Abstract
The integration of Strap-down Inertial Navigation System (SINS) and Global Positioning System(GPS)can not merely reduce the error of navigation system, which would enhance the system dynamic performance. GPS Carrier phase rate is a high-precision measurement without integer ambiguity problem. Moreover, only one GPS receiver is needed for SINS/GPS carrier phase rate integrated navigation system. The measurement of GPS carrier phase rate is derived and a integrated scheme of SINS and GPS carrier phase rate is proposed. Common used nonlinear filter, extended Kalman filter (EKF) has high-order truncation errors which affects the system accuracy. An improved cubature Kalman filter(CKF) used square root is introduced. The square-root CKF calculate avoids calculating the Jacobian matrix and has better estimate precision.
Highlights
GPS carrier phase rate eliminates the integer ambiguity problem
The velocity of the carrier can be obtained by deriving the GPS carrier rate, which can be used to combine Strap-down Inertial Navigation System (SINS)[1]to be a loose coupled system[2].As a original Observation, carrier phase rate can be combined with output from SINS[3].The carrier phase rate measurement model is derived and the combination principle is explanted
In order to improve the precision of the intergraded system, square-root cubature Kalman filter (CKF) is introduced to make nonlinear filtering
Summary
GPS carrier phase rate eliminates the integer ambiguity problem. EKF is effective only when the nonlinear system is approximate linear, which reach only first order accuracy[4].And EKF needs to calculate the Jacobian matrix, which is trivial. In order to improve the precision of the intergraded system, square-root CKF is introduced to make nonlinear filtering. According to spherical-radial cubature rule[5], CKF does't need to linearize the nonlinear equation and it can reach three order accuracy[6].Commonly used Kalman filter has stability problem. The square-root CKF can ensure half positive definitiveness of the covariance matrix and improve the stability of filter process. Results show that square-root CKF can get less error than EKF for the integrated system
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