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Signal Processing and Propagation for Aeroacoustic Sensor Networks
Published in S. Sitharama Iyengar, Richard R. Brooks, Distributed Sensor Networks, 2016
Richard J. Kozick, Brian M. Sadler, D. Keith Wilson
(12.85) Coherent combining is feasible only if the phase shifts θ(i; ωl) are known or are constant with i. Our assumptions imply that the random variables in (12.84) are independent over l, as are the random variables in (12.85). The probability distribution functions (pdfs) for PC and PI are noncentral chi-squared distributions.* We let χ2(D, δ) denote the standard noncentral chi-squared distribution with D degrees of freedom and noncentrality parameter δ. Then the random variables in (12.84) and (12.85) may be scaled so that their pdfs are standard noncentral chi-squared distributions () PC(ωl)[Ω(ωl)S(ωl)+σω˜2(ωl)]/(2T)~χ2(2,δ(ωl)), () PI(ωl)[Ω(ωl)S(ωl)+σω˜2(ωl)]/(2T)~χ2(2T,δ(ωl)),
A Robust Unscented Kalman Filter applied to Ultra-wideband Positioning
Published in International Journal of Image and Data Fusion, 2020
Chuanyang Wang, Yipeng Ning, Xin Li, Haobo Li
When the innovation is normal, the test statistic term is smaller than the threshold of the test statistic, and should be Chi-square distributed with the dimension of the observation vector as the degree of freedom (DOF). The null hypothesis is confirmative. If is larger than , the value of test statistic will fall in the right tail-area of the distribution, and the null hypothesis will be rejected. It shows that the model does not conform with the specifications. We can believe that the outliers in the observation do occur and the stochastic model of observation error is not correct. The test statistic term will follow a non-central Chi-square distribution with non-central parameter. Then observation covariance is updated based on the robust factor.
Monitoring location and scale of multivariate processes subject to a multiplicity of assignable causes
Published in Quality Technology & Quantitative Management, 2020
Konstantinos A. Tasias, George Nenes
As already mentioned, follows a non-central chi-square distribution with degrees of freedom and non-centrality parameter . By denoting the cumulative distribution function of by , the probabilities for to be either in the central, warning or action zone, are: