Bias analysis of maximum likelihood target location estimator

Rui, Liyang; Ho, K. C.

doi:10.1109/taes.2014.130318

Cited by 23 publications

(21 citation statements)

References 36 publications

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“…To complement the investigation, we shall examine the bias of the object location estimate for the three elliptic localization approaches, when the MLE is used. We shall apply the bias formula of the MLE for a generic localization problem derived in [48] to elliptic positioning.…”

Section: B Biasmentioning

confidence: 99%

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Elliptic Localization: Performance Study and Optimum Receiver Placement

Rui

2014

IEEE Trans. Signal Process.

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165

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Range based localization often relies on TOA that creates a circular contour or TDOA that yields hyperbolic surface to determine the position of an emitting object. Another approach that has gained attention recently is elliptic localization. Elliptic localization uses an active transmitter to send out a signal and several receivers to acquire the reflected or relayed signal from an object to obtain its location. This paper performs a fundamental investigation on the performance of elliptic localization, for both the synchronous and asynchronous cases between the transmitter and the receivers. Their performance is also characterized with respect to the hyperbolic localization. The study is based on the Cramér-Rao lower bound (CRLB) for the object location under Gaussian measurement noise as well as Gaussian errors in the transmitter and receiver positions. When the receiver positions are controllable, we derive the optimum receiver placement for elliptic positioning to improve the localization accuracy. We conclude the study with simulation results to demonstrate the elliptic localization performance using the CRLBs and the Maximum Likelihood estimators.

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Section: B Biasmentioning

confidence: 99%

“…Putting (45) to (44) gives (47) Upon using (36) and followed by (37), (47) can further be reduced to (48) The right side of (48) attains the minimum value at . The minimum possible error is .…”

Section: B 3dmentioning

confidence: 99%

Elliptic Localization: Performance Study and Optimum Receiver Placement

Rui

2014

IEEE Trans. Signal Process.

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165

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“…They found that in contrast with the closed-form estimator, the MLE provided asymptotic unbiased estimates. Rui and Ho [15], [22] derived the bias by performing Taylor-series expansion of the maximum likelihood (ML) cost function up to second order. This method can achieve a good result at small or moderate noise level with good geolocation geometry.…”

Section: Introductionmentioning

confidence: 99%

Bias Compensation for AOA-Geolocation of Known Altitude Target Using Single Satellite

Zhang

Guo

2019

IEEE Access

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To reduce the passive localization bias caused by the nonlinearity between the target position and measurements under high noise level and poor geometry conditions, the bias compensation method for known altitude target geolocation using angles of arrival (AOA) obtained by a single satellite is proposed. The basic idea of this method is to estimate the bias first, and then subtract it from the estimation of the target position. Different from existing bias estimate methods which perform Taylor-series expansion on the maximum likelihood (ML) cost function, the proposed method directly applies Taylor-series expansion on the closed-form target location estimate. Interestingly, the expectations of the odd-order expansion terms of the Taylor-series in the proposed method are equal to zero, which indicates that higher bias estimation accuracy can be achieved with the same order of expansion compared with the existing methods. Furthermore, the theoretical analysis is performed and the result indicates that the Euclidean norm of the bias is independent of the azimuth angle and is positively correlated with the elevation angle. Finally, the computer simulations verify the superior performance of the proposed method and the theoretical analysis. INDEX TERMS Angle of arrival, bias compensation, passive localization, satellite, Taylor-series expansion.

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“…One of the most studied localisation methods is based on the Gauss–Newton algorithm using the Taylor‐series expansion [1]. The bias of the location estimate stemming from the Gaussian measurement noise and sensor position errors has been analysed in [2]. The total least squares method has been used to eliminate the bias in the conventional location estimator [3].…”

Section: Introductionmentioning

confidence: 99%

Sequential source localisation and range estimation based on shrinkage algorithm

Park

Chang

2018

IET signal process.

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This study presents the shrinkage-based sequential source localisation and range estimation algorithms. The shrinkage factor is found using the variance of the estimate in the existing shrinkage algorithm. However, the variance of the estimate is difficult to calculate when the form of the estimate is complex. To circumvent this problem, the authors propose a shrinkage algorithm that employs the Cramér-Rao lower bound (CRLB) instead of the variance for the maximum likelihood (ML) estimate. The variance of the ML estimate and CRLB were found to be similar in simulation results. Furthermore, Stein's unbiased risk estimator and Ledoit-Wolf methods are used to determine the shrinkage factor. The resulting estimation accuracy of the proposed shrinkage-based sequential source localisation and range estimation methods was similar with that of the existing shrinkage algorithm.

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Bias analysis of maximum likelihood target location estimator

Cited by 23 publications

References 36 publications

Elliptic Localization: Performance Study and Optimum Receiver Placement

Elliptic Localization: Performance Study and Optimum Receiver Placement

Bias Compensation for AOA-Geolocation of Known Altitude Target Using Single Satellite

Sequential source localisation and range estimation based on shrinkage algorithm

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