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Noise Statistics Across the Three Axes of a Tri-Axial Velocity Sensor Constructed of Pressure Sensors

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This paper analyzes the noise statistics of a “tri-axial velocity sensor”. This tri-axial sensing system comprises of three orthogonal axes. Along each axis, a “uni-axial velocity sensor” is realized through two isotropic pressure sensors displaced along that axis. Hence, a “tri-axial velocity sensor” may be
implemented with as few as four isotropic sensors: one at the Cartesian origin and one at each Cartesian axis. (Please see Figure 1.) Each isotropic sensor’s noise would contribute to its axis’ “effective” noise. As the three axes share one isotropic sensor in common, the three axes’ “effective” noises would be crosscorrelated, but how? This is answered in this paper, through rigorous mathematics that analytically derives the statistical “codifference” across the three axes’ “effective” noises. This analysis models the noises accommodatingly as -stable distributed, which includes the special cases of the Gaussian distribution, the Cauchy distribution, and many other heavy-tailed probability distributions. This finding is then generalized from the aforementioned velocity sensors (i.e., differential sensors of the first order) to differential sensors of arbitrarily high orders.

Andriy Y. Olenko

Field of Interest

“The field of interest shall be the organization, systems engineering, design, development, integration, and operation of complex systems for space, air, ocean, or ground environments. These systems include but are not limited to navigation, avionics, mobile electric power and electronics, radar, sonar, telemetry, military, law-enforcement, automatic test, simulators, and command and control."


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