Statistical geodesy—An engineering perspective

Nash, Raymond A.; Jordan, Stanley K.

doi:10.1109/proc.1978.10959

Cited by 36 publications

(20 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First note that (2.14) is equivalent to (2,15) or equivalently that cations in the equations that define our algorithm, and we will discuss these at the end of this section.…”

Section: Yi(t) H(t)x(t)mentioning

confidence: 99%

“…Problems of this type arise in the mapping of gravitational anomalies given data obtained along tracks over the ocean [2,14] and the mapping of meteorological variables from data gathered by …”

Section: Yi(t) H(t)x(t)mentioning

confidence: 99%

“…Other, essentially equally trivial cases can be found in which (3.116) is satisfied, but the condition is quite restrictive. induced in an inertial navigation system aboard a ship [2,9]. In this case we want the (real-time) estimates of y.…”

Section: T1 T1mentioning

confidence: 99%

“…Either a local or regional map is generated for each of these surveys and the problem is either to combine these local maps optimally, or to update an overall map as each new survey becomes available. Problems of this type arise in many applications including the mapping of vertical temperature profiles of the atmosphere given data provided by satellites [1] and the mapping of anomalies in the earth's gravitational field and the effects of such anomalies on errors in inertial navigation systems [2,14].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Combining and updating of local estimates and regional maps along sets of one-dimensional tracks

Willsky

Bello

Castañón

et al. 1982

IEEE Trans. Automat. Contr.

213

View full text Add to dashboard Cite

In this paper we consider the problem of combining and updating estimates that may have been generated in a distributed fashion or may represent estimates, generated at different times, of the same process sample path.The first of these cases has applications in decentralized estimation, while the second has applications in updating maps of spatiallydistributed random quantities given measurements along several tracks. The method of solution for the second problem uses the result of the first, and the similarity in the formulation and solution of these problems emphasizes the conceptual similarity between many problems in decentralized control and in the analysis of random fields.

show abstract

“…First note that (2.14) is equivalent to (2,15) or equivalently that cations in the equations that define our algorithm, and we will discuss these at the end of this section.…”

Section: Yi(t) H(t)x(t)mentioning

confidence: 99%

Section: Yi(t) H(t)x(t)mentioning

confidence: 99%

Section: T1 T1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Combining and updating of local estimates and regional maps along sets of one-dimensional tracks

Willsky

Bello

Castañón

et al. 1982

IEEE Trans. Automat. Contr.

213

View full text Add to dashboard Cite

show abstract

“…A problem of the type just described arises in the mapping of the Earth's gravitational field (Nash and Jordan 1978). A wide variety of sensors, sensitive to different ranges of spatial wavelength, is available for this application.…”

Section: With X(o) = T[i + T;a'(o)e>r(o)a(o)t + T;h'(o)r -1(o)h(o)mentioning

confidence: 99%

Construction and applications of discrete-time smoothing error models

Bello¹,

Willsky

Levy

1989

International Journal of Control

View full text Add to dashboard Cite

We present a unified perspective on techniques for constructing both forward and backward markovian realizations of the error process associated with discrete-time fixed-interval smoothing. Several alternative approaches are presented, each of which provides additional insight and connections with other results in linear estimation theory. In addition, two applications of such models are described. The first is a problem in the validation of an error model for a measurement system, while the second concerns the problems of updating and combining smoothed estimates. We also present an example of the use of our updating solution for the mapping of random fields based on several sets of data tracks. IntroductionThis paper is concerned with the characterization, derivation, and application of markovian models for the error in fixed-interval smoothed estimates. Models of this type are required in several applications, including two that are investigated in the last few sections of this paper. In particular, we describe a model validation process in which one set of data is used to evaluate the validity of a noise model for a second set of data. We also describe a solution to estimate updating and combining problems. In the former, a smoothed estimate based on one set of data is updated with a new set of data. In the latter, estimates based on separate data sets are combined. Such problems arise in the construction of maps of random fields, and we describe an application of this type in which the data sets represent non-coincident and non-parallel tracks across a two-dimensional random field.In each of these applications, smoothing error models are required: in the first problem in order to compute the likelihood function for the validity of the specified model; in the second, to specify a model for the error in the map based on the first set of data which is then used as the basis for incorporating the new data.We consider the construction of smoothing error models from four perspectives:

show abstract