Control Segment and User Performance

Russell, S. S.; Schaibly, John H.

doi:10.1002/j.2161-4296.1978.tb01327.x

Cited by 15 publications

(9 citation statements)

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“…where the pij are the elements of the error covariance matrix P. Now, our objective will be to determine the particular linear combination in (1) which results in a relatively large a2 in (2). Since a large cr2 would indicate poor observability, this term should be maximized subject to the constraint vTv = 1.…”

Section: Significance Of the Eigenvalues And Eigenvectors Of The Erromentioning

confidence: 99%

“…This has made it feasible to implement considerably more complicated filters than one would have dreamed possible 20 years ago. For example, in the global positioning system (GPS) ground control segment, the state vector being estimated will contain over 200 elements when the system becomes fully operational [2].In complex estimation applications, it becomes most difficult for the analyst to maintain good physical insight into the problem. The difficulty with most computer analyses of higher order systems is that the analyst is provided with an utter deluge of information without, at the same time, being provided with means of sorting the relatively important information from that which is not.…”

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Observability, Eigenvalues, and Kalman Filtering

Ham

Brown

1983

IEEE Trans. Aerosp. Electron. Syst.

189

106

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In higher order Kalman filtering applications the analyst often has very little insight into the nature of the observability of the system. For example, there are situations where the filter may be estimating certain linear combinations of state variables quite well, but this is not apparent from a glance at the error covariance matrix. It is shown here that the eigenvalues and eigenvectors of the error covariance matrix, when properly normalized, can provide useful information about the observability of the system. In the two decades since R.E. Kalman [1] introduced the idea of least square recursive filtering, there have been fantastic advances in computer technology. This has made it feasible to implement considerably more complicated filters than one would have dreamed possible 20 years ago. For example, in the global positioning system (GPS) ground control segment, the state vector being estimated will contain over 200 elements when the system becomes fully operational [2].In complex estimation applications, it becomes most difficult for the analyst to maintain good physical insight into the problem. The difficulty with most computer analyses of higher order systems is that the analyst is provided with an utter deluge of information without, at the same time, being provided with means of sorting the relatively important information from that which is not. The discussion that follows is intended to help the analyst with this sorting process and to help provide additional insight into complicated estimation problems.It is certainly apparent to those familiar with estimation and control theory that there is a close connection between observability and estimation. Observability in a deterministic sense simply means that an observation of the output over the time span (0,t) provides sufficient information to determine the initial state of the system [3]. This, along with knowledge of the system driving function, uniquely specifies the state at any other time within the interval. However, there are problems in applying the observability concept to complicated situations. The difficulties are essentially twofold: (1) The test for observability is not easy to apply in higher order systems. In a fixed-parameter system it requires determination of the rank of a large rectangular matrix; in a time-variable system it suffices to say that the usual test is even more difficult to apply [3]. (2) Even when one can apply the test of observability successfully, it only provides a yes-no type answer. It tells one nothing about the degree of observability. One might think that these difficulties are solved by doing off-line Kalman filter analysis, and, in a sense, this is true. However, as mentioned before, the problem here is that the computer tells the analyst more than he wants to know. In a few minutes a computer can output more numbers than one can intelligently digest in months of study! Allowing for symmetry, there are n(n + 1)/2 terms to examine in the error covariance matrix. If n = 200, the analyst must at least glan...

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Section: Significance Of the Eigenvalues And Eigenvectors Of The Erromentioning

confidence: 99%

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confidence: 99%

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Observability, Eigenvalues, and Kalman Filtering

Ham

Brown

1983

IEEE Trans. Aerosp. Electron. Syst.

189

106

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“…The spacecraft-centered coordinates ( The strategy adopted for fine tuning of the solar pressure parameters was to adjust G•, Gy, G: per satellite as constant parameters over the multiday arc. Nominal solar radiation pressure parameters were taken from the hybrid postfit ephemeris supplied by the Naval Surface Weapons Center (NSWC) [Russel and Schaibly, 1978]. That ephemeris was considered to be accurate to about 15-25 m (1 m in altitude, 15 m in each of cross-track, and downtrack components) and was determined from a 1-week batch fit (with up to 1-week orbit prediction).…”

Section: Solar Radiation Pressure Modelmentioning

confidence: 99%

Strategies for high‐precision Global Positioning System orbit determination

1987

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High‐precision orbit determination of Global Positioning System (GPS) satellites is a key requirement for GPS‐based precise geodetic measurements and precise low‐Earth orbiter tracking. We explore different strategies for orbit determination with data from 1985 GPS field experiments. The most successful strategy uses multiday arcs for orbit determination and incorporates fine tuning of spacecraft solar pressure coefficients and stochastic station zenith tropospheric delays using the GPS data. Average rms orbit repeatabilities for five of the GPS satellites are 1.0, 1.2, and 1.7 m in altitude, cross‐track, and downtrack components, when two independent 5‐day fits are compared. Orbits predicted up to 24 hours outside a 7‐day arc show average rms component differences of 1.5–2.5 m when compared to independent solutions obtained with a separate, nonoverlapping 5‐day arc. For a 246‐km baseline, with 6‐day arc carrier phase solutions for GPS orbits, baseline repeatability is 2 parts in 108 (0.4–0.6 cm) for east, north, and length components and 8 parts in 108 for the vertical component. For a 1314‐km baseline with the same orbits, baseline repeatability is about 2 parts in 108 for the north component (2.5 cm) and 4 parts in 108 or better for east, length, and vertical components. When GPS carrier phase is combined with pseudorange, the 1314‐km baseline repeatability improves further to 5 parts in 109 for the north (0.6 cm) and 2 parts in 108 for the other components (2–3 cm).

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“…The satellite position error vectors RAD, ATK, and XTK are in the radial, along-track, and crosstrack directions, respectively. The relationship among the angle o, the radius of the satellite's orbit R,, the radius of the user R,, and the earth angle E (SOR or SOU) between the satellite and the user and reference station is given in equation (2).…”

Section: Introductionmentioning

confidence: 99%

Extended Differential GPS

Brown

1989

Navigation

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The Radio Technical Commission for Maritime Services (RTCM) Special Committee (SC)‐104 on Differential GPS has established a standard data format for providing differential GPS services. The satellite pseudorange corrections that are broadcast in the RTCM SC‐104 differential GPS navigation message lump together the errors from a number of different sources. This results in a degradation of the differential navigation accuracy if the user is operating at a distance from the differential reference station. Generally, the user must be within 100 nmi of the reference station to benefit fully from the differential GPS corrections. This paper presents an Extended Differential GPS concept that extends the range of operation of the differential GPS message. By using a network of differential GPS stations, one can compute a differential GPS message that provides corrections for the different components of the pseudorange error. This allows the differential GPS navigation accuracy to be extended to a range of 1000 nmi from the master differential station.

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Control Segment and User Performance

Cited by 15 publications

References 0 publications

Observability, Eigenvalues, and Kalman Filtering

Observability, Eigenvalues, and Kalman Filtering

Strategies for high‐precision Global Positioning System orbit determination

Extended Differential GPS

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