# Fundamentals of statistical signal processing: Estimation theory: by Steven M. KAY; Prentice Hall signal processing series; Prentice Hall; Englewood Cliffs, NJ, USA; 1993; xii + 595 pp.; $65; ISBN: 0-13-345711-7

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### Cites background from "Fundamentals of statistical signal ..."

...Full additivity requires the abundances in a to sum to one [14], and this requirement restricts the solution to lie on the hyperplane given by...

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^{1}

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### Cites background from "Fundamentals of statistical signal ..."

...Thus, we can obtain from (21) and (22) that Similarly, we have Since the above bounds are independent of , we obtain the following estimates for the unconditioned means (23) Let be the mse of the centralized BLUE [defined in (7)] (24) Now we calculate the part of mse due to the channel distortion....

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...Recall from the property of BLUE (2) that the optimal weight of is proportional to ....

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...The estimator at the fusion center is a generalized version of the BLUE estimator (2) which weighs the message functions linearly with weights decided by both the observation noise and the quantization noise....

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...,K} to the fusion center, the fusion center can simply perform the linear minimum MSE estimation to recover θ which leads to the following Best Linear Unbiased Estimator (BLUE) [13] θK = Γ(x1, x2, ....

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...4, the percentage of active sensors versus the normalized deviation of channel path losses is plotted by keeping distribution of local sensor noise variances fixed choosing , and the target mse where is the mse of the centralized BLUE defined in (3)....

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### Cites methods from "Fundamentals of statistical signal ..."

...Figure 1 shows the mean square range errors (MSREs) of the TOA-based CWLS and NLS estimators as well as CRLB versus power of distance error based on the TOA measurements....

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...(104) From the figures, we observe that the performance of all the proposed methods approached the corresponding CRLBs for sufficiently small measurement errors, which verified their optimality at sufficiently high SNRs....

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...The optimum value ofΨ is also determined based on the BLUE as follows....

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...PERFORMANCE ANALYSIS As briefly mentioned in Section 1, the CWLS and WLS estimators in Section 3 can achieve zero bias and the CRLB approximately when the noise is uncorrelated and small in power....

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...We have proved that for small uncorrelated noise disturbances, the performance of all the proposed CWLS and WLS algorithms attains zero bias and the Cramér-Rao lower bound (CRLB) approximately....

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