• Title/Summary/Keyword: Cramer-Rao Lower bound

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Improving $L_1$ Information Bound in the Presence of a Nuisance Parameter for Median-unbiased Estimators

  • Sung, Nae-Kyung
    • Journal of the Korean Statistical Society
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    • v.22 no.1
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    • pp.1-12
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    • 1993
  • An approach to make the information bound sharper in median-unbiased estimation, based on an analogue of the Cramer-Rao inequality developed by Sung et al. (1990), is introduced for continuous densities with a nuisance parameter by considering information quantities contained both in the parametric function of interest and in the nuisance parameter in a linear fashion. This approach is comparable to that of improving the information bound in mean-unbiased estimation for the case of two unknown parameters. Computation of an optimal weight corresponding to the nuisance parameter is also considered.

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Iterative Target Localization Method for Distributed MIMO Radar System (반복적 연산을 이용하는 Distributed MIMO 레이다 시스템의 위치 추정 기법)

  • Shin, Hyuksoo;Chung, Young-Seek;Yang, Hoon-Gee;Kim, Jong-mann;Chung, Wonzoo
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.28 no.10
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    • pp.819-824
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    • 2017
  • This paper presents a target localization scheme for distributed Multi-input Multi-output(MIMO) radar system using ToA measurements obtained from multiple transmitter and receiver pairs. The proposed method can locate the target from an arbitrary initial point by iteratively finding the Taylor linear approximation equation. The simulation results show that proposed method achieves the better mean square error(MSE) performance than the existing target localization methods, and furthermore, attains Cramer-Rao Lower Bound(CRLB).

System Performance Bound in Target Motion Analysis

  • Yoon, Dong-Hun
    • The Journal of the Acoustical Society of Korea
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    • v.17 no.3E
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    • pp.22-26
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    • 1998
  • This paper proposes a simple method to measure system's performance in target tracking problems. Essentially employing the Cramer-Rao Lower Bound (CRLB) on tracking accuracy, an algorithm of predicting system's performance under various scenarios is developed. The input data is a collection of measurements over tim from sensors embedded in Gaussian noise. The target of interest may not maneuver over the processing time interval while the own ship observing platform may maneuver in an arbitrary fashion. The proposed approach is demonstrated and discussed through simulation results.

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Lifetime Estimation for Mixed Replacement Grouped Data in Competing Failures Model

  • Lee, Tai-Sup;Yun, Sang-Un
    • International Journal of Reliability and Applications
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    • v.2 no.3
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    • pp.189-197
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    • 2001
  • The estimation of mean lifetimes in presence of interval censoring with mixed replacement procedure is examined when the distributions of lifetimes are exponential. It is assumed that, due to physical restrictions and/or economic constraints, the number of failures is investigated only at several inspection times during the lifetime test; thus there is interval censoring. The maximum likelihood estimator is found in an implicit form. The Cramor-Rao lower bound, which is the asymptotic variance of the estimator, is derived. The estimation of mean lifetimes for competing failures model has been expanded.

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Theoretical Limits Analysis of Indoor Positioning System Using Visible Light and Image Sensor

  • Zhao, Xiang;Lin, Jiming
    • ETRI Journal
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    • v.38 no.3
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    • pp.560-567
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    • 2016
  • To solve the problem of parameter optimization in image sensor-based visible light positioning systems, theoretical limits for both the location and the azimuth angle of the image sensor receiver (ISR) are calculated. In the case of a typical indoor scenario, maximum likelihood estimations for both the location and the azimuth angle of the ISR are first deduced. The Cramer-Rao Lower Bound (CRLB) is then derived, under the condition that the observation values of the image points are affected by white Gaussian noise. For typical parameters of LEDs and image sensors, simulation results show that accurate estimates for both the location and azimuth angle can be achieved, with positioning errors usually on the order of centimeters and azimuth angle errors being less than $1^{\circ}$. The estimation accuracy depends on the focal length of the lens and on the pixel size and frame rate of the ISR, as well as on the number of transmitters used.

Efficient Sequential Estimation in a Compound Poisson Process

  • Bai, Do-Sun;Kim, Myung-Soo;Jang, Joong-Soon
    • Journal of the Korean Statistical Society
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    • v.15 no.2
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    • pp.87-96
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    • 1986
  • Sequential estimation of parameters in a compound Poisson process whose jump sizes are one-parameter exponential class random variables is discussed. Cramer-Rao type information inequality is used as an efficiency cirterion. Unbiased estimators for certain parametric functions whose variance attain the lower bound are all characterized with the corresponding sampling plans.

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Cramér-Rao Lower Bound of Multipath Angle Estimation for Low-Flying Target of Dual-Frequency Airborne Radar (항공기 레이다에 있어 두 개의 주파수를 사용하였을 때 저고도 표적 다중경로 각도 추정의 CRLB)

  • Jung, Ji Hyun;Kim, Jinuk;Lee, Joohyun;Chun, Joohwan;Oh, Yougeun;Suh, Jinbae
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.30 no.5
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    • pp.373-379
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    • 2019
  • If two signals with the same single-tone frequency and differing phases impinge simultaneously on an antenna at slightly differing angles, then a large error in the angle estimation might occur if the phase difference is either $0^{\circ}$ or $180^{\circ}$. This phenomenon might arise with an airborne fire-control radar, which has a relatively small bandwidth, for a low-flying target over the sea or terrain surface. In this paper, we show that the $Cram{\acute{e}}r$-Rao lower bound for such a target can be significantly lowered with the use of two frequencies.

A Subspace-based Array Shape Estimation Method Using Nearfield Source Model (근거리 신호 모델을 이용한 부공간 근사 기반의 어레이 형상 추정 기법)

  • 박희영;오원천;강현우;윤대희;이충용
    • The Journal of the Acoustical Society of Korea
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    • v.23 no.2
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    • pp.125-133
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    • 2004
  • Most of the way shape estimation method using reference sources assume that the reference sources are in the farfield. That is, the reference sources are assumed to be far from the array. However, in applications of the array with reference sources, the reference sources are not far from the way, so that in practical ocean environments, the conventional method using farfield source model fail to estimate the positions of the hydrophones. In this paper, based on the nearfield source model, a subspace-based array shape estimation method was proposed. In the proposed method, nearfield reference source is modeled using the differential time delay at each hydrophone, and nearfield parameters are derived. Using these parameters, a subspace-based array shape estimation method that generalizes the existing farfield subspace fitting method which can work regardless of the range of the source is proposed. The Cramer-Rao lower bound for the proposed method is investigated. The results of the numerical experiments indicate that the proposed method performs well in estimating the shape of a perturbed way regardless of the ranges of the reference sources.

An Improved frequency Synchronization Method Based on Autocorrelation function with Reduced Complexity (낮은 복잡도를 가지는 향상된 자기 상관 함수 기만의 주파수 동기화 기법)

  • Yang, Hyun;Jeong, Kwang-Soo;Lee, Kyeong-Il;Yi, Jae-Hoon;You, Young-Hwan
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.34 no.4C
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    • pp.424-429
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    • 2009
  • This paper suggests an autocorrelation function (AF) based carrier frequency offset (CFO) estimator based on a training sequence in flat fading channels. The proposed CFO estimator has the reduced computational burdens in the calculation of the AF when compared to AF-based conventional frequency estimators. The simulation results show that the proposed estimator achieves a better performance than the existing estimators. Furthermore, the performance of the proposed method has been observed to lie close to the Cramer-Rao lower bound (CRLB).

Performance evaluation of estimation methods based on analysis of mean square error bounds for the sparse channel (Sparse 채널에서 최소평균오차 경계값 분석을 통한 채널 추정 기법의 성능 비교)

  • Kim, Hyeon-Su;Kim, Jae-Young;Park, Gun-Woo;Choi, Young-Kwan;Chung, Jae-Hak
    • Journal of Satellite, Information and Communications
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    • v.7 no.1
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    • pp.53-58
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    • 2012
  • In this paper, we evaluate and analyze representative estimation methods for the sparse channel. In order to evaluate error performance of matching pursuit(MP) and minimum mean square error(MMSE) algorithm, lower bound of MMSE is determined by Cramer-Rao bound and compared with upper bound of MP. Based on analysis of those bounds, mean square error of MP which is effective in the estimation of sparse channel can be larger than that of MMSE according to the number of estimated tap and signal-to-noise ratio. Simulation results show that the performances of both algorithm are reversed on the sparse channel with Rayleigh fading according to signal-to-noise ratio.