyperparameters, was thoroughly investigated.…”

Section: Introductionmentioning

confidence: 99%

Bayesian cramér-rao type bound for risk-unbiased estimation with deterministic nuisance parameters

Bar

Tabrikian

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this paper, we derive a Bayesian Cramér-Rao type bound in the presence of unknown nuisance deterministic parameters. The most popular bound for parameter estimation problems which involves both deterministic and random parameters is the hybrid Cramér-Rao bound (HCRB). This bound is very useful especially, when one is interested in both the deterministic and random parameters and in the coupling between their estimation errors. The HCRB imposes locally unbiasedness for the deterministic parameters. However, in many signal processing applications, the unknown deterministic parameters are treated as nuisance, and it is unnecessary to impose unbiasedness on these parameters. In this work, we establish a new Cramér-Rao type bound on the mean square error (MSE) of Bayesian estimators with no unbiasedness condition on the nuisance parameters. Alternatively, we impose unbiasedness in the Lehmann sense for a risk that measures the distance between the estimator and the minimum MSE estimator which assumes perfect knowledge of the nuisance parameters. The proposed bound is compared to the HCRB and MSE of Bayesian estimators with maximum likelihood estimates for the nuisance parameters. Simulations show that the proposed bound provides tighter lower bound for these estimators.

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Notes on the Tightness of the Hybrid CramÉr–Rao Lower Bound

Cited by 101 publications

References 33 publications

Waveform Diversity and Design for Interoperating Radar Systems

Waveform Diversity and Design for Interoperating Radar Systems

A Ziv-Zakaï type bound for hybrid parameter estimation

Bayesian cramér-rao type bound for risk-unbiased estimation with deterministic nuisance parameters

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Notes on the Tightness of the Hybrid CramÉr–Rao Lower Bound

Cited by 101 publications

References 33 publications

Waveform Diversity and Design for Interoperating Radar Systems

Waveform Diversity and Design for Interoperating Radar Systems

A Ziv-Zaka&#x00EF; type bound for hybrid parameter estimation

Bayesian cram&#x00E9;r-rao type bound for risk-unbiased estimation with deterministic nuisance parameters

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Product

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A Ziv-Zakaï type bound for hybrid parameter estimation

Bayesian cramér-rao type bound for risk-unbiased estimation with deterministic nuisance parameters