Optical EngineeringError propagation in two-sensor three-dimensional position estimation
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The accuracy of 3D position estimation using two angles-only sensors (such as passive optical imagers) is investigated. Beginning with the basic multisensor triangulation equations used to estimate a 3D target position, error propagation equations are derived by taking the appropriate partial derivatives with respect to various measurement errors. Next the concept of Gaussian measurement error is introduced and used to relate the standard deviation of various measurement errors to the standard deviation of the target 3D position estimate. Plots of the various error propagation coefficients are generated. These analytical results are verified using a Monte Carlo statistical approach. The result is a set of equations and graphs useful for designing a two-sensor system to meet a required accuracy specification.