On constrained integrated total Kalman filter for integrated direct geo-referencing

A constrained integrated total Kalman filter algorithm is developed. It considers a quadratic constraint which may appear in some problems of integrated direct geo-referencing in particular when INS data is used as system equations of a Kalman filter algorithm. In such a case one encounters with a dynamic errors-in-variables (DEIV) model for system equations, although DEIV model has been already considered for equations of the Kalman filter algorithm and a solution namely integrated total Kalman filter (ITKF) has been given to it. Also this algorithm can be simplified to unconstraint case which is useful for some problems. It considers DEIV model for both observation equations and system equations of the Kalman filter algorithm. The predicted residuals for all variables including the random noise at the first epoch, the observational noise, the random system noise and the corresponding noise of two coefficient matrixes (in the system equations and the observation equations) besides the variance matrix of the unknown parameters are obtained. In two numerical examples, integrated direct geo-referencing problem is solved for a GPS-INS system.