An Extended Kalman Filtering Technique for Geodetic First Order Data Assimilation

Abstract Data assimilation allows merging of different sources of data to estimate possible states of a system as it evolves in time. This therefore supports the idea of combining classical observations with Global Positioning System (GPS) observations to improve the integrity of first order geodetic controls in Nigeria. Given that these geodetic controls, which were established using traditional techniques and whose algorithms are still in use, the task of optimizing the coordinate values of these monuments to improve efficiency and accuracy in conventional geodetic operations around Nigeria is still a challenge. This study introduces the Extended Kalman Filter (EKF) technique for the modeling of these observations and their uncertainties in addition to exogenous noise, which is handled by an approximate set-valued state estimator. The proposed EKF provides a feasible linearization process in merging classical and GPS data collection modes as shown in our study. 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 setup, the EKF constrains the system state in order to balance and strengthen the integrity of these first order monuments. The relationship of the derived system state with GPS coordinates (R 2 = 0.85) and classical observations (R 2 = 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 data assimilation techniques in geodetic operations.