Unscented Kalman Filter And Application On SINS Initial Alignment

Initial alignment is a key technology for SINS. Filter which is state estimation plays a crucial role in the initial alignment. When the error model is linear, Kalman filter has a very good estimation. When the error model is nonlinear, different nonlinear filtering methods have different precision.Unscented Kalman filter (UKF) is a good kind of nonlinear filtering methods, which has a good performance. It has been used widely all the time. The free adjustable parameter is very essential for the precision and stability of filter. When the traditional value of ? meets the relation of n + ?= 3 (n is the dimension of state variable), it thinks the UKF has the most optimal performance all the time. But with the generation of Cubature Kalman Filter (CKF),the traditional value of ? is faced with a huge problem. From the point of filtering method,CKF is a special case of UKF which has the value of ? = 0. The two kinds of filtering methods have different precision with different dimensions. So the ? is the core of the article,it mainly studies the influence of ? for the filtering precision. At the same time, two kinds of modeling UKF were given when the filtering model has a linear equation.Firstly, the article introduces the definitions of characteristics of the gravitational field,the definition of shape which the earth has and the definition of latitude and longitude. It defines the parameters used in the navigation, coordinate system and coordinate transformation. On this basis, it derives the error equations of SINS. It gives the process of augmented and non-augmented UT transformation. At the same time, it gives the augmented and non-augmented of UKF algorithm. In order to compare the methods of filter, it derives the Taylor expansion of the expression of augmented and non- augmented UKF. Being based on it, it analyses the precision of filter with different dimensions and values of adjustable parameters. Simultaneously, it also compares the precision of filters which are based on the mean, variance and odd moment. Thus, it points out that how to select the augmented or non-augmented UKF will be better under both adjustable parameter values.At the same time, it derives the expression of approximate error which is the mean of UKF. And it proves the value of ? is related to the model of system. So it proposes the online adjustment algorithm, namely self-adjusting UKF algorithm. In the algorithm, it chooses the value of ? based on the model throughout the first initial selected value.Moreover,it must achieve a minimum error. Then, the K should be online adjusted which be based on the measured information of one step prediction so as to achieve the good performance. Being compared to the traditional UKF,the self-adjusting UKF can improve the precision at the expense of calculation.When the state equation or the measurement equation is linear, the UKF algorithm will be simplified. So it prives two kinds of modeling UKF. It analyses the calculation of two kinds of modeling UKF. Being compared to the traditional UKF, modeling UKF can ensure the precision of the algorithm, while the calculation will be reduced.At last, being based on the characteristics of initial alignment of nonlinear model about SINS, it puts self-adjusting UKF and modeling UKF to the initial alignment of SINS. They will solve the lower precision and larger calculation respectively. The simulation results show that the two kinds of nonlinear filter are effectiveness. And it provides a strong guarantee of the theory for practical application.