Improved UKF And Its Application In Multi Rate SINS/GPS

With the quick development of navigation system and its application in various fields,the performance of navigation system , such as the accuracy, the reliability and so on, are much more required. In pratical system, most of the system models used are nonlinear, and Extended Kalman filter (Extended Kalman Filter, EKF) is used as the main way to deal with the nonlinear system. EKF is applied to the nonlinear function by using the first oder Taylor expansion,and it is inevitable to introduce the linear error and the truncation error. Unscented Kalman Filter Unscented (UKF) is a nonlinear filtering method, which can be used to approximate the nonlinear system so that the influence of linear error to the system is effectively reduced. Therefore,since the date of its production,it has been widely used in engineering. In this paper, the main work of this paper is to study the UKF expansion:Firstly, commonly used coordinate system and the transformation between the coordinate system in the strapdown inertial navigation system is introduced. Then,derived the mechanical layout equation of the strapdown inertial navigation system,and this basis,the nonlinear error model of the strapdown inertial navigation system is deduced. Otherwise,the way about combination of SINS and GPS is simply introduced, and the structure diagram of each combination mode is given.Secondly, the general form of the Gauss filter is introduced, on this basis, derived UT transform, which is the core of UKF. At the moment, the process of UKF filtering algorithm is also derived. Selected the navigation parameters ,SINS output, as state variables, and the UKF is applied to the combination by direct method, and then do some comparison to EKF.Then, Aiming at the limitations of UKF in the process of application , the QR decomposition and SVD decomposition are proposed to be used in UKF, which can replace the Cholesky decomposition and matrix inversion in UKF. Through this way, the covariance matrix of non-positive or non-] symmetric can be very good avoided. The use of UKF is in the assumption that the system noise and the measurement noise is zero mean white noise, but,the statistical characteristics of the noise may be not completely known, in this case, UKF is not available. Aiming at this problem, the paper proposes a SVD-AQUKF based on the maximum likelihood function estimation, combines QR decomposition and SVD decomposition.The data fusion between GPS and SINS needs to be performed at the same time, but the sampling rate of SINS and GPS is different. Generally, choose the large sampling period as the filtering period, and the data fusion is completed in each large sampling period, which caused the waste of data. According to this problem,this paper proposes the idea of multi rate data fusion. Choose the small sampling period as the filtering period,combinate with UKF,the process of data fusion is divided into time updating and measurement updating. At each filtering time, by judging whether new measurement is used or not, to select which kind of updating to realize, so that the output of both navigation system can be better used, which improve the redundancy and the utilization of the data. And when the GPS output is abnormal,the system will be considered as no new measurement is input, only do the time updating.This also avoids the abnormal work when realize the data fusion which caused by the abnormal GPS subsystem.Combinated the proposed UKF with the ideal of multi rate, and used in SINS/GPS.Selecting the combination of tight mode to achieve data fusion.