GNSS DOPPLER VELOCITY BASED ON ADAPTIVE ROBUST KALMAN FILTERING

The main factors affecting the error of Doppler velocity measurement mainly come from the measurement errors of GNSS data, influence of different motion states on GNSS velocity measurement and the noise of different receiver types. To improve the precision of GNSS velocity estimation, an algorithm of adaptive robust Kalman filter based on the PDOP was put forward. PDOP value as well as the number of satellite in each epoch are used as a criterion in the velocity processing. While the PDOP value is greater than the threshold value, which means the observation accuracy is low, then the robust Kalman filter based on IGG – III scheme is introduced. While the PDOP value is between the threshold values, which means the observation precision is normal, adaptive factor could be determined normally, and the single-factor three-stage adaptive model is applied for Kalman filtering. If the above two conditions are not consistent, it indicates that the prediction accuracy of the local epoch satellite is high, and Kalman filtering can be directly used. Through the experiment of shipborne GNSS velocity measurement, it was proved that comparing with conventional least square, the algorithm based on the adaptive robust Kalman filtering can improve the accuracy and stability of the GNSS velocity determination.


INTRODUCTION
Velocity based on the position difference, Doppler, carrier-phase derived Doppler are the three common ways of the velocity estimation.position difference mainly using precise coordinates of GNSS with adjacent epoch, the original Doppler calculated the instantaneous GNSS velocity, which related to the type of receiver, and the out Doppler is derived by carrier phase observations in adjacent epoch with high precision, but which need to eliminate the influence of the cycle slip (Zheng ,Tang, 2015). Kalman filtering is the most commonly used in GNSS position and velocity estimation (Wang, Liang, 2018;Li et al. 2018). In theory, as the grown in quantity of observation data, more accurate valuation could be obtained by the state of the Kalman filter. But sometimes the noise of GNSS dynamic motion may not be able to accurately model or is not a normal distribution, so the accuracy of the results of using Kalman filter for dynamic calculating may be affected, which lead to larger error between actual state and the state. At the same time, the filtering divergence phenomenon happens (Gao S et al. 2011).
In order to solve the above problem, scholars have successively put forward the adaptive Kalman filter algorithm and apply it in dynamic navigation and positioning. A new adaptive differential filtering theory was established , which applies the principle of differential resistance estimation to control abnormal observations, and introduces the adaptive factor to control the effect of the error in dynamic model. Four kinds of error learning statistics were successively constructed, namely, state mismatch statistics , prediction residual statistics (Yang ,Gao,2006), the variance component ratio statistics based on observation information and dynamic model prediction information (Yang,Xu,2003), and the mismatch statistics based prediction velocity model and calculation velocity (Cui ,Yang,2006).Four kinds of adaptive factors were established, namely three-segment function model (Yang et al.2001), two-segment function model ), exponential function model (Yang ,Gao,2005) and weight function model (Ren et al. 2005). When multi-factor becomes single factor, multi-factor adaptive filtering is single factor adaptive filtering. While only the position parameter factor and velocity factor are included in the multi-factor, the multi-factor adaptive filter becomes the classification factor adaptive filter.
Adaptive robust Kalman filtering can effectively restrain the influence of the error in abnormal observation and error in dynamic model. Based on this, an adaptive Kalman filtering algorithm for out Doppler velocity based on single point station was put forward. the method select the resistance model and adaptive model based on the PDOP value and the number of the satellite in each epoch, using IGGIII estimation scheme to control the effect of abnormal observations, at the same time, using the single-factor three-stage adaptive model to adjust the proportion between the covariance matrix of the predicted value and the covariance matrix of state vector. In order to test the accuracy of the algorithm, through a set of shipborne GNSS/INS dynamic test data, the accuracy of the velocity filtering method and the least squares velocity measurement in this paper were compared and analyzed.
2.1 Principle of GPS single point velocity measurement GNSS Pseudo-range difference is a widely used differential positioning technology. Its principle is to set up a reference station on a known coordinate point, calculate the true distance between the reference station and the satellite through the known coordinate, and then make a difference between the calculated true distance and the observed pseudo-distance to obtain pseudo-distance correction and send it to the user for correction.
Pseudo-range observation equation (XU et al. 2016): (1) Deriving the pseud-orange observation equation: In the formula,  is the carrier wavelength; Out Doppler observations using the adjacent epoch differential structure can effectively eliminate the ambiguity parameters.
Using the basic principle of the difference between the epochs before and after the phase, the out Doppler can be expressed as ( He, 2015).
In the formula,  means for the sampling interval.

Kalman filtering
Kalman filtering is divided into the following two processes (Yang ,Gao, 2006) (1) Time upate: The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-3/W10, 2020 International Conference on Geomatics in the Big Data Era (ICGBD), 15-17 November 2019, Guilin, Guangxi, China While s X denote the vector of the receiver displacement, velocity and acceleration, respectively, T X means the vector of the receiver clock and receiver clock drift.
According to the basic principle of the current statistical model, the state can be expressed as (Yang ,Gao,2006): the Observation equation construction are given by From the above filters, we can see that in addition to establishing the state model and observation model of the system, the following problems need to be solved in solving user state ): setting of initial state X and error covariance matrix P, setting of process noise variance matrix Q, setting of observation noise variance matrix R. Regarding the setting of X, the least square method is used to provide the initial state quantity.
The process noise w of linear discrete stochastic systems obeys the Gauss-Markon process, and the initial value of Q is determined by the lower value (Tu, 2014).
Where  is the sampling rate, I is a 3 3 Observed noise variance matrix: The variance matrix of pseudo-distance observations and out Doppler: , p D   Is also a n n  diagonal matrix.

Adaptive robust Kalman filtering
Corresponding to the standard Kalman filter model, the rewritten gain matrix and the PDOP (Phillips et al. 1984 (1) IGG-III robust model: The IGGIII scheme (Galili et al. 1987) is the most widely used, and it divides the weight of measured values into three cases.
the expression is ： Where 0 k is the security point; 1 k is the elimination point; i p is the weight matrix of the observation; i v is the normalized residual of the i observation; i P is the weight after the i observation is reduced. It can be seen from the above formula that the IGGIII scheme divides the residual value into three parts. When obeying the normal distribution, the weight of the observed value remains unchanged; if the observed value exceeds a certain range, the weighting process is performed; if individual observations appear obviously abnormal, the weight is 0 at this time. Therefore, the IGGIII program has the best resistance.
(2) Single-factor three-stage adaptive model: adaptive equivalence weights xk P Can be expressed as: where  is adaptive factor, The three-stage adaptive factor is constructed by referring to the IGGIII equivalent weight Yang et al. 2006 ), which set the prediction residual value as a statistic, and the three-stage adaptive factor can be constructed as: Where 0 1 , c c are also constants . Generally both can be set to 1.0~1.5 or 3.0~8.5 3 Algorithm flow chart We can seen from the Fig.2 and Fig.3 that the true error of the ARKF methods is better than 1.00m/s in the U direction, and the RMS of the total speed is also better than 1.00cm/s. The  the ARKF method has better accuracy than L-S and has better denoising effect.

kinematic test
In order to verify the feasibility and accuracy of the ARKF The type of kinemaic GNSS receiver is NovAtel GPSCard, the sampling frequency is 1Hz, the sampling frequency of the HYDRINS is 200HZ, and a NovAtel GPSCard receiver is placed on the shore as a base station which sampling frequency is also 1HZ for simultaneous sampling(as shown in Fig. 4).
Since the tight combination mode of Internial Explorer (IE) software solves the velocity with an accuracy better than 0.2cm/s, the IE velocity is used as the reference true value.
It can be seen from Fig  As can be seen from Fig 6,  the ship is maneuvering. In view of the fact that the precision of the dynamic condition is lower than the static fact, it can be considered that the observation error of carrier phase accuracy in dynamic condition is lower than the static condition, and the observation environment is more complicated. The influence of the ionosphere and troposphere is more significant in the differential process, which is also consistent with the GNSS observation.

CONCLUSION
In this paper ,the processing results of static and dynamic data was analyzed which shows that compared with the solution of least squares, the ARKF method has higher accuracy and abnormality. Therefore, the method can be applied to dynamic navigation and velocity measurement.