Characterizing the Convergence Behavior of Gauss’s Method of Initial Orbit Determination

Dichter, Michal J.; Wojcik, Jeremy

doi:10.2514/1.g004866

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…Other measurement models exist for goniometric systems [21][22][23]. In this paper, we assume that a measurement can obtain the right ascension α t and the declination δ t centred on the optical sensor as two independent values, and the measurement error follows the Gaussian distribution [20]. The measured data are defined as follows:…”

Section: Uvmmentioning

confidence: 99%

“…The iterative process is very complex. Dichter [20] characterized the convergence behaviours of the orbit determination algorithm applied to the three anglesonly data. There is no perfect method to determine whether UVM applied to multiple angles-only data converges so far.…”

Section: Validating the Gdop Using Monte Carlo Simulation Experimentsmentioning

confidence: 99%

“…Studying the effect of observation geometry on the initial orbit determination of short-arc angles-only data can help to understand the surveillance capability of space surveillance systems in different regions in space. When the initial orbit is calculated using three angles-only data by the Laplacian method or the Gaussian method [6,20], it is generally considered that the orbit solution is very sensitive to measurement errors when the angle between the target and the optical sensor orbit plane is close to 0 • . It can be argued that the optical sensor has a poor surveillance capability for such targets.…”

Section: Introductionmentioning

confidence: 99%

“…It can be argued that the optical sensor has a poor surveillance capability for such targets. Michal [20] obtained the preconditions for the convergence of the Gaussian iterations by calculating the signal-to-noise ratio of the line-of-sight determinant. Therefore, the angle between the target and optical sensor orbital planes is an important factor affecting the observation geometry.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Effect of Observation Geometry on Short-Arc Angles-Only Initial Orbit Determination

Zhao

Qiao

et al. 2022

Applied Sciences

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Space-based optical sensors are attracting increasing research attention as they can measure the angle of space targets over large areas, facilitating low-cost, wide-area space target surveillance. Studying the effect of observation geometry on short-arc angles-only initial orbit determination is important for analysing the surveillance capability of systems that use optics as the main means for surveilling different areas of space. In this paper, the initial orbit is calculated based on the unit vector method (UVM); the geometric dilution of precision (GDOP)—derived under the condition that the approximate Lagrangian coefficient and distance are constant—is used as the parameter for the uncertainty distribution of the target orbit solution. A suitable coordinate system transformation is conducted and all possible observation geometry relationships between the target and the sensor are expressed in terms of the angle between orbital planes and the right ascension of the target and sensor in the transformed coordinate system. Simulation experiments show that the GDOP is approximately equal to that obtained statistically through Monte Carlo simulation experiments. The accuracy of the initial orbit solution is poor when the target and optical sensor are at the same right ascension and declination, or in the same orbital plane.

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Section: Uvmmentioning

confidence: 99%

Section: Validating the Gdop Using Monte Carlo Simulation Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of Observation Geometry on Short-Arc Angles-Only Initial Orbit Determination

Zhao

Qiao

et al. 2022

Applied Sciences

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Differential algebra enabled multi-target tracking for too-short arcs

et al. 2021

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Positioning Error Estimation Method for Short-Arc Angles-Only Initial Orbit Determination

Feng,

Yan,

et al. 2024

Journal of Guidance, Control, and Dynamics

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The development of space surveillance capabilities has received increased emphasis with time. Suitable evaluation parameters are investigated to analyze the effects of multiple factors on short-arc angles-only initial orbit determination. This investigation is crucial for designing surveillance system parameters. In this paper, the orbit determination equations where the target state is linear were derived by assuming that Lagrangian coefficients are constant and taking the minimum residual sum as the optimization objective. From this paper’s analysis, it was demonstrated that because the position uncertainty distribution primarily lies in the line-of-sight vector, the upper limit of relative positioning error (RPE) can be used as the evaluation parameter of the determination accuracy in scenarios where a high-orbit target is observed by a low-orbit sensor observes. An empirical relationship was also found, indicating that the upper limit of RPE is proportional to the observation error, −2.5 power of the observation arc length, and the 0.5 power of the observation interval.

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Characterizing the Convergence Behavior of Gauss’s Method of Initial Orbit Determination

Cited by 3 publications

References 18 publications

Effect of Observation Geometry on Short-Arc Angles-Only Initial Orbit Determination

Effect of Observation Geometry on Short-Arc Angles-Only Initial Orbit Determination

Differential algebra enabled multi-target tracking for too-short arcs

Positioning Error Estimation Method for Short-Arc Angles-Only Initial Orbit Determination

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