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Least-Squares Estimation and Kalman Filtering

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Springer Handbook of Global Navigation Satellite Systems

Part of the book series: Springer Handbooks ((SHB))

Zusammenfassung

This chapter presents the estimation and filtering principles as used in global navigation satellite system (GlossaryTerm

GNSS

) data processing. Estimation and filtering are concerned with retrieving or recovering parameters of interest from noisy measurements. The least-squares (LS) principle is the standard approach for estimating unknown parameters from uncertain data. Various forms of LS estimation, such as partitioned-LS, recursive-LS, constrained-LS, and nonlinear-LS, are discussed.

The parameters of interest, as well as the dominant error sources, are often time varying. If these time variations can be modeled, the parameters can be resolved based on minimum mean squared error prediction, filtering, and smoothing techniques. Of the various such techniques, the Kalman filter is most prominent. It recursively estimates the state of a dynamic system. Different forms of the Kalman filter are discussed, together with its linkage to recursive smoothing techniques. Several GNSS examples are included in support of the general introduction on the principles and properties of LS estimation and Kalman filtering.

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Abbreviations

BLUE:

best linear unbiased estimation

BLUP:

best linear unbiased prediction

CORS:

continuously operating reference station

EKF:

extended Kalman filter

GNSS:

global! navigation satellite system

GPS:

Global Positioning System

IGS:

International GNSS Service

MLE:

maximum likelihood estimation

PDF:

probability density function

WLS:

weighted least-squares

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Acknowledgements

The second author is the recipient of an Australian Research Council Federation Fellowship (project number FF0883188). This support is gratefully acknowledged.

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Authors and Affiliations

  1. Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628 CN, Delft, Netherlands

    Sandra Verhagen

  2. Dept. of Spatial Sciences, Curtin University, WA 6845, Perth, Australia

    Peter J.G. Teunissen

Authors
  1. Sandra Verhagen
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  2. Peter J.G. Teunissen
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Corresponding author

Correspondence to Sandra Verhagen .

Editor information

Editors and Affiliations

  1. Dept. of Spatial Sciences, Curtin University, WA 6845, Perth, Australia

    Peter J.G. Teunissen

  2. Department of Geoscience and Remote Sensing, Delft University of Technology, 2600 GA, Delft, Netherlands

    Peter J.G. Teunissen

  3. German Aerospace Center (DLR), Münchener Str. 20, 82234, Wessling, Germany

    Oliver Montenbruck

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Verhagen, S., Teunissen, P.J. (2017). Least-Squares Estimation and Kalman Filtering. In: Teunissen, P.J., Montenbruck, O. (eds) Springer Handbook of Global Navigation Satellite Systems. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-42928-1_22

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