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A solution to dynamic errors-in-variables within system equations

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Abstract

We noticed that if INS data is used as system equations of a Kalman filter algorithm for integrated direct geo-referencing, one encounters with a dynamic errors-in-variables (DEIV) model. Although DEIV model has been already considered for observation equations of the Kalman filter algorithm and a solution namely total Kalman filter (TKF) has been given to it, this model has not been considered for system equations (dynamic model) of the Kalman filter algorithm. Thus, in this contribution, for the first time we consider DEIV model for both observation equations and system equations of the Kalman filter algorithm and propose a least square prediction namely integrated total Kalman filter in contrast to the TKF solution of the previous approach. The variance matrix of the unknown parameters are obtained. Moreover, the residuals for all variables are predicted. In a numerical example, integrated direct geo-referencing problem is solved for a GPS–INS system.

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Authors and Affiliations

  1. School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Vahid Mahboub, Mohammad Saadatseresht & Alireza A. Ardalan

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  1. Vahid Mahboub
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  2. Mohammad Saadatseresht
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  3. Alireza A. Ardalan
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Correspondence to Mohammad Saadatseresht.

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Mahboub, V., Saadatseresht, M. & Ardalan, A.A. A solution to dynamic errors-in-variables within system equations. Acta Geod Geophys 53, 31–44 (2018). https://doi.org/10.1007/s40328-017-0201-0

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