# Candidate Orbital Covariance Matrix Types

**Policy**: Expert Review

**Authority**: CCSDS.MOIMS.NAV

**OID**: 1.3.112.4.57.6

**References**:

## Contents

**16** records in registry

#### Object Identifier

#### Label

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Details | Status | Name | Description And Reference | Nomenclature | Default Units/Type | References | OID | |
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Provisional |
TADBARV |
7x7: Time & Spherical 6-element set errors (right ascension +E°, declination +N°, inertial flight path angle measured from the radial direction to inertial velocity direction (e.g. 90° for circular orbit), inertial azimuth angle measured from local North to projection of inertial velocity in local horizontal plane, radius magnitude, and velocity magnitude) |
\(T, α, δ, β, A, r, v \) |
$$1 \times s,$$$$4 \times deg,$$$$1 \times km,$$$$1 \times \frac{km}{s}$$ |
1.3.112.4.57.6.1 |
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Provisional |
TCARTP |
4x4: Time & Cartesian 3-element position errors (X, Y, Z) |
T, X, Y, Z |
$$1 \times s,$$$$3 \times km$$ |
1.3.112.4.57.6.2 |
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Provisional |
TCARTPV |
7x7: Time & Cartesian 6-element position and velocity errors (X, Y, Z, XD, YD, ZD) |
T, X, Y, Z, XD, YD, ZD |
$$1 \times s,$$$$3 \times km,$$$$3 \times \frac{km}{s}$$ |
1.3.112.4.57.6.3 |
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Provisional |
TCARTPVA |
10x10: Time & Cartesian 9-element position, velocity, and acceleration errors (X, Y, Z, XD, YD, ZD, XDD, YDD, ZDD) |
T, X, Y, Z, XD, YD, ZD, XDD, YDD, ZDD |
$$1 \times s,$$$$3 \times km,$$$$3 \times \frac{km}{s},$$$$3 \times \frac{km}{s^2}$$ |
1.3.112.4.57.6.4 |
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Provisional |
TDELAUNAY |
7x7: Time & Delaunay element errors as defined in David A. Vallado, Fundamentals of Astrodynamics and Applications, 4th Ed., Microcosm Press and Springer, ISBN 978-1881883180. Delaunay elements employ a set of canonical action-angle variables, which are commonly used in general perturbation theories. The element set consists of three conjugate action-angle pairs. Lower case letters represent the angles while upper case letters represent the conjugate actions. Delaunay variables coordinate type is not available if a Fixed coordinate system is selected. |
$$T,$$$$l_{d} = M,$$$$g_{d} = ω,$$$$h_{d} = Ω,$$$$L_{d} = \sqrt{μa},$$$$G_{d} = h = \sqrt{μp},$$$$H_{d} = \sqrt{μa (1 - e^2)} \cos{i}$$ |
$$1 \times s,$$$$3 \times deg,$$$$3 \times \frac{km^2}{s}$$ |
1.3.112.4.57.6.5 |
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Provisional |
TDELAUNAYMOD |
7x7: Time & Modified Delaunay element errors (where the Modified Delaunay elements are a geometric version of the Delaunay set independent of the central body, with \(L_{d}, G_{d} \;and\; H_{d}\) “action” variables of the standard Delaunay element set divided by the square root of the central-body gravitational constant). |
$$T,$$$$l_{dm} = M,$$$$g_{dm} = ω,$$$$h_{dm} = Ω,$$$$L_{dm} = \sqrt{a},$$$$G_{dm} = \sqrt{p},$$$$H_{dm} = \sqrt{a (1 - e^2)} \cos{i}$$ |
$$1 \times s,$$$$3 \times deg,$$$$3 \times \sqrt{km}$$ |
1.3.112.4.57.6.6 |
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Provisional |
TEIGVAL3EIGVEC3 |
13x13: Time & 12-element eigenvalue/eigenvector representation time history errors (corresponding to the 3x3 position covariance time history, with each line containing Time, the three (major, medium and minor) eigenvalues IN DESCENDING ORDER, and the corresponding three eigenvectors matching the major, medium, and minor eigenvalues). |
$$T,$$$$EigMaj,$$$$EigMed,$$$$EigMin,$$$$EigVecMaj,$$$$EigVecMed,$$$$EigVecMin$$ |
$$1 \times s,$$$$3 \times km,$$$$9 \times NonDim$$ |
1.3.112.4.57.6.7 |
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Provisional |
TEQUINOCTIAL_P |
7x7: Time & Equinoctial 6-element set errors as defined in David A. Vallado, Fundamentals of Astrodynamics and Applications, 4th Ed., Microcosm Press and Springer, ISBN 978-1881883180 (omitting \(f_{r}\) from the set, with \(f_{r} = +1\), valid for all orbits except for inclinations at or near 180°). |
$$T,$$$$a,$$$$a_{f} = e \cos{(ω + Ω)},$$$$a_{g} = e \sin{(ω + Ω)},$$$$χ = \tan{(\frac{i}{2}) \sin{Ω}},$$$$ψ = \tan{(\frac{i}{2}) \cos{Ω}},$$$$L = (M + ω + Ω )$$ |
$$1 \times s,$$$$1 \times km,$$$$4 \times NonDim,$$$$1 \times deg$$ |
1.3.112.4.57.6.8 |
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Provisional |
TEQUINOCTIAL_N |
7x7: Time & Equinoctial 6-element set errors as defined in David A. Vallado, Fundamentals of Astrodynamics and Applications, 4th Ed., Microcosm Press and Springer, ISBN 978-1881883180 (omitting \(f_{r}\) from the set, with \(f_{r} = -1\) valid for all orbits except for inclinations at or near 0°). |
$$T,$$$$a,$$$$a_{f} = e \cos{(ω - Ω)},$$$$a_{g} = e \sin{(ω - Ω)},$$$$χ = \cot{(\frac{i}{2}) \sin{Ω}},$$$$ψ = \cot{(\frac{i}{2}) \cos{Ω}},$$$$L = (M + ω - Ω )$$ |
$$1 \times s,$$$$1 \times km,$$$$4 \times NonDim,$$$$1 \times deg$$ |
1.3.112.4.57.6.9 |
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Provisional |
TEQUINOCTIALMOD_P |
7x7: Time & Modified Equinoctial element set errors per David A. Vallado, Fundamentals of Astrodynamics and Applications, 4th Ed., Microcosm Press and Springer, ISBN 978-1881883180, (omitting \(f_{r}\) from the set, with \(f_{r} = +1\) valid for all orbits except for inclinations at or near 180°). |
$$T,$$$$p = a (1 - e^2),$$$$a_{f} = e \cos{(ω + Ω)},$$$$a_{g} = e \sin{(ω + Ω)},$$$$χ = \tan{(\frac{i}{2}) \sin{Ω}},$$$$ψ = \tan{(\frac{i}{2}) \cos{Ω}},$$$$L'= (ν + ω + Ω)$$ |
$$1 \times s,$$$$1 \times km,$$$$4 \times NonDim,$$$$1 \times deg$$ |
1.3.112.4.57.6.10 |

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