Self-Contained Satellite Navigation Systems

Frazier, Melissa; Kriegsman, B. A.; Nesline, F.

doi:10.2514/3.2058

Cited by 9 publications

(8 citation statements)

References 2 publications

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“…No uncorrelated errors are included as their presence would tend to mask the effect to be studied. The results of Frazier et al 1 of observables rather than the repetition of essentially identical measurements, an improvement in performance would be expected. Rotation of the horizon tracker as a method of changing the observables seems worthy of investigation.…”

Section: Radar Altimetermentioning

confidence: 87%

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Self-contained orbital navigation systems with correlated measurement errors.

Wilcox¹

1966

Journal of Spacecraft and Rockets

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A self-contained orbital navigation system using earth horizon measurements in the 14-16 ju carbon dioxide absorption band is analyzed using Kalman's linear filter theory. The spatial correlation of the horizon height deviations is converted into time correlation of the sensor measurement errors. The orbital dynamics, horizon phenomenology, and the horizon tracker, star tracker, radar altimeter, and inertial measurement unit instrument errors are represented by linearized differential equations in the Kalman canonical form. A generalized error analysis computer program is used to perform the calculations. The results demonstrate that high sampling rates, which produce marked improvement in performance in the presence of uncorrelated errors, are of no value for reducing the effects of correlated errors for the chosen set of observables. The system performance as a function of time is presented for different values of the error sources. The efficacy of a radar altimeter in reducing the inplane navigation error, especially during the initial transient, is shown. Nomenclature a, b = possible values of ka A = matrix in canonical differential equation B = transformation matrix for horizon height measurements d = const of integration d = horizon deviations reduced to position errors D = transformation matrix for horizon height measurements E = gravitation matrix h = horizon tracker instrument error I = identity matrix kjj -const in autocorrelation function K = Kalman filter matrix M = measurement matrix n = number of states 0 = zero vector O = zero matrix p = covariance matrix of state vector Q = covariance matrix of errors caused by white noise r = perturbation position vector R = nominal position vector R = earth radius matrix R e = radius of earth s = time since last fix S = star tracker instrument error S = covariance matrix of white noise sources t -time u = white noise column vector v = inertial velocity vector w = error caused by white noise column vector We* = acceleration time constant matrix x = state column vector x = estimated state column vector x = error in estimated state column vector y = measurement column vector a = acceleration uncertainty vector p t = horizon tracker measurement angles Presented at the AIAA/ION Guidance and Control Conference, August 16-18, 1965 (no preprint number; published in bound volume of preprints of the meeting); T = gyro drift rate vector 5 = Dirac delta function 8= great circle distance between measurement points 5 e = characteristic distance for horizon deviations €t = horizon height deviations n = IMU misalignment vector from computed local vertical coordinate system 0 = geocentric range angle X = auxiliary variable fj, = gravitational const of earth p = position vector a = standard deviation of error source; subscripts h, s, and e refer to horizon tracker instrument, star tracker, and horizon deviation, respectively T = time const of error source Td = horizon deviation time const as seen by instrument T 6 = horizon deviation time const c = autocorrelation function of...

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Section: Radar Altimetermentioning

confidence: 87%

“…The state variables of the system and the error sources are combined into the n vector x, referred to as the state vector. The differential equations of the system are represented by (Ox (1) where A is an n x n matrix whose coefficients are functions of time, and u is an n vector Gaussian white noise process such that and <u(*)> = 0…”

Section: Kalman Modelmentioning

confidence: 99%

Self-contained orbital navigation systems with correlated measurement errors.

Wilcox¹

1966

Journal of Spacecraft and Rockets

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“…±3ca; = ±6y (hr (11)(12)(13)(14)(15)(16) The first solutions (±ju>) are oscillatory. The second set implies instability when positive sign applies (major axis) and stability in the other case (minor axis).…”

Section: Effects Of Equatorial Ellipticity On Synchronous Orbitsmentioning

confidence: 99%

“…Thus, we can conclude that if one uses as variables the radius and the geocentric longitude observed once per day, one can study the satellite drift in a neighborhood of the minor axis from the simple decoupled Lqs. (II - 19) and (11)(12)(13)(14)(15)(16)(17)(18)(19)(20).…”

Section: ^ Vttt^mentioning

confidence: 99%

Automatic Orbit Control of the Lincoln Experimental Satellite Les-6

Braga-Illa¹

1969

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“…14 " 23 The most complete study is perhaps Battin's 16 ; he also solved the interesting problem of selecting the best star to use as a reference in making angular measurements. Frazier et al 17 examined the possibility of approximating the values of satellite anomaly and the subtense of the principal body with polynomials in time and found that in general it is preferable to use the linearized form of the known dynamic equations to smooth the data, leading to more complex data processing requirements.…”

Section: Introductionmentioning

confidence: 99%

Orbit determination from the satellite.

Braga-Illa

1969

Journal of Spacecraft and Rockets

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This paper presents simple methods for determining moderately eccentric orbits from the satellite; linear combinations of time-of-flight measurements are used exclusively. The method is based on a third-order expansion of the satellite law of motion in terms of orbital eccentricity €. Thus, the approximation is very good for e < 0.1. The worst-case error in determining the center of the earth with these methods is | e 2 rad. A simple technique, which is insensitive to systematic sensor errors, is proposed to circularize an orbit automatically. Another application is the automatic station-keeping of satellites, which has been realized for the first time, using the ideas of this paper, in the recently launched Lincoln Experimental Satellite LES-6. With respect to the effect of spin-or yaw-axis misalignment on the orbit determination accuracy, a ^worst-case error of ~ 0.5° in anomaly is seen to result from 1.0°m isalignment.

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Self-Contained Satellite Navigation Systems

Cited by 9 publications

References 2 publications

Self-contained orbital navigation systems with correlated measurement errors.

Self-contained orbital navigation systems with correlated measurement errors.

Automatic Orbit Control of the Lincoln Experimental Satellite Les-6

Orbit determination from the satellite.

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