Modified Single Propagation Unscented Kalman Filter

When using single-point spread unscented Kalman filter, it is found that there may be large errors in estimating Jacobian matrix model with constant, resulting in poor estimation accuracy and even divergence. An improved single-point propagation unscented Kalman filter algorithm is proposed to solve this problem. By introducing the scaling factor, the influence of large distance between sampling points on the center point is reduced. Furthermore, the estimation accuracy and robustness of the single-point spread unscented Kalman filter algorithm are improved. In the simulation experiment, the ungm model is estimated. The performance of the single-point spread unscented Kalman filter, the unscented Kalman filter and the extended Kalman filter with different scaling factors are compared. A better scaling factor value is obtained. The improved algorithm is used to solve the measured data of indoor positioning, which proves the effectiveness of the algorithm. Introduction Unscented kalman Filter (UKF) is a filtering method for nonlinear systems proposed by S. Julier et al.Unlike the traditional method of linearizing the nonlinear function, UKF uses the unscented kalman filter to deal with the non-linear transfer problem of mean and covariance based on the framework of kalman filter [1-3]. Because sigma points are used to approximate the posterior probability density rather than the non-linear function, UKF does not neglect the higher-order terms, which makes UKF have higher calculation accuracy for the non-linear system and effectively overcomes the shortcomings of low estimation accuracy and poor stability of extended kalman filter (EKF) [4]. UKF has higher accuracy and stability than EKF, but the propagation of sigma points requires a large amount of computation, which makes the computation burden very heavy. In real-time systems, computing time is a major constraint. Many real-time systems have very limited computing power for many reasons [5], which results in sigma point propagation needs a lot of time to calculate, the use of UKF is limited, EKF has become the current preferred. How to solve the problem of large amount of calculation of UKF has become the key to whether UKF can be applied to real-time systems. In the existing research, the most important way to reduce the calculation time of UKF is to reduce the number of sigma points, that is, to improve the way of traceless transformation [6,7]. Julier and Uhlmann proposed a method that only needs to calculate n+1 sigma points [8], and proposed a new method of SSUT (Spherical Simplex Unscented Transform), which improves the computational efficiency but reduces the estimation accuracy to a certain extent. Document [9] proposes the method of using MUT (Marginal Unscented Transformation) to improve the nonlinear model with linear substructures, which has some limitations. In reference [10], a SPUKF algorithm (Single Propagation Unscented Kalman Filter) is proposed, which propagates according to the posterior mean state variables. The sigma point is approximated by the first-order Taylor expansion. In the non-linear vehicle model, the calculation time is reduced by 90.5%-92.6%, which greatly improves the speed of UKF operation. However, in practical application, it is found that this method has a large error in estimating Jacobian matrix model with large constants. In this paper, MSPUKF algorithm (Modified Single Propagation Unscented Kalman Filter) is 378 proposed. The algorithm of SPUKF is improved by introducing scaling factor lambda before Jacobian matrix. In the simulation experiment, the one-dimensional UNGM model and the multi-dimensional uniformly accelerated linear motion model are estimated. SPUKF is compared with UKF and EKF under different scaling factors, and a better scaling factor value is obtained. It is proved that the improved algorithm under this model has higher accuracy than the original algorithm under almost the same computing time. SPUKF SPUKF algorithm is a one-step prediction method similar to EKF in the framework of UKF. It uses sigma point center point and Jacobian matrix to make one-step prediction to reduce computing time. Predictive observations, kalman gain matrix, mean and covariance are calculated in the same way as UKF. The flow chart of the algorithm is as follows: A continuous nonlinear system model is as follows (t) (t,X(t), v(t)) X f  (1) (k) h(X(k)) w(k) Z   (2) where t is time, k is time after discretization, X is an n-dimensional state variable. , (k) Z is observation. , f and h are non-linear functions, v(t) is system noise. , w(k) is measurement noise. Time update The sigma point of the momentis t (t) (t) (i 1,2,3,.2n) i i X X X       (3) ( (n ) P) , 1 ~ i i X i n      (4) ( (n ) P) , 1 ~ 2 i i X i n n        (5) where  is scale the scale parameter to reduce the prediction error, ( )i P is the column of the square root of a matrix of formulas. t t   is the sigma point obtained by UT transformation is