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This paper deals with data fusion for the purpose of estimation. Three fusion architectures are considered: centralized, distributed, and hybrid. A unified linear model and general framework for these three architectures are established. Optimal fusion rules in the sense of best linear unbiased estimation (BLUE), weighted least squares (WLS), and their generalized versions are presented for cases with either complete, incomplete, or no prior information. These rules are much more general and flexible than previous results. For example, they are in a unified form that are optimal for all the three fusion architectures with arbitrary correlation of local estimates or observation noises across sensors or across time.. They are also in explicit forms convenient for implementation. The relationships among these rules are also presented.

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A new algorithm is proposed for computing the embedding dimension and delay time in phase space reconstruction. It makes use of the zero of the nonbias multiple autocorrelation function of the chaotic time series to determine the time delay, which efficiently depresses the computing error caused by tracing arbitrarily the slop variation of average displacement (AD) in AD algorithm. Thereafter, by means of the iterative algorithm of multiple autocorrelation and Γ test, the near-optimum parameters of embedding dimension and delay time are estimated. This algorithm is provided with a sound theoretic basis, and its computing complexity is relatively lower and not strongly dependent on the data length. The simulated experimental results indicate that the relative error of the correlation dimension of standard chaotic time series is decreased from 4.4% when using conventional algorithm to 1.06% when using this algorithm. The accuracy of invariants in phase space reconstruction is greatly improved.

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