CN109459778B - Code pseudo range/Doppler joint velocity measurement method based on robust variance component estimation and application thereof - Google Patents

Abstract

The invention discloses a code pseudo range/Doppler combined velocity measurement method based on robust variance component estimation. The method provided by the invention can break through the limitation that the single-frequency satellite receiver only uses single information for speed measurement at present, can inhibit the influence of observation gross error, and obviously improves the robustness, unbiased property and stability of the combined speed measurement method.

Description

Code pseudorange/Doppler joint velocity measurement method based on robust variance component estimation and its application

technical field

The invention belongs to the technical field of GNSS (Global Navigation Satellite System) positioning and navigation, and in particular relates to code pseudorange/Doppler joint measurement of the moving speed of a receiver based on robust variance component estimation.

Background technique

Speed is one of the important motion parameters in aviation flight, intelligent navigation, unmanned driving, maritime traffic and other fields. The high precision, real-time and cheap characteristics of GNSS speed measurement make it widely used in these fields. Through differential data simulation tests, foreign scholars have obtained the relationship between the speed measurement error and the carrier's motion speed and acceleration rate, and the error range ranges from sub-millimeters per second to several meters per second. Domestic scholars have also systematically analyzed and evaluated the speed measurement model and speed measurement accuracy of pseudorange, carrier wave, Doppler and their differential observations. In detail, the pseudorange, carrier wave and Doppler observations can all measure the receiver velocity, and the average velocity can be obtained by directly using the GNSS positioning results for position difference, but this is very dependent on the accuracy of the positioning results and is not very practical. In addition, the average velocity within the differential time can be obtained by the pseudo-range difference between epochs, but due to the influence of code pseudo-range accuracy, the speed measurement error is large; the average velocity within the differential time can also be obtained by using the phase difference between epochs, and The accuracy is high, but the carrier phase is susceptible to interference and frequent cycle slips, or even no output, and the reliability is low; Doppler observations can obtain high-precision instantaneous speed, which is not sensitive to orbit errors, receiver clock errors, and atmospheric errors , there is no cycle slip, and the influence of the pseudo-range single-point positioning error on the speed measurement accuracy is also at the millimeter level, which is a relatively practical and reliable observation value.

There are many kinds of observation information or speed measurement methods, but how to integrate different types of observation information to maximize the realization of high-precision and stable speed measurement is an urgent problem in engineering applications.

Contents of the invention

Technical problem: Aiming at the above-mentioned existing technologies, and referring to the idea of multi-source information fusion, a method of joint calculation of receiver velocity using single frequency code pseudorange and Doppler observations with different precision is proposed, and at the same time based on robust estimation and The combination of variance component estimation is used to explore the establishment of a more reasonable and effective random model to maximize the effect of the joint model.

Technical solution: Based on the code pseudorange/Doppler joint speed measurement method based on robust variance component estimation, first use the observation information of code pseudorange, Doppler, carrier-to-noise ratio, and satellite elevation angle to establish a function model and a random model of speed measurement respectively ; Then use the least squares robust estimation method to obtain a robust stochastic model that can suppress the influence of gross errors; finally, the code pseudorange and Doppler velocity function model and the robust random model are combined to form a joint velocity measurement model, and the variance component is used to estimate The method iteratively solves the motion velocity of the satellite receiver.

Further, the code pseudorange/Doppler joint velocity measurement method based on robust variance component estimation includes the following specific steps:

Step 1), using code pseudorange, Doppler, carrier-to-noise ratio, and satellite elevation angle observation information to establish a function model and a random model of speed measurement respectively, including the following specific steps:

a), the rate of change of code pseudorange and carrier is obtained by means of difference between epochs, as shown in formula (1):

分别为码伪距及其变化率，

和

分别为载波相位及其变化率，D为多普勒观测值，Δt为差分时间，其中各项的下标k、k+1分别为第k时刻和第k+1时刻；In the formula, ρ and

are code pseudoranges and their rate of change, respectively,

and

are the carrier phase and its rate of change, D is the Doppler observation value, Δt is the differential time, and the subscripts k and k+1 of each item are respectively the kth moment and the k+1st moment;

b), using code pseudo-range and Doppler observations to establish a function model of speed measurement, generally the GNSS observation equation is shown in formula (2):

为接收机载波观测值，N₀为整周模糊度，λ为载波波长，R为接收机与卫星间的真实几何距离，c为光速，δt为钟差，δρ_ion为电离层延迟，δρ_trop为对流层延迟，ε_ρ和

为包含轨道误差、多路径效应、观测噪声在内的其他误差项，其中各项的上标s和下标r分别代表卫星和接收机。In the formula, ρ is the receiver code pseudo-range observation value,

is the receiver carrier observation value, N ₀ is the integer ambiguity, λ is the carrier wavelength, R is the real geometric distance between the receiver and the satellite, c is the speed of light, δt is the clock difference, δρ _ion is the ionospheric delay, δρ _trop is the tropospheric delay, ε _ρ and

are other error items including orbit error, multipath effect, and observation noise, where the superscript s and subscript r of each item represent the satellite and the receiver, respectively.

According to the GNSS observation equation, the time t is derived and linearized, as shown in formula (3):

表示随时间t的变化率，且In the formula, each

represents the rate of change over time t, and

为ECEF(Earth-Centered,Earth-Fixed)坐标系下的卫星位置、速度列向量，r_r、

为ECEF坐标系下接收机位置、速度列向量，R₀为由接收机概略坐标r_r0求得的接收机与卫星间的几何距离，

为接收机概略速度，x、y和z为位置矢量在ECEF坐标系下的投影，v_x、v_y和v_z为速度矢量在ECEF坐标系下的投影。联合公式(1)、(3)和(4)可得到相应的测速函数模型；In the formula, r ^s ,

is the satellite position and velocity column vector in the ECEF (Earth-Centered, Earth-Fixed) coordinate system, r _r ,

is the receiver position and velocity column vector in the ECEF coordinate system, R ₀ is the geometric distance between the receiver and the satellite obtained from the receiver’s rough coordinate r _r0 ,

is the approximate velocity of the receiver, x, y and z are the projections of the position vector in the ECEF coordinate system, and v _x , v _y and v _z are the projections of the velocity vector in the ECEF coordinate system. Combined with formulas (1), (3) and (4), the corresponding speed measurement function model can be obtained;

c), use the carrier-to-noise ratio, satellite elevation angle and other observation information to establish a random model of speed measurement, as shown in formula (5):

In the formula, σ is the covariance, E is the satellite elevation angle, the subscript i is the satellite number, S is the scaling factor, and the constant items a ₀ , a ₁ and E ₀ are defined in Table A:

Table A

Among them, the scaling factor S is defined by the satellite carrier-to-noise ratio, as shown in formula (6):

In the formula, C/N ₀ represents the satellite carrier-to-noise ratio, and int(*) is the rounding function. By the formula (5), (6) and table A can determine the prior random model of speed.

Step 2), using the least squares robust estimation method to obtain a robust random model that can suppress the influence of gross errors, including the following specific steps:

a), the residual vector and the corresponding cofactors are obtained by least square estimation, as shown in formula (7):

待估参数，V为残差向量，Q_vv为残差协因数。In the formula, B is the design matrix, P is the prior weight, l is the observation value vector, Q is the observation value cofactor,

Parameters to be estimated, V is the residual vector, and Q _vv is the residual cofactor.

b) Through the IGG III equivalent weight scheme proposed by Zhou Jiangwen, a robust stochastic model that can suppress the influence of gross errors is obtained, as shown in formula (8):

为标准化残差，k₀和k₁为常量，一般k₀∈[1.0～1.5]，k₁∈[2.5～8.0]，

为抗差等价权，下标i代表第i个观测值。In the formula,

is the standardized residual, k ₀ and k ₁ are constants, generally k ₀ ∈ [1.0~1.5], k ₁ ∈ [2.5~8.0],

is the equivalent weight of robustness, and the subscript i represents the ith observed value.

Step 3), the velocity measurement function model of the code pseudorange and Doppler and the robust stochastic model are combined to form a joint velocity measurement model, and the method of variance component estimation is used to iteratively solve the motion velocity of the satellite receiver, including the following specific steps:

a) Combine the code pseudo-range and Doppler speed function model and the robust random model to form a joint speed measurement model, as shown in formula (9):

In the formula, the subscripts 1 and 2 represent the code pseudorange and Doppler respectively, and N and W represent the corresponding combination items respectively;

b), using the method of variance component estimation to iteratively adjust the weights of various observations, as shown in formula (10):

为单位权方差的估计值，V为残差向量，

为抗差等价权，各项的下标1和2分别代表码伪距和多普勒。通过求解方程组(10)式，得到单位权方差

的估值

代入式(11)获得调整后的各类观测值权重：In the formula, tr(*) represents the matrix trace, E(*) represents the expectation, n is the number of observations,

is the estimated value of unit weight variance, V is the residual vector,

For the equivalence weight of robustness, the subscripts 1 and 2 of each item represent code pseudorange and Doppler, respectively. By solving equations (10), the unit weight variance is obtained

valuation

Substituting into formula (11) to obtain the adjusted weights of various observations:

表示单次迭代调整得到的权重，C为常数，可固定选取

中任一个，各项的下标1和2分别代表码伪距和多普勒。In the formula,

Indicates the weight obtained by a single iteration adjustment, C is a constant, which can be fixedly selected

Any of them, the subscripts 1 and 2 of each item represent code pseudorange and Doppler, respectively.

c), using the joint speed measurement model adjusted by variance component estimation to solve the motion speed of the satellite receiver, as shown in formula (12):

为估计的速度矢量，上标-1代表矩阵求逆运算；In the formula,

is the estimated velocity vector, and the superscript -1 represents the matrix inversion operation;

Repeat steps a), b), and c) until the estimates of the variances of various unit weights are equal or equal after hypothesis testing, and then the final moving speed of the receiver can be obtained.

Furthermore, when performing step 3), if after 4 to 5 iterations of the loop, the unit weight variance estimation is still not satisfied or the hypothesis test is passed, then jump out of the loop and directly use the robust solution as the final solution result.

由公式(8)获得。这是抗差估计领域普遍采用且抗差效果较好的抗差估计方法，已被业界广泛应用和推崇，成为了公知的实用抗差方法。公式(8)是其提出的各套抗差方法当中运用最广的一套方法中的核心公式。本发明也是采用其抗差方法进行粗差的抑制。In addition, the above quoted Zhou Jiangwen, who is a geodesist, and the IGG III scheme is the third set of robust estimation methods proposed by Zhou Jiangwen in 1989 based on the boundedness of measurement errors, that is, the equivalent weight of robustness

Obtained by formula (8). This is a robust estimation method commonly used in the field of robust estimation and has a good robustness effect. It has been widely used and praised in the industry, and has become a well-known practical robustness method. Formula (8) is the core formula in the most widely used set of methods among the various robustness methods proposed by him. The present invention also uses its anti-error method to suppress gross errors.

Beneficial effects: a code pseudorange/Doppler joint speed measurement method based on robust variance component estimation proposed by the present invention, by using code pseudorange and Doppler observation information to jointly solve the receiver speed, breaks through the current single-frequency The satellite receiver only uses a single observation value for speed measurement; in view of the problem that the joint speed measurement model is easily affected by bad observation values such as gross errors, the principle of equivalent weight robustness estimation is used to suppress the influence of internal gross errors of similar observations on the model; for When merging multi-source information for joint speed measurement, there are problems of incompatibility among various types of information and inconsistent accuracy. The variance component estimation method is used to balance the weight ratio between different types of observations, and adaptively adjust the stochastic model of joint speed measurement. Using the method proposed by the present invention can realize full and effective utilization of single-frequency observation information, and significantly improve the robustness, unbiasedness and stability of the joint velocity measurement method.

Description of drawings

The accompanying drawings are used to provide a further understanding of the present invention, and constitute a part of the description, together with the following specific embodiments, are used to explain the present invention, but do not constitute a limitation to the present invention. In the attached picture:

Fig. 1 is the flow chart of the code pseudo-range/Doppler joint velocity measuring method based on robust variance component estimation in an embodiment of the present invention;

Fig. 2 is the true error of speed measurement of each solution scheme in an embodiment of the present invention;

Fig. 3 is the true error of single point positioning N, E direction in an embodiment of the present invention;

Fig. 4 is the true error of the X-axis speed measurement of each solution scheme in an embodiment of the present invention;

Fig. 5 is the combined speed error of each solution scheme in an embodiment of the present invention;

Detailed ways

Specific embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described here are only used to illustrate and explain the present invention, and are not intended to limit the present invention.

A code pseudorange/Doppler joint speed measurement method based on robust variance component estimation, using code pseudorange, Doppler, carrier-to-noise ratio, satellite altitude angle and other observation information to establish a function model and a random model of speed measurement respectively, using The least squares robust estimation method obtains a robust stochastic model that can suppress the influence of gross errors, and the code pseudorange and Doppler velocity function model and the robust random model form a joint velocity measurement model, which is iteratively solved based on the variance component estimation method The speed of movement of the satellite receiver.

In the GNSS speed measurement solution, the position or speed information is obtained by establishing the observation equation and solving (estimating) the unknown parameters (such as position and speed) in the equation. The observation equation can be divided into two parts: the functional model of the observed value and the stochastic model. The function model describes the mathematical relationship between the observed value and the estimated value (that is, the natural physical laws are expressed by mathematical equations, such as displacement = velocity * time, etc., where the displacement is the observed value at each time node, and the velocity is the parameter to be estimated); random The model describes the noise (that is, error) of the observed value and the correlation between the observed values. To obtain an accurate and effective solution (estimation) for the parameters to be estimated, it is necessary to establish an accurate function model and a matching stochastic model. In the actual solution, the function model can be obtained more accurately from the definite physical meaning, but due to the random or non-random comprehensive influence of the observation equipment and the environment, it is often difficult to guarantee the accurate error of the obtained observation value, that is, the stochastic model is difficult to obtain. Accurately get established. Therefore, in order to establish an accurate stochastic model, the present invention jointly establishes a priori stochastic model by the main characteristic information (i.e., signal-to-noise ratio, satellite elevation angle, etc.) of the observed value, and then uses the function model And the random model is carefully adjusted to make the function model match the random model as much as possible, and can accurately reflect the actual measurement situation. The main feature of the present invention is that the observation value not only adopts a single conventional code pseudo-range observation value, but also integrates the Doppler observation value, which are two different types of observation values, and the physical meaning and observation error level of the observation values are inconsistent. Therefore, it is necessary to establish not only the function model of the joint speed measurement, but also an accurate random model to improve the estimation accuracy of the speed information. The method adopted is the variance component estimation method with robustness.

Example 1

A code pseudorange/Doppler joint velocity measurement method based on robust variance component estimation comprises the following specific steps:

Step 1), using observation information such as code pseudorange, Doppler, carrier-to-noise ratio, satellite elevation angle, etc. to establish a function model and a random model of speed measurement respectively, including the following specific steps:

a), the rate of change of code pseudorange and carrier is obtained by means of difference between epochs, as shown in formula (1):

分别为码伪距及其变化率，

和

分别为载波相位及其变化率，D为多普勒观测值，Δt为差分时间，其中各项的下标k、k+1分别为第k时刻和第k+1时刻。In the formula, ρ and

are code pseudoranges and their rate of change, respectively,

and

are the carrier phase and its rate of change, D is the Doppler observation value, Δt is the differential time, and the subscripts k and k+1 of each item are the kth moment and the k+1st moment, respectively.

b), using code pseudo-range and Doppler observations to establish a function model of speed measurement, generally the GNSS observation equation is shown in formula (2):

为接收机载波相位观测值，N₀为整周模糊度，λ为载波波长，R为接收机与卫星间的真实几何距离，c为光速，δt为钟差，δρ_ion为电离层延迟，δρ_trop为对流层延迟，ε_ρ和

为包含轨道误差、多路径效应、观测噪声在内的其他误差项，其中各项的上标s和下标r分别代表卫星和接收机。In the formula, ρ is the receiver code pseudo-range observation value,

is the receiver carrier phase observation value, N ₀ is the integer ambiguity, λ is the carrier wavelength, R is the real geometric distance between the receiver and the satellite, c is the speed of light, δt is the clock error, δρ _ion is the ionospheric delay, δρ _trop is the tropospheric delay, ε _ρ and

are other error items including orbit error, multipath effect, and observation noise, where the superscript s and subscript r of each item represent the satellite and the receiver, respectively.

According to the GNSS observation equation, the time t is derived and linearized, as shown in formula (3):

表示随时间t的变化率，且In the formula, each

represents the rate of change over time t, and

为ECEF(Earth-Centered,Earth-Fixed)坐标系下的卫星位置、速度列向量，r_r、

为ECEF坐标系下接收机位置、速度列向量，R₀为由接收机概略坐标r_r0求得的接收机与卫星间的几何距离，

为接收机概略速度，x、y和z为位置矢量在ECEF坐标系下的投影，v_x、v_y和v_z为速度矢量在ECEF坐标系下的投影。联合公式(1)、(3)和(4)可得到相应的测速函数模型；In the formula, r ^s ,

is the satellite position and velocity column vector in the ECEF (Earth-Centered, Earth-Fixed) coordinate system, r _r ,

is the receiver position and velocity column vector in the ECEF coordinate system, R ₀ is the geometric distance between the receiver and the satellite obtained from the receiver’s rough coordinate r _r0 ,

is the approximate velocity of the receiver, x, y and z are the projections of the position vector in the ECEF coordinate system, and v _x , v _y and v _z are the projections of the velocity vector in the ECEF coordinate system. Combined with formulas (1), (3) and (4), the corresponding speed measurement function model can be obtained;

c), use the carrier-to-noise ratio, satellite elevation angle and other observation information to establish a random model of speed measurement, as shown in formula (5):

In the formula, σ is the covariance, E is the satellite elevation angle, the subscript i is the satellite number, S is the scaling factor, and the constant items a ₀ , a ₁ and E ₀ are defined in Table A:

Table A

Among them, the scaling factor S is defined by the satellite carrier-to-noise ratio, as shown in formula (6):

In the formula, C/N ₀ represents the satellite carrier-to-noise ratio, and int(*) is the rounding function. By the formula (5), (6) and table A can determine the prior random model of speed.

Step 2), using the least squares robust estimation method to obtain a robust random model that can suppress the influence of gross errors, including the following specific steps:

a), the residual vector and the corresponding cofactors are obtained by least square estimation, as shown in formula (7):

待估参数，V为残差向量，Q_vv为残差协因数。In the formula, B is the design matrix, P is the prior weight, l is the observation value vector, Q is the observation value cofactor,

Parameters to be estimated, V is the residual vector, and Q _vv is the residual cofactor.

b) Through the IGG III equivalent weight scheme proposed by Zhou Jiangwen, a robust stochastic model that can suppress the influence of gross errors is obtained, as shown in formula (8):

为标准化残差，k₀和k₁为常量，一般k₀∈[1.0～1.5]，k₁∈[2.5～8.0]，

为抗差等价权，下标i代表第i个观测值。In the formula,

is the standardized residual, k ₀ and k ₁ are constants, generally k ₀ ∈ [1.0~1.5], k ₁ ∈ [2.5~8.0],

is the equivalent weight of robustness, and the subscript i represents the ith observed value.

Step 3), the velocity measurement function model of the code pseudorange and Doppler and the robust stochastic model are combined to form a joint velocity measurement model, and the method of variance component estimation is used to iteratively solve the motion velocity of the satellite receiver, including the following specific steps:

a) Combine the code pseudo-range and Doppler speed function model and the robust random model to form a joint speed measurement model, as shown in formula (9):

In the formula, the subscripts 1 and 2 represent code pseudorange and Doppler, respectively.

b), using the method of variance component estimation to iteratively adjust the weights of various observations, as shown in formula (10):

为单位权方差的估计值，V为残差向量，

为抗差等价权，各项的下标1和2分别代表码伪距和多普勒。通过求解方程组(10)式，得到单位权方差

的估值

代入式(11)获得调整后的各类观测值权重：In the formula, tr(*) represents the matrix trace, E(*) represents the expectation, n is the number of observations,

is the estimated value of unit weight variance, V is the residual vector,

For the equivalence weight of robustness, the subscripts 1 and 2 of each item represent code pseudorange and Doppler, respectively. By solving equations (10), the unit weight variance is obtained

valuation

Substituting into formula (11) to obtain the adjusted weights of various observations:

表示单次迭代调整得到的权重，C为常数，可固定选取

中任一个，各项的下标1和2分别代表码伪距和多普勒。In the formula,

Indicates the weight obtained by a single iteration adjustment, C is a constant, which can be fixedly selected

Any of them, the subscripts 1 and 2 of each item represent code pseudorange and Doppler, respectively.

c), using the joint speed measurement model adjusted by variance component estimation to solve the motion speed of the satellite receiver, as shown in formula (12):

为估计的速度矢量，上标-1代表矩阵求逆运算；In the formula,

is the estimated velocity vector, and the superscript -1 represents the matrix inversion operation;

Repeat steps a), b), and c) until the estimates of the variances of various unit weights are equal or equal after hypothesis testing, and then the final moving speed of the receiver can be obtained. Wherein, when step 3) is performed, if after 4 to 5 loop iterations, the unit weight variance estimation is still not satisfied or the hypothesis test is passed, then jump out of the loop and directly use the robust solution as the final solution result.

In this embodiment, the gross error judgment threshold k ₀ is set to 1.2, k ₁ is set to 5.5, and the maximum cycle threshold is set to 4.

Example 2

The following is an example of the application scenario of the code pseudorange/Doppler joint speed measurement method based on robust variance component estimation:

In order to comprehensively compare the actual calculation effect of the method proposed in the present invention, three test methods, such as static, static simulation dynamic and on-board dynamic, were designed, and were compared in four calculation schemes:

Scheme A: Least squares estimation, that is, directly use the prior random model and the function model of the joint speed measurement to solve the least squares adjustment.

Scheme B: Variance component estimation, that is, on the basis of scheme A, directly adopt the conventional method component estimation method to adjust the prior random model of pseudorange and Doppler.

Scheme C: Least squares robust estimation, that is, for the prior weight matrix of pseudorange and Doppler respectively, the weight of bad observations is adjusted by robust least squares estimation, and then combined into a joint velocity measurement model for least squares Calculate by multiplying the difference.

Scheme D: Robust variance component estimation, that is, adding variance component estimation on the basis of scheme C, so as to form an estimation method combining robustness and variance components to adjust the pseudorange and Doppler joint velocity measurement model.

1), static test

Figure 2 is the true error diagram of speed measurement for each solution scheme. The static observation data of Curtin University CUT0 station in Australia with an annual accumulation of 148 days is selected, and the pseudorange and Doppler observation information collected by the Trimble Net R9 receiver on GPS L1 and BDS B1 are used for calculation. The true velocity error of conventional least squares estimation has obvious fluctuations, and due to the influence of bad observations such as elevating and descending satellites, the true velocity error has a certain degree of jumping. After robust estimation, this kind of fluctuation and jump has been suppressed to a certain extent. In addition, the conventional variance component estimation can achieve similar effects, but the estimation method based on the combination of robust estimation and variance component has the best effect.

Table 1 below is the true error statistics table of each solution scheme. Among the mean values of each solution scheme, the mean value of the velocity estimated by the robust variance component is closest to the true value of zero, followed by the variance component estimate and the robust estimate, and the least squares estimate is the worst. According to the unbiasedness of parameter estimation, the unbiased estimation of the velocity of the robust variance component is the best, so it can be considered that the robust variance component estimation method can effectively balance the weights between observations of different precision and correct the influence of systematic deviation , which is also verified by the fact that the internal and external coincidence statistics are basically consistent. In addition, the internal and external coincidence accuracy of the robust variance component estimation is lower than that of other schemes. According to the validity of parameter estimation, the robust variance component estimation is the best among the four schemes.

Table 1

2), static simulation dynamic test

Figure 3 shows the true errors in the N and E directions of single point positioning. The static simulation dynamic test is carried out by using GPS and BDS single-frequency observation data of a CORS station in Jiangsu with a cumulative day of 152 days, a duration of 12 hours, and a frequency of 1 Hz. Except for spikes and jumps caused by bad observations such as a small amount of gross errors, the positioning errors in all directions of the single-point positioning are within 5m.

Figure 4 shows the true error of speed measurement in X direction for each solution scheme. It can be seen from the figure that the variance component estimation is affected by bad observations, and there is a speed estimation that deviates significantly from the true value, which can be suppressed to a large extent by robust estimation, so that the estimation of the robust variance component has been improved. . This shows that variance component estimation is more sensitive to bad observations, and the robust performance is improved by combining it with robust estimation.

The following table 2 is the true error statistics table of each scheme. The statistical performance of each solution scheme is basically consistent with Table 1, and the robust variance component estimation is still the optimal estimation among the four parameter estimation methods. The difference is that compared with Table 1, the amount of velocity error has increased, which indicates that the velocity measurement accuracy is closely related to the quality of the original observations, so it is necessary to add robust estimation to the variance component estimation.

Table 2

3), exercise test

Figure 5 shows the speed measurement error synthesized by each solution scheme. By installing the SPAN series high-precision optical fiber closed-loop inertial navigation system and the Ublox NEO-M8T single-frequency receiver module of the Canadian NovAtel company on the motor vehicle, both of which share the same satellite antenna, the dynamic data collection test was carried out in the urban area of Nanjing. The high-precision post-processing Inertial Explorer software is used to calculate the speed of the integrated navigation as a reference value and the speed of the single-frequency data collected by Ublox is calculated by each solution scheme. It can be seen from the speed measurement error diagram in Figure 5 that, except for the tunnel and the initial parking period of epoch 553-581, when the satellite signal is blocked and interfered, the speed estimation error obtained for other road sections can be guaranteed to be within 1.

Table 3 below is the error statistics table of each solution scheme. It can be seen from Table 3 that the performance of each statistic is basically consistent with Table 1 and Table 2, which further verifies the general rule.

table 3

Example 3

A global navigation satellite system, including a receiver, is characterized in that: the system includes a code pseudorange/Doppler joint velocity measurement method based on robust variance component estimation. The satellite data is collected through the receiver, and when the velocity is calculated, the observation data output by the receiver is calculated on the computing platform (such as a computer, mobile phone, etc.) and the velocity information is output or displayed.

It can be understood that, the above embodiments are only exemplary embodiments adopted for illustrating the principle of the present invention, but the present invention is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also regarded as the protection scope of the present invention.

Claims (7)

1. A code pseudo range/Doppler joint velocity measurement method based on robust variance component estimation is characterized in that: the method comprises the following steps:

(1) Establishing a speed measuring function model and a random model;

(2) Obtaining an robust random model capable of inhibiting gross errors;

(3) Forming a combined velocity measurement model by a code pseudorange and Doppler velocity measurement function model and an robust random model;

(4) Solving the motion speed of the satellite receiver;

the method comprises the following specific steps of forming a combined velocity measurement model by a code pseudorange and Doppler velocity measurement function model and an robust random model, and iteratively solving the motion velocity of the satellite receiver by adopting a variance component estimation method: a) And combining a code pseudorange and Doppler velocity measurement function model and an robust random model into a combined velocity measurement model, wherein the formula (9) is as follows:

in the formula, subscripts 1 and 2 represent code pseudorange and doppler, respectively, and N and W represent corresponding combination terms, respectively; b) Iteratively adjusting the weight of each type of observed value by adopting a variance component estimation method, wherein the formula (10) is as follows:

in the formula, tr (x) represents matrix tracing, E (x) represents expectation, n is the number of observed values,

is an estimate of the unit weight variance, V is the residual vector,

subscripts 1 and 2 of each item represent code pseudorange and doppler, respectively, for robust equivalence weights;

the unit weight variance is obtained by solving the equation (10)

Evaluation of

Obtaining the weight of each type of observation value after adjustment by substituting formula (11):

in the formula (I), the compound is shown in the specification,

represents the weight obtained by single iteration adjustment, C is constant and can be fixedly selected

Subscripts 1 and 2 of each item represent code pseudorange and doppler, respectively;

c) And solving the motion speed of the satellite receiver by using the combined velocity measurement model after the estimation and adjustment of the component of the power difference, wherein the formula (12) is as follows:

in the formula (I), the compound is shown in the specification,

for the estimated velocity vector, superscript-1 represents the matrix inversion operation;

repeating the steps a), b) and c) until the estimated values of the unit weight variances of all types are equal or are verified to be equal by hypothesis, and then obtaining the final movement speed of the receiver;

when the step of iteratively solving the motion speed of the satellite receiver by adopting a variance component estimation method is carried out, if the equal unit weight variance estimation value can not be met or hypothesis test is passed through 4-5 times of loop iteration, a loop is skipped, and the robust solution is directly adopted as a final solving result.

2. The robust variance component estimation-based code pseudorange/doppler joint velocity measurement method according to claim 1, characterized in that: the velocity measurement function model and the random model are established according to observation information of code pseudo range, doppler, carrier-to-noise ratio and satellite altitude.

3. The robust variance component estimation based code pseudorange/doppler joint velocity measurement method as claimed in claim 1, wherein: the robust random model is obtained by adopting a least square robust estimation method and can inhibit the influence of gross errors.

4. The robust variance component estimation-based code pseudorange/doppler joint velocity measurement method according to claim 1, characterized in that: and solving the motion speed of the satellite receiver by adopting a variance component estimation method to carry out iterative solution.

5. The code pseudorange/doppler joint velocity measurement method based on robust variance component estimation according to claim 2, characterized by comprising the following specific steps:

the method comprises the following steps of respectively establishing a function model and a random model for speed measurement by adopting code pseudorange, doppler, carrier-to-noise ratio and satellite altitude observation information:

a) And calculating the change rate of the code pseudo range and the carrier wave by a differential mode among epochs, wherein the formula (1) is as follows:

wherein ρ and

respectively the code pseudorange and its rate of change,

and

respectively a carrier phase and a change rate thereof, D is a Doppler observed value, delta t is differential time, and subscripts k and k +1 of each item are respectively a kth moment and a kth +1 moment;

b) Establishing a function model for speed measurement by using the code pseudo range and the Doppler observed value, wherein a GNSS observation equation is shown as a formula (2):

where ρ is the receiver code pseudorange observation,

for receiver carrier phase observations, N ₀ Lambda is the carrier wavelength, R is the true geometric distance between the receiver and the satellite, c is the speed of light, δ t is the clock error, δ ρ _ion To ionospheric delay, δ ρ _trop For tropospheric delay, epsilon _ρ And

the method comprises the following steps of (1) taking other error items including orbit errors, multipath effects and observation noise, wherein superscripts s and subscripts r of the items represent a satellite and a receiver respectively;

the time t is derived and linearized according to a GNSS observation equation, as shown in equation (3):

in the formula (I)

Represents the rate of change with time t, and

in the formula, r ^s 、

Is a satellite position and velocity column vector, r, in the ECEF coordinate system _r 、

Is a receiver position and velocity column vector R in an ECEF coordinate system ₀ To be approximated by a receiver _r0 The geometric distance between the receiver and the satellite is obtained,

for the receiver approximate velocity, x, y and z are the projections of the position vector in the ECEF coordinate system, v _x 、v _y And v _z The projection of the velocity vector under the ECEF coordinate system;

corresponding speed measurement function models can be obtained by combining the formulas (1), (3) and (4);

c) And establishing a random model for speed measurement by utilizing the carrier-to-noise ratio and the satellite altitude angle observation information, wherein the formula (5) is as follows:

where σ is covariance, E is satellite altitude, subscript i is satellite number, S is scaling factor, and constant term a ₀ 、a ₁ And E ₀ Defined by the following table:

wherein the scaling factor S is defined by the satellite carrier-to-noise ratio, as shown in equation (6):

in the formula, C/N ₀ Representing the satellite carrier-to-noise ratio, and int (—) is an integer function; is composed of equations (5), (6) and constant term a ₀ 、a ₁ And E ₀ Can determine a prior random model of velocity measurement.

6. The robust variance component estimation based code pseudorange/doppler joint velocity measurement method as claimed in claim 3, wherein: the method for obtaining the robust random model capable of inhibiting the gross error influence by adopting the least square robust estimation method comprises the following specific steps:

a) And obtaining a residual vector and a corresponding co-factor through least square estimation, as shown in formula (7):

wherein B is a design matrix, P is a prior weight, l is an observed value vector, Q is an observed value co-factor,

the parameter to be estimated, V is the residual vector, Q _vv Is a residual error co-factor;

b) And obtaining an robust random model capable of inhibiting gross error influence by an IGG III equivalent weight scheme, wherein the robust random model is shown as a formula (8):

in the formula (I), the compound is shown in the specification,

to normalize the residual, k ₀ And k ₁ Is a constant value of k ₀ ∈[1.0～1.5]，k ₁ ∈[2.5～8.0]，

For robust equivalence, subscript i represents the ith observation.

7. A global navigation satellite system comprising a receiver characterized by: the system adopts a code pseudo-range/Doppler joint velocity measurement method based on robust variance component estimation as claimed in any one of claims 1-6; the satellite data is collected through the receiver, and when the speed is resolved, the speed information is resolved and output or displayed on the computing platform through observation data output by the receiver.

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