The pseudorange measurement equations and their solution for satellite navigation

The common pseudorange measurement equations and their solution for satellite navigation are discussed. The errors in these pseudorange measurement equations computed with mathematical models will increase the load of computation and will usually lead to poor results due to change of conditions. In this paper the new pseudorange hyperboloidic measurement equations subject to height constraint for satellite navigation are developed and demonstrated. For these equations are all nonlinear, the methods of solving these nonlinear equations must be sought. The linearization of these nonlinear equations must be done before the iterative computation, but it is usually difficult to compute the Jacobian matrix of the nonlinear equations. The Unscented Kalman Filter (UKF) is presented for its ease of implementation and more accuracy for nonlinear equations. As a result, these nonlinear pseudorange measurement equations subject to height constraint solved with the UKF performs better than the common measurement equations computed with the iterative method. The conclusion is testified with experimental results last.