# Orbital Covariance Matrix Types

Creation date: 2019-07-08 17:22:09 Update date: 2019-08-19 15:31:18

Policy: Expert Review

Authority: CCSDS.MOIMS.NAV

OID: 1.3.112.4.57.6

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## Contents

16 records in registry

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1.3.112.4.57.6
Orbital Covariance Matrix Types

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Details Status Name Description And Reference Nomenclature Default Units/Type References OID

Provisional

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

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

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

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

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

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

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

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

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

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

Provisional

TEQUINOCTIALMOD_N

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 0°).

$$T,$$$$p = a (1 - e^2),$$$$a_{f} = e \cos{(ω - Ω)},$$$$a_{g} = e \sin{(ω - Ω)},$$$$χ = \cot{(\frac{i}{2}) \sin{Ω}},$$$$ψ = \cot{(\frac{i}{2}) \cos{Ω}},$$$$L' = (ν + ω - Ω)$$

$$1 \times s,$$$$1 \times km,$$$$4 \times NonDim,$$$$1 \times deg$$

1.3.112.4.57.6.11

Provisional

TGEODETIC

7x7: Time & geodetic elements errors (longitude, geodetic latitude, fixed frame flight path angle, fixed frame azimuth, altitude above oblate spheroid, and velocity relative to the fixed frame).

$$T, λ, ϕ_{GD}, β, Α, h, v_{rel}$$

$$1 \times s,$$$$4 \times deg,$$$$1 \times km,$$$$1 \times \frac{km}{s}$$

1.3.112.4.57.6.12

Provisional

TKEPLERIAN

7x7: Time & Keplerian 6-element classical set errors ($$aeiΩων$$: semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and true anomaly).

$$T, a, e, i, Ω, ω, ν$$

$$1 \times s,$$$$1 \times km,$$$$1 \times NonDim,$$$$4 \times deg$$

1.3.112.4.57.6.13

Provisional

TKEPLERIANMEAN

7x7: Time & Keplerian 6-element classical set errors ($$aeiΩωM$$: semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and mean anomaly).

$$T, a, e, i, Ω, ω, M$$

$$1 \times s,$$$$1 \times km,$$$$1 \times NonDim,$$$$4 \times deg$$

1.3.112.4.57.6.14

Provisional

TLDBARV

7x7: Time & modified spherical 6-element set errors (Earth longitude +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).

$$T, λ, δ, β, A, r, v$$

$$1 \times s,$$$$4 \times deg,$$$$1 \times km,$$$$1 \times \frac{km}{s}$$

1.3.112.4.57.6.15

Provisional

TPOINCARE

7x7: Time & canonical counterpart of equinoctial 6-element set errors. See David A. Vallado, Fundamentals of Astrodynamics and Applications, 4th Ed., Microcosm Press and Springer, ISBN 978-1881883180).

$$T,$$$$(λ_{M} = M + ω + Ω) ,$$$$g_{p},$$$$h_{p},$$$$L_{p},$$$$G_{p},$$$$H_{p}$$

$$1 \times s,$$$$1 \times deg,$$$$2 \times \frac{km}{s^{0.5}},$$$$1 \times \frac{km^2}{s},$$$$2 \times \frac{km}{s^{0.5}}$$

1.3.112.4.57.6.16