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Geodetic first order data assimilation using an extended Kalman filtering technique

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Abstract

The poor horizontal reference frame in Nigeria lacks the integrity of a twenty-first century geodetic frame because the traditional techniques, which were used in developing them had limited accuracy and are now obsolete. These geodetic controls are still in use today, especially in the execution of local geodetic operations around the country. To address this problem (e.g., poor accuracy) and improve the integrity of first order geodetic controls in Nigeria, we propose an optimization model for these controls to improve their efficiency and accuracy by integrating classical geodetic observations with data from the Global Positioning System (GPS) using the Extended Kalman Filtering (EKF) technique. Specifically, the overall aim of this study is to introduce the EKF technique through data assimilation (DA) for the modeling of these observations and their uncertainties in addition to exogenous noise. Results from this study show that the proposed EKF provides a feasible linearization process in merging classical and GPS data collection modes. For each discrete time in the analysis step, it employs the Kalman gain computation, which attempts to weigh and balance uncertainties between the estimate and observation before proceeding to the analysis step. In this experimental setup, the EKF constrains the system state in order to balance and strengthen the integrity of these first order geodetic monuments. The relationship of the derived system state with GPS coordinates (R2 = 0.85) and classical observations (R2 = 0.92) over Nigeria using a multi linear regression analysis is considerably strong. This outcome provides insight to the performance of the test algorithm and builds on the usefulness of DA techniques in geodetic operations.

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Data availability

One hundred and fifty-seven first-order geodetic controls spread across Nigeria were used in this study. These controls were obtained from the office of the surveyor general of the Nigerian federation (OSGOF) and made available for academic purposes and not yet available to the general public.

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Acknowledgments

The authors are grateful to the office of the surveyor general of Nigeria (OSGOF), and the department of geoinformatics and surveying, University of Uyo, for all the data used in this study.

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Authors and Affiliations

  1. Department of Geoinformatics & Surveying, University of Uyo P.M.B., Uyo, 1017, Nigeria

    Ikechukwu Kalu, Onuwa Okwuashi & Aniekan E. Eyoh

  2. School of Environment & Science, Griffith University, Nathan, QLD 4111, Australia

    Christopher E. Ndehedehe

  3. Australian Rivers Institute, Griffith University, Nathan, QLD 4111, Australia

    Christopher E. Ndehedehe

  4. School of Earth Sciences and Engineering, Hohai University, Nanjing, China

    Vagner G. Ferreira

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  1. Ikechukwu Kalu
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  2. Christopher E. Ndehedehe
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  4. Aniekan E. Eyoh
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  5. Vagner G. Ferreira
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Contributions

Ikechukwu Kalu: Writing – original draft, Writing – review & editing, Methodology, Formal analysis, Conceptualization, Investigation, Software. Christopher E. Ndehedehe: Conceptualization, Writing – original draft, Writing – review & editing, Supervision, Software. Onuwa Okwuashi: Conceptualization, Writing – review & editing, Formal analysis. Aniekan Eyoh: Resources. Vagner G. Ferreira: Conceptualization, Writing – review & editing, Formal analysis.

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Correspondence to Christopher E. Ndehedehe.

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Communicated by: H. Babaie

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Kalu, I., Ndehedehe, C.E., Okwuashi, O. et al. Geodetic first order data assimilation using an extended Kalman filtering technique. Earth Sci Inform 15, 2585–2599 (2022). https://doi.org/10.1007/s12145-022-00869-6

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