Geodetic first order data assimilation using an extended Kalman filtering technique

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.