阅读说明：本技术 基于姿态差分补偿的垂线偏差测量方法、系统、终端、介质 (Method, system, terminal and medium for measuring plumb line deviation based on attitude difference compensation ) 是由 何泓洋 邸建琛 詹国强 安文 江鹏飞 许江宁 于 2021-09-09 设计创作，主要内容包括：本发明属于垂线偏差测量技术领域,公开了一种基于姿态差分补偿的垂线偏差测量方法、系统、终端、介质,用姿态差对惯导解算中的重力项进行垂线偏差补偿,在消除垂线偏差误差的同时又引入了特性明确的常值误差、缓变误差和周期误差；把缓变误差建模为一阶高斯马尔科夫过程,周期误差作为输入,建立垂线偏差补偿后的SINS/GNSS组合导航方程,针对系统噪声变化的问题,将渐消记忆Kalman滤波用于状态估计,估计出的姿态不受垂线偏差影响,以该姿态作为姿态基准与垂线偏差未补偿时SINS/GNSS组合解算的姿态做差,差分结果即为垂线偏差。(The invention belongs to the technical field of vertical deviation measurement, and discloses a vertical deviation measurement method, a system, a terminal and a medium based on attitude difference compensation, wherein the attitude difference is used for performing vertical deviation compensation on a gravity item in inertial navigation solution, and a constant error, a slowly varying error and a periodic error with definite characteristics are introduced while the vertical deviation error is eliminated; modeling the slowly-varying error into a first-order Gaussian Markov process, taking the periodic error as input, establishing an SINS/GNSS combined navigation equation after vertical deviation compensation, aiming at the problem of system noise change, using fading memory Kalman filtering for state estimation, wherein the estimated attitude is not influenced by the vertical deviation, taking the attitude as an attitude reference, and making a difference with the attitude solved by the SINS/GNSS combination when the vertical deviation is not compensated, wherein the difference result is the vertical deviation.)

1. A vertical deviation measuring method based on attitude differential compensation is characterized by comprising the following steps of:

combined navigation is carried out by using SINS and GNSS, and attitude rotation matrix is solved

Combining gyro components Gyros and GNSS in SINS to calculate attitude rotation matrix

By usingAndcarrying out difference, wherein the difference result comprises vertical deviation and a Gyros/GNSS attitude error item with definite characteristics;

modeling a low-frequency trend item in a Gyroso/GNSS attitude error item into a first-order Markov process, and taking a periodic item in the Gyroso/GNSS attitude error as prior information;

vertical deviation compensation is carried out on a gravity item in the SINS inertial solution equation by using an attitude difference result, a vertical deviation item is eliminated, and a modeled Gyros/GNSS attitude error item with definite characteristics is introduced;

carrying out fading memory Kalman filtering on the compensated SINS calculation model, and estimating an attitude rotation matrix without vertical deviation information

By usingTaking the reference and calculating the attitude rotation matrix with the SINS/GNSS combined navigationMaking difference, wherein the difference result is the vertical line deviation information on the recovered track;

finding out the optimal fading factor for the fading memory Kalman filter by using the fading factor screening method taking the minimum sum of pure inertia resolving speed errors as a target function;

the initial value of the fading factor is 1, and the step length is 0.01; performing fading memory Kalman filtering once every time an fading factor is traversed, judging whether the filtering is diverged, and if so, terminating the algorithm; if not, a pair of horizontal misalignment angles is estimated

Fourier transform is performed on the horizontal misalignment angle estimated by the filter, and whether the frequency spectrum is at the frequency omega of the input quantity or not is judged_inThere is a spike; if not, the filtering result is not accurate, and the loop is ended; if so, the filtering result is in accordance with the prior condition, and the deviation of the vertical line is calculated;

compensating and correcting a gravity term in pure inertia calculation by using the calculated vertical deviation eta (i) and xi (i), and calculating the sum of speed calculation errors;

and analyzing a curve of the sum of the speed errors, wherein the vertical deviation corresponding to the minimum sum of the speed errors is the recovered vertical deviation, and the fading factor of the cycle is the optimal fading factor.

2. The method of claim 1, wherein the direction cosine matrix solved by the SINS/GNSS combined navigation is recorded as

The direction cosine matrix calculated by the Gyros/GNSS combined navigation is recorded as

Said useAnddifferentiating to eliminate the direction cosine matrix reflecting true postureThe method comprises the following steps:

ignoring the second order fractional amount, equation (3) is written as:

define θ phi-psi, which is written as an east and north projection:

by theta_EAnd theta_NAnd (3) compensating the vertical line deviation, and writing a compensated speed differential equation as follows:

in the formula (6), V^cIn order to calculate the speed of the vehicle,for the purpose of the direction cosine matrix of the calculation,for specific force measurements involving accelerometer device errors,andare respectively asAndthe calculated value of (a); the compensated velocity error equation is written as:

in the formula (I), the compound is shown in the specification,representing the inertially resolved attitude misalignment angle after vertical deviation compensation.

3. The method of claim 1, wherein the gyro attitude error ψ comprises a constant term, a slowly-increasing term, and a periodic term, and the angular frequency of the periodic term is equal toSize of (2)The last term of equation (7) is modeled as:

in the formula, a_E1(t) and a_N1(t) represents a time-dependent function, a_E2(ω_int) and a_N2(ω_int) represents an angular frequency of ω_inA periodic function of (a); a is_E1(t)，a_N1(t) each comprises a constant term and a slowly-increasing term, the characteristics of the constant term and the slowly-increasing term are very similar to those of the gyro drift, the constant error term is similar to the zero-offset repeatability error of the gyro drift, and the slowly-increasing term is similar to the zero-offset stability error of the gyro; a is_E1(t) and a_N1The model of (t) is expressed as:

in the formula, a_E11(t)，a_N11(t) are each a_E1(t) and a_N1Constant term in (t), a_E12(t)，a_N12(t) are each a_E1(t) and a_N1Slowly growing terms in (t), modeled as a first order Markov process, τ_EAnd τ_NIs a correlation time, w_EAnd w_NIs white noise.

4. The attitude differential compensation-based vertical deviation measurement method according to claim 1, wherein the error equation of the vertical deviation compensated SINS/GNSS integrated navigation system is written as:

in the formula, x is a state quantity, w is noise, and u is an input quantity; a is to_E1(t) and a_N1(t) as a state variable, the period term a_E2(ω_int) and a_N2(ω_int) as an input quantity;u＝(0_1×3 a_E2a_N2 0 0_1×13)^Tthe time variable t is omitted; noise vector w ═ (w)_g w_ax+w_E0 w_ay+w_N0 w_az 0_1×10 w_E 0 w_N)^TWherein w is_gRepresenting noise of the gyro, w_ax、w_ayAnd w_azIs the noise of the accelerometer, w_E0And w_N0The vertical deviation is compensated for by modeling the model noise generated by inaccuracy of the psi modeling in the model.

5. The attitude differential compensation-based vertical deviation measurement method according to claim 4, wherein the integrated navigation process is divided into an inertial solution process and a filtering process, and the inertial solution attitude error transmission process has a low-pass characteristic; frequency omega of input quantity_inThe small error attenuation is almost zero in the error transfer process and is completely reflected in the attitude error, so that the frequency spectrum of the attitude error is in omega_inThere is a spike; taking this analysis conclusion as a priori information, equation (11) reduces to a standard integrated navigation state equation:

the measurement equation of the SINS/GNSS combined navigation system after vertical deviation compensation is written by taking the position information provided by the carrier phase differential GNSS as reference:

y＝Hx+v (13)

wherein y is measurement quantity, y is δ P, H is measurement matrix, and v is measurement noise; wherein, the expressions of A and H are:

H＝[0_3×6 I_3×3 0_3×10]；

equations (12) and (13) are expressed discretely as:

in the formula phi_k/k-1Representing the discretized system matrix, w_kAnd v_kRepresents a gaussian white noise sequence and satisfies the following relationship:

in the formula, delta_jkIs the Dirac delta function.

6. An attitude differential compensation based vertical deviation measurement system according to claim, wherein said attitude differential compensation based vertical deviation measurement system comprises:

an attitude rotation matrix acquisition module for performing integrated navigation by using SINS and GNSS to calculate an attitude rotation matrixAnd the method is also used for utilizing gyro components Gyros and GNSS in SINS to carry out combination and calculating an attitude rotation matrix

A priori information acquisition module forAndcarrying out difference, wherein the difference result comprises vertical deviation and a Gyros/GNSS attitude error item with definite characteristics; modeling a low-frequency trend item in a Gyroso/GNSS attitude error item as a first-order Markov process, and taking a periodic item in the Gyroso/GNSS attitude error as prior information;

the attitude rotation matrix estimation module is used for performing vertical deviation compensation on a gravity item in the SINS inertial solution equation by using an attitude difference result, eliminating a vertical deviation item and introducing a Gyros/GNSS attitude error item with known characteristics which is modeled; carrying out fading memory Kalman filtering on the compensated SINS inertial solution model, and estimating an attitude rotation matrix without vertical deviation information

An optimal fading factor acquisition module forTaking the reference and calculating the attitude rotation matrix with the SINS/GNSS combined navigationMaking a difference, wherein the difference result is the vertical line deviation information on the recovered track; finding out the optimal fading factor for the fading memory Kalman filter by using the fading factor screening method taking the minimum sum of pure inertia resolving speed errors as a target function;

the vertical line deviation calculation module is used for setting the initial value of the fading factor to be 1 and setting the step length to be 0.01; performing fading memory Kalman filtering once every time an fading factor is traversed, judging whether the filtering is diverged, and if so, terminating the algorithm; if not, a pair of horizontal misalignment angles is estimatedFourier transform is carried out on the horizontal misalignment angle estimated by the filter, and whether the frequency spectrum is in omega or not is judged_inThere is a spike; if not, the filtering result is not accurate, and the loop is ended; if so, the filtering result is in accordance with the prior condition, and the deviation of the vertical line is calculated;

the optimal fading factor acquisition module is used for compensating and correcting a gravity term in the SINS pure inertia calculation by using the calculated vertical line deviation eta (i) and xi (i) and calculating the sum of speed calculation errors; and analyzing a curve of the sum of the speed errors, wherein the vertical line deviation corresponding to the minimum sum of the speed errors is the recovered vertical line deviation, and the fading factor of the cycle is the optimal fading factor.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, and the computer program, when executed by the processor, causes the processor to execute the method for measuring a vertical deviation based on attitude difference compensation according to any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to execute the attitude difference compensation-based vertical deviation measurement method according to any one of claims 1 to 6.

9. An information data processing terminal, characterized in that the information data processing terminal is used for implementing the vertical deviation measuring method based on attitude difference compensation according to any one of claims 1 to 5.

Technical Field

The invention belongs to the technical field of vertical deviation measurement, and particularly relates to a method, a system, a terminal and a medium for measuring vertical deviation based on attitude differential compensation.

Background

At present, due to the irregular shape of the earth, the internal mass is not uniform, the true gravity is not equal to the normal gravity, and the difference between the two is called gravity disturbance, including gravity anomaly and vertical deviation. Accurate vertical deviation data has important value in the fields of geohorizon determination, earthquake monitoring, engineering survey, space exploration, national defense safety, national comprehensive PNT system construction and the like.

Vertical deviation measurement based on a combination of a Strapdown Inertial Navigation System (SINS) and a Global Navigation Satellite System (GNSS) is a vertical deviation measurement scheme under study. The current commonly used method for measuring the vertical deviation based on the SINS/GNSS combination is mainly divided into a direct difference calculation method and a modeling estimation method. The direct difference solving method is based on a specific force equation, the specific force measured by an accelerometer and the inertial acceleration measured by a GNSS are subjected to difference to obtain a gravity vector, and then the deviation of a vertical line is calculated through simple mathematical operation; the modeling estimation method is characterized in that vertical deviation is introduced into an SINS error equation, modeling is carried out on the vertical deviation, and then the vertical deviation is estimated by utilizing reference information provided by GNSS and combining a Kalman filter.

When the vertical deviation is solved by using a direct difference method, the specific force needs to be converted from a carrier system to a navigation coordinate system by using a direction cosine matrix, which means that the calculation of the vertical deviation is influenced by the error of the direction cosine matrix. However, the calculation error of the direction cosine matrix is affected by the deviation of the vertical line, which forms a closed loop which is difficult to break. The accuracy of the vertical deviation recovered by the modeling estimation method depends on the degree of coincidence between the gravity model and the true gravity vector. The high-precision vertical line deviation needs a high-precision gravity field model, but the characteristics of the gravity field model of an unknown area are difficult to obtain in advance in actual work. Therefore, a new method for recovering the deviation of the vertical line based on the attitude difference compensation is needed.

Through the above analysis, the problems and defects of the prior art are as follows:

(1) in the existing direct difference solving method, the calculation error of the direction cosine matrix is influenced by the deviation of the vertical line, and a closed loop which is difficult to break is formed.

(2) In the existing modeling estimation method, high-precision vertical deviation needs a high-precision gravity field model, but the characteristics of the gravity field model of an unknown area are difficult to obtain in advance in actual work.

The difficulty in solving the above problems and defects is:

(1) controlling errors;

(2) and obtaining a high-precision gravity field model.

The significance of solving the problems and the defects is as follows: the invention provides a novel method for measuring vertical deviation, which not only relieves the coupling of direction cosine matrix calculation error and vertical deviation, but also avoids model inaccuracy error without modeling unknown vertical deviation.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a method, a system, a terminal and a medium for measuring the deviation of a perpendicular line based on attitude difference compensation.

The invention is realized in such a way that the method for measuring the vertical deviation based on the attitude differential compensation comprises the following steps:

step one, performing integrated navigation by using SINS and GNSS, and solving an attitude rotation matrix

Step two, combining gyro components Gyros and GNSS in SINS to calculate attitude rotation torque matrix

Step three, useAndcarrying out difference, wherein the difference result comprises vertical deviation and a Gyros/GNSS attitude error item with definite characteristics;

modeling a low-frequency trend item in the Gyroso/GNSS attitude error item into a first-order Markov process, and taking a periodic item in the Gyroso/GNSS attitude error as prior information;

fifthly, vertical deviation compensation is carried out on a gravity item in the SINS inertial solution equation by using the attitude difference result, a vertical deviation item is eliminated, and a Gyros/GNSS attitude error item with known modeling characteristics is introduced;

step six, carrying out fading memory Kalman filtering on the compensated SINS inertial solution model, and estimating an attitude rotation matrix without vertical deviation information

Step seven, useTaking the reference and calculating the attitude rotation matrix with the SINS/GNSS combined navigation in the step oneMaking a difference, wherein the difference result is the vertical line deviation information on the recovered track;

step eight, a method for screening the fading factors by using the minimum sum of pure inertia resolving speed errors as a target function finds out the optimal fading factors for the fading memory Kalman filter in the step six;

step nine, the initial value of the fading factor is 1, and the step length is 0.01; performing fading memory Kalman filtering once every time an fading factor is traversed, judging whether the filtering is diverged, and if so, terminating the algorithm; if not, a pair of horizontal misalignment angles is estimated

Step ten, carrying out Fourier transformation on the horizontal misalignment angle estimated by the filter, and judging whether the frequency spectrum is in omega_inThere is a spike; if not, the filtering result is not accurate, and the loop is ended; if so, explaining that the filtering result meets the prior condition, and further calculating the vertical line deviation according to the seventh step;

step eleven, compensating and correcting a gravity term in the SINS pure inertia calculation by using the calculated vertical line deviation eta (i) and xi (i), and calculating the sum of speed calculation errors;

and step twelve, observing a curve of the sum of the speed errors, wherein the corresponding vertical deviation when the sum of the speed errors is minimum is the recovered vertical deviation, and the fading factor of the cycle is the optimal fading factor.

Further, in the step one, the direction cosine matrix calculated by using the SINS/GNSS combined navigation is recorded as

Further, in the second step, the direction cosine matrix solved by the gyro/GNSS integrated navigation is recorded as

Further, in step three, the useAnddifference and cancelDirection cosine matrix for reflecting real postureThe method comprises the following steps:

ignoring the second order fractional amount, equation (3) is written as:

define θ phi-psi, which is written as an east and north projection:

by theta_EAnd theta_NAnd (3) compensating the vertical line deviation, and writing a compensated speed differential equation as follows:

in the formula (6), V^cIn order to calculate the speed of the vehicle,for the purpose of the direction cosine matrix of the calculation,for specific force measurements involving accelerometer device errors,andare respectively asAndthe calculated value of (a); the compensated velocity error equation is written as:

in the formula (I), the compound is shown in the specification,representing the inertially resolved attitude misalignment angle after vertical deviation compensation.

Further, in step four, the gyro/GNSS attitude error ψ includes a constant term, a slowly-increasing term, and a periodic term, the angular frequency of the periodic term being equal toSo the last term of equation (7) is modeled as:

in the formula, a_E1(t) and a_N1(t) represents a time-dependent function, a_E2(ω_int) and a_N2(ω_int) represents an angular frequency of ω_inIs used to determine the period function of (2). a is_E1(t)，a_N1(t) each comprises a constant term and a slowly-increasing term, the characteristics of the constant term and the slowly-increasing term are very similar to those of the gyro drift, a constant error term is similar to a zero-offset repeatability error of the gyro drift, and a slowly-increasing term is similar to a zero-offset stability error of the gyro; a is_E1(t) and a_N1The model of (t) is expressed as:

in the formula, a_E11(t)，a_N11(t) are each a_E1(t) and a_N1Constant term in (t), a_E12(t)，a_N12(t) are each a_E1(t) and a_N1Slowly growing terms in (t), modeled as a first order Markov process, τ_EAnd τ_NIs a correlation time, w_EAnd w_NIs white noise.

Further, in step five, the error equation of the SINS/GNSS integrated navigation system after the vertical deviation compensation is written as:

in the formula, x is a state quantity, w is noise, and u is an input quantity. A is to_E1(t) and a_N1(t) as a state variable, the period term a_E2(ω_int) and a_N2(ω_int) as an input quantity; u＝(0_1×3a_E2a_N200_1×13)^Tthe time variable t is omitted; noise vector w ═ (w)_g w_ax+w_E0 w_ay+w_N0 w_az 0_1×10 w_E 0 w_N)^TWherein w is_gRepresenting noise of the gyro, w_ax、w_ayAnd w_azIs the noise of the accelerometer, w_E0And w_N0The vertical deviation is compensated for by modeling the model noise generated by inaccuracy of the psi modeling in the model.

Further, the integrated navigation process is divided into an inertial resolving process and a filtering process, and the attitude error transmission process of the inertial resolving has a low-pass characteristic. Frequency omega of input quantity_inThe small attenuation is almost not reduced in the error transfer process, and the attenuation is completely reflected in the attitude error, so that the frequency spectrum of the attitude error is in omega_inThere is a spike. Will be provided withThis analysis conclusion, as a priori information, equation (11) can be reduced to a standard combined navigational state equation:

the measurement equation of the SINS/GNSS combined navigation system after vertical deviation compensation is written by taking the position information provided by the carrier phase differential GNSS as reference:

y＝Hx+v (13)

wherein y is measurement quantity, y is δ P, H is measurement matrix, and v is measurement noise; wherein, the expressions of A and H are:

H＝[0_3×6 I_3×3 0_3×10]。

equations (12) and (13) are expressed discretely as:

in the formula phi_k/k-1Representing the discretized system matrix, w_kAnd v_kRepresents a gaussian white noise sequence and satisfies the following relation:

in the formula, delta_jkIs the Dirac delta function.

Further, in the sixth step, the parameters of the historical noise variance matrix are reset by the evanescent memory Kalman filter at the current filtering moment, the filter pays more attention to the functions of new measurement and new state, and is relatively tolerant to noise change and model inaccuracy, and the evanescent memory Kalman filtering equation under the discrete model is as follows:

(1) and (3) one-step prediction:

(2) one-step prediction of variance matrix:

(3) one-step prediction measurement:

(4) innovation:

(5) second order distance of innovation:

(6)

(7) filtering gain:

(8) and (3) state estimation:

(9) state estimation variance:

wherein D is_k＝diag(d_1k d_2k d_3k … d_nk) Is an evanescent factor matrix, is a diagonal matrix, the diagonal elements are evanescent factors given to different state quantities, when d_iWhen 1 is equal to or less than i and equal to or less than n, the i-th state quantity is not faded away. Since the amount of disturbance in the equation is only applied to east and north velocity errors, D_k＝diag([ones(1,3) d_k4 d_k5 1 ones(1,9)])。

Another object of the present invention is to provide a vertical deviation measuring system based on attitude difference compensation, comprising: an attitude rotation matrix acquisition module for performing integrated navigation by using SINS and GNSS to calculate an attitude rotation matrixAnd the method is also used for utilizing gyro components Gyros and GNSS in SINS to carry out combination and calculating an attitude rotation matrix

A priori information acquisition module forAndcarrying out difference, wherein the difference result comprises vertical deviation and a Gyros/GNSS attitude error item with definite characteristics; and will GyModeling a low-frequency trend item in the ros/GNSS attitude error item as a first-order Markov process, and taking a periodic item in the Gyros/GNSS attitude error as prior information;

the attitude rotation matrix estimation module is used for performing vertical deviation compensation on a gravity item in the SINS inertia calculation equation by using an attitude difference result, eliminating a vertical deviation item and introducing a Gyros/GNSS attitude error item with known modeling characteristics; carrying out fading memory Kalman filtering on the compensated SINS inertial solution model, and estimating an attitude rotation matrix without vertical deviation information

An optimal fading factor acquisition module forTaking the reference and calculating the attitude rotation matrix with the SINS/GNSS combined navigationMaking a difference, wherein the difference result is the vertical line deviation information on the recovered track; finding out the optimal fading factor for the fading memory Kalman filter by using the fading factor screening method taking the minimum sum of pure inertia resolving speed errors as a target function;

the vertical line deviation calculation module is used for setting the initial value of the fading factor to be 1 and setting the step length to be 0.01; performing fading memory Kalman filtering once every time an fading factor is traversed, judging whether the filtering is diverged, and if so, terminating the algorithm; if not, a pair of horizontal misalignment angles is estimatedFourier transform is carried out on the horizontal misalignment angle estimated by the filter, and whether the frequency spectrum is in omega or not is judged_inThere is a spike; if not, the filtering result is not accurate, and the cycle is ended; if so, the filtering result is in accordance with the prior condition, and then the vertical deviation is calculated;

the optimal fading factor acquisition module is used for compensating and correcting a gravity term in the SINS pure inertia calculation by using the calculated vertical line deviation eta (i) and xi (i) and calculating the sum of speed calculation errors; and analyzing a curve of the sum of the speed errors, wherein the vertical deviation corresponding to the minimum sum of the speed errors is the recovered vertical deviation, and the fading factor of the cycle is the optimal fading factor.

Another object of the present invention is to provide a computer apparatus including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to execute the attitude difference compensation-based vertical deviation measurement method.

Another object of the present invention is to provide a computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to execute the method for measuring a vertical deviation based on attitude difference compensation.

Another object of the present invention is to provide an information data processing terminal for implementing the method for measuring a vertical deviation based on attitude difference compensation.

By combining all the technical schemes, the invention has the advantages and positive effects that: the method for measuring the vertical deviation based on the attitude difference compensation is different from a direct difference solving method, the direct difference solving method is used for carrying out difference on the acceleration, the attitude is differentiated, the gravity field characteristics of an unknown area do not need to be known in advance, the unknown vertical deviation does not need to be modeled, and model inaccuracy errors in a modeling estimation method are avoided.

The attitude measured by combining the gyro assembly in the SINS and the GNSS is not influenced by the deviation of the vertical line and is only influenced by the error of the gyro, and the attitude error has definite characteristics. And the attitude difference between the attitude measured by the Gyroso/GNSS combination and the attitude measured by the SINS/GNSS can eliminate the real attitude, wherein the attitude difference comprises a vertical deviation, a constant error item, a slowly varying error item and a periodic error item. And vertical deviation compensation is carried out on the gravity item in inertial navigation solution by using the attitude difference, and a constant error, a slowly varying error and a periodic error with definite characteristics are introduced while the vertical deviation error is eliminated. Modeling the slowly-varying error into a first-order Gaussian Markov process, taking the periodic error as input, establishing an SINS/GNSS combined navigation equation after vertical deviation compensation, aiming at the problem of system noise change, using fading memory Kalman filtering for state estimation, wherein the estimated attitude is not influenced by the vertical deviation, taking the attitude as an attitude reference, and making a difference with the attitude solved by the SINS/GNSS combination when the vertical deviation is not compensated, wherein the difference result is the vertical deviation. In order to find out the optimal fading factor, the recovered vertical line deviation is used for vertical line deviation compensation in pure inertia calculation, the corresponding fading factor when the sum of the speed errors is minimum is the optimal fading factor, and the corresponding vertical line deviation is the vertical line deviation along the track.

Technical effect or experimental effect of comparison.

The invention uses a section of simulation test data to verify the method. A section of ocean test flight path is simulated, as shown in figure 1(a), and the deviation of the vertical line on the flight path is shown in figure 1 (b). The ship speed was set to 10m/s and the SINS and GNSS error parameters used were measured as shown in Table 1.

TABLE 1 SINS and GNSS error parameters

When normal gravity is used in the resolving process, SINS/GNSS combined navigation and Gyroso/GNSS attitude resolving are respectively carried out, the horizontal attitude resolved by the two methods is shown as figure 2, and the horizontal attitude error is shown as figure 3. From fig. 2, it can be seen that in the SINS/GNSS integrated navigation solution, the true attitude of inertial navigation is coupled with the vertical deviation, which is difficult to distinguish. The gyro/GNSS attitude calculation is not influenced by vertical deviation, and on the basis of the real attitude, periodic oscillation and slow drift with the period of approximately 24h are shown.

The SINS/GNSS attitude is differentiated from the Gyroso/GNSS attitude, so that the shared real attitude can be eliminated, and the difference result shown in FIG. 4 not only contains vertical deviation, but also contains Gyroso/GNSS horizontal attitude error.

The gravity used in SINS calculation is compensated by the attitude difference result, so that the influence of the vertical deviation on the SINS attitude calculation result can be eliminated theoretically, but the Gyross/GNSS attitude error can be introduced into the SINS calculation process while the vertical deviation is compensated, and becomes a new error source. In the SINS/GNSS combined navigation mode, this error will be reflected in the horizontal attitude error with little attenuation. Therefore, after the vertical deviation compensation is performed by using the attitude difference result, ω is certainly included in the horizontal attitude error of the SINS_inThe period term, as shown in FIG. 5.

As shown in fig. 6, there is an offset between the estimated north attitude error and the true north attitude error, which causes the SINS horizontal attitude error and ultimately the solution error of the vertical bias.

After correcting the SINS attitude error caused by the Gyros/GNSS error, the SINS horizontal attitude contains neither vertical deviation nor Gyros/GNSS attitude error, as shown in fig. 7. After the filtering is stabilized, the SINS horizontal attitude error is almost near zero, but due to the constant error of the north component of Gyross/GNSS attitude solution, the error causes a constant offset error of the SINS roll direction. The attitude without vertical deviation is taken as the reference and then is differed from the SINS/GNSS attitude without vertical deviation compensation, and the difference result is shown in fig. 8. It can be seen that the method for measuring the plumb line deviation based on attitude difference compensation can recover the plumb line deviation on the flight path. However, since the north attitude error has a constant offset, a recovery result of the vertical deviation of the prime plane finally has a constant error, but the error can be better corrected through end point matching, and fig. 8(a) also shows the corrected vertical deviation of the prime plane. The out-of-line deviation conforming accuracy of the corrected prime plane is 3.04%, and the out-of-line deviation conforming accuracy of the meridian plane is 3.86%. The error is mainly in the first 10 hours, and in the time period, the algorithm is in the convergence process and has large overshoot. Except for this process, the exo-coincidence accuracies for η and ξ were 1.06 "and 1.17", respectively, for the last 62 hours.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a chart of vertical deviation from track and track of a ship in accordance with an embodiment of the present invention. FIG. 1(a) a boat track; FIG. 1(b) vertical deviation on track.

FIG. 2 is a horizontal attitude diagram solved by a different method provided by an embodiment of the invention. FIG. 2(a) pitch angle; FIG. 3(b) shows a roll angle.

FIG. 3 is a horizontal attitude error map solved by a different method provided by an embodiment of the present invention.

FIG. 3(a) φ_E(ii) a FIG. 3(b) φ_N。

FIG. 4 is a horizontal attitude difference diagram of the SINS/GNSS and Gyroso/GNSS according to the present invention. FIG. 4(a) east attitude difference; FIG. 4(b) northbound attitude difference.

FIG. 5 is a horizontal attitude error plot compensated for "vertical deviation" provided by an embodiment of the present invention. FIG. 5(a) φ_E(ii) a FIG. 5(b) φ_N。

FIG. 6 is a diagram illustrating an estimate of the horizontal attitude error after "vertical deviation" compensation provided by an embodiment of the present invention; FIG. 6(a) φ_E(ii) a FIG. 7(b) φ_N。

FIG. 7 is a horizontal attitude error plot after compensation of vertical bias and Gyross/GNSS attitude errors provided by embodiments of the present invention. FIG. 7(a) φ_E(ii) a FIG. 7(b) φ_N。

Fig. 8 is a graph of vertical deviation of recovery provided by an embodiment of the present invention. FIG. 8(a) η; fig. 8(b) ξ.

Fig. 9 is a flowchart of a method for recovering a vertical deviation based on attitude difference compensation according to an embodiment of the present invention.

Fig. 10 is a flowchart of an optimal fading factor searching algorithm provided by an embodiment of the present invention.

Fig. 11 is a flowchart of calculating vertical deviation according to an embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

In view of the problems in the prior art, the present invention provides a method, a system, a terminal, and a medium for measuring a vertical deviation based on an attitude difference compensation, and the present invention is described in detail below with reference to the accompanying drawings.

The method for measuring the vertical deviation based on the attitude difference compensation comprises the following steps:

step 1, using SINS and GNSS to carry out integrated navigation and solve attitude rotation matrix

Step 2, combining gyro components Gyros and GNSS in SINS to calculate attitude rotation torque matrix

Step 3, usingAndcarrying out difference, wherein the difference result comprises vertical deviation and a Gyros/GNSS attitude error item with definite characteristics;

step 4, modeling a low-frequency trend item in the Gyroso/GNSS attitude error item as a first-order Markov process, and taking a periodic item in the Gyroso/GNSS attitude error as prior information;

step 5, vertical deviation compensation is carried out on a gravity item in the SINS inertial solution equation by using the attitude difference result, a vertical deviation item is eliminated, and a modeled Gyros/GNSS attitude error item with definite characteristics is introduced;

step 6, forThe compensated SINS resolving model carries out fading memory Kalman filtering, and an attitude rotation matrix without vertical deviation information is estimated

Step 7, usingTaking the reference and calculating the attitude rotation matrix with the SINS/GNSS combined navigationMaking difference, wherein the difference result is the vertical line deviation information on the recovered track;

step 8, an evanescent factor screening method using the minimum sum of pure inertia resolving speed errors as a target function is used for finding out an optimal evanescent factor for an evanescent memory Kalman filter;

step 9, setting the initial value of the fading factor to be 1 and the step length to be 0.01; performing fading memory Kalman filtering once every time an fading factor is traversed, judging whether the filtering is diverged, and if so, terminating the algorithm; if not, a pair of horizontal misalignment angles is estimated

Step 10, performing Fourier transform on the horizontal misalignment angle estimated by the filter, and judging whether the frequency spectrum is in omega_inThere is a spike; if not, the filtering result is not accurate, and the loop is ended; if so, explaining that the filtering result meets the prior condition, and further calculating the deviation of the vertical line;

step 11, compensating and correcting a gravity term in pure inertia calculation by using the calculated vertical deviation eta (i) and xi (i), and calculating the sum of speed calculation errors;

and 12, observing a curve of the sum of the speed errors, wherein the corresponding vertical deviation when the sum of the speed errors is minimum is the recovered vertical deviation, and the fading factor of the cycle is the optimal fading factor.

The invention also provides aPerpendicular deviation measurement system based on attitude difference compensation includes: an attitude rotation torque matrix acquisition module for performing integrated navigation by using SINS and GNSS to calculate an attitude rotation matrixAnd the method is also used for utilizing gyro components Gyros and GNSS in SINS to carry out combination and calculating an attitude rotation matrix

A priori information acquisition module forAndcarrying out difference, wherein the difference result comprises vertical deviation and a Gyros/GNSS attitude error item with definite characteristics; modeling a low-frequency trend item in a Gyroso/GNSS attitude error item as a first-order Markov process, and taking a periodic item in the Gyroso/GNSS attitude error as prior information;

the attitude rotation matrix estimation module is used for performing vertical deviation compensation on a gravity item in the SINS inertia calculation equation by using an attitude difference result, eliminating a vertical deviation item and introducing a Gyros/GNSS attitude error item with known modeling characteristics; carrying out fading memory Kalman filtering on the compensated SINS inertial solution model, and estimating an attitude rotation matrix without vertical deviation information

An optimal fading factor acquisition module forTaking the reference and calculating the attitude rotation matrix with the SINS/GNSS combined navigationMaking a difference, wherein the difference result is the vertical line deviation information on the recovered track; finding out the optimal fading factor for the fading memory Kalman filter by using the fading factor screening method taking the minimum sum of pure inertia resolving speed errors as a target function;

the vertical line deviation calculation module is used for setting the initial value of the fading factor to be 1 and setting the step length to be 0.01; performing fading memory Kalman filtering once every time an fading factor is traversed, judging whether the filtering is diverged, and if so, terminating the algorithm; if not, a pair of horizontal misalignment angles is estimatedFourier transform is carried out on the horizontal misalignment angle estimated by the filter, and whether the frequency spectrum is in omega or not is judged_inThere is a spike; if not, the filtering result is not accurate, and the cycle is ended; if so, the filtering result is in accordance with the prior condition, and then the vertical deviation is calculated;

the optimal fading factor acquisition module is used for compensating and correcting a gravity term in the SINS pure inertia calculation by using the calculated vertical line deviation eta (i) and xi (i) and calculating the sum of speed calculation errors; and analyzing a curve of the sum of the speed errors, wherein the vertical deviation corresponding to the minimum sum of the speed errors is the recovered vertical deviation, and the fading factor of the cycle is the optimal fading factor.

The present invention will be further described with reference to the following examples.

Example 1

The invention provides a vertical line deviation measuring method based on attitude difference compensation. The method is different from a direct difference method, wherein the direct difference method is used for carrying out difference on acceleration, and the method is used for carrying out difference on attitude. In addition, the method does not need to acquire the gravity field characteristics of an unknown area in advance, does not need to model unknown vertical deviation, and avoids inaccurate errors of the model in a modeling estimation method.

The invention provides a method for recovering vertical line deviation based on attitude difference compensation, and the algorithm flow is shown in figure 9, and the method specifically comprises the following steps:

(1) first of all, using SINS and GNSS for groupingSynthesizing navigation, solving out attitude rotation matrix

(2) Then, gyro components Gyroso and GNSS in SINS are used for combination to calculate attitude rotation matrix

(3) By usingAndand carrying out difference. The difference result comprises vertical deviation and a Gyros/GNSS attitude error item with definite characteristics;

(4) modeling a low-frequency trend item in a Gyroso/GNSS attitude error item into a first-order Markov process, and taking a periodic item in the Gyroso/GNSS attitude error as prior information;

(5) vertical deviation compensation is carried out on a gravity term in the SINS inertial solution equation by using an attitude difference result, the vertical deviation term can be eliminated, but a Gyros/GNSS attitude error term with known characteristics and modeled is introduced;

(6) carrying out fading memory Kalman filtering on the compensated SINS resolving model, and estimating an attitude rotation matrix without vertical deviation information

(7) Finally useTaking the reference and calculating the attitude rotation matrix with the SINS/GNSS combined navigationMaking a difference, wherein the difference result is the vertical line deviation information on the recovered track;

(8) in order to find out the optimal fading factor for the fading memory Kalman filter, a fading factor screening method using the minimum sum of pure inertia resolving speed errors as a target function is provided, as shown in FIG. 10;

(9) the initial value of the fading factor is 1, and the step length is 0.01; performing fading memory Kalman filtering once every time an fading factor is traversed, judging whether the filtering is diverged, and if so, terminating the algorithm; if not, a pair of horizontal misalignment angles is estimated

(10) Then, Fourier transform is carried out on the horizontal misalignment angle estimated by the filter, and whether the frequency spectrum is in omega or not is judged_inIf the peak exists, the filtering result is not accurate, and the loop is ended; if so, the filtering result is in accordance with the prior condition, and the deviation of the vertical line is calculated;

(11) the calculation flow of the vertical deviation is as shown in fig. 11, the gravity term in the pure inertia calculation is compensated and corrected by the calculated vertical deviation eta (i) and xi (i), and the sum of the speed calculation errors is calculated;

(12) a plot of the sum of the velocity errors is observed. And when the sum of the speed errors is minimum, the corresponding vertical deviation is the recovered vertical deviation, and the fading factor of the cycle is the optimal fading factor.

Example 2

The invention provides a vertical line deviation recovery method based on attitude difference compensation, which comprises the following detailed mathematical processes:

the direction cosine matrix calculated by SINS/GNSS combined navigation is recorded asThe direction cosine matrix calculated by the Gyros/GNSS combined navigation solution is recorded as

The direction cosine matrix reflecting the real attitude can be eliminated by carrying out attitude difference on the formula (1) and the formula (2)As shown in formula (3),

ignoring the second order fractional amount, equation (3) is written as:

define θ phi-psi, which is written as an east and north projection:

by theta_EAnd theta_NAnd (3) compensating the vertical line deviation, and writing a compensated speed differential equation as follows:

in the formula (6), V^cIn order to calculate the speed of the vehicle,for the purpose of the direction cosine matrix of the calculation,for specific force measurements involving accelerometer device errors,andare respectively asAndthe calculated value of (a). The compensated velocity error equation is written as:

in the formula (I), the compound is shown in the specification,representing the inertially resolved attitude misalignment angle after vertical deviation compensation. Compared with the SINS velocity error equation when the vertical deviation is not compensated for, the new error equation changes only in the last term. The new equation converts the vertical deviation item which is difficult to model into a Gyros/GNSS attitude error item which has definite characteristics and is easy to model. The Gyros/GNSS attitude error psi comprises a constant term, a slowly increasing term and a periodic term, and the angular frequency of the periodic term is equal toThe size of (2). The last term of equation (7) is thus modeled as:

in the formula, a_E1(t) and a_N1(t) represents a time-dependent function, a_E2(ω_int) and a_N2(ω_int) represents an angular frequency of ω_inOf (2)A period function. a is_E1(t)，a_N1And (t) comprises a constant value term and a slow increasing term, the characteristics of the constant value term and the slow increasing term are very similar to the characteristics of the gyro drift, the constant value error term is similar to the zero offset repeatability error of the gyro drift, and the slow increasing term is similar to the zero offset stability error of the gyro. a is_E1(t) and a_N1The model of (t) is expressed as:

in the formula, a_E11(t)，a_N11(t) are each a_E1(t) and a_N1Constant term in (t), a_E12(t)，a_N12(t) are each a_E1(t) and a_N1Slowly growing terms in (t), modeled as a first order Markov process, τ_EAnd τ_NIs a correlation time, w_EAnd w_NIs white noise.

The error equation of the SINS/GNSS integrated navigation system after vertical deviation compensation is written as follows:

in the formula, x is a state quantity, w is noise, and u is an input quantity. A is to_E1(t) and a_N1(t) as a state variable, the period term a_E2(ω_int) and a_N2(ω_int) as input quantity. u＝(0_1×3a_E2 a_N200_1×13)^TThe representation here omits the time variable t. Noise vector w ═ (w)_g w_ax+w_E0 w_ay+w_N0 w_az0_1×10w_E 0w_N)^TWherein w is_gRepresenting noise of the gyro, wax, w_ayAnd w_azIs the noise of the accelerometer, w_E0And w_N0Modeling psi in the vertical deviation compensation modelAccurately generated modeling noise.

The integrated navigation process is divided into an inertial resolving process and a filtering process, and the attitude error transmission process of the inertial resolving has a low-pass characteristic. Frequency omega of input quantity_inThe small attenuation is almost not reduced in the error transfer process, and the attenuation is completely reflected in the attitude error, so that the frequency spectrum of the attitude error is in omega_inThere is a spike. Taking this analysis conclusion as a priori information, equation (11) can be reduced to a standard integrated navigation state equation,

the measurement equation of the SINS/GNSS combined navigation system after vertical deviation compensation is written by taking the position information provided by the carrier phase differential GNSS as reference:

y＝Hx+v (13)

where y is the measurement quantity, y is δ P, H is the measurement matrix, and v is the measurement noise. Equations (24) and (25) are the combined equations of SINS/GNSS, wherein the expressions of A and H are shown in appendix one.

Equations (12) and (13) are expressed discretely as:

in the formula phi_k/k-1Representing the discretized system matrix, w_kAnd v_kRepresents a gaussian white noise sequence and satisfies the following relation:

in the formula, delta_jkIs the Dirac delta function.

The noise vector of the SINS/GNSS combined navigation model after vertical deviation compensation contains modeling noise generated by psi modeling inaccuracy, but the magnitude of the noise is unknown. In order to improve the filtering accuracy, it is desirable that the filter be relatively tolerant to the noise variance matrix Q. The parameters of the historical noise variance array are reset by the fading memory Kalman filter at the current filtering moment, and the filter pays more attention to the functions of new measurement and new state, so that the noise change and model inaccuracy are relatively tolerant. The memory elimination Kalman filtering equation under the discrete model is as follows:

(1) and (3) one-step prediction:

(2) one-step prediction of variance matrix:

(3) one-step prediction measurement:

(4) innovation:

(5) second order distance of innovation:

(6)

(7) filtering gain:

(8) and (3) state estimation:

(9) state estimation variance:

D_k＝diag(d_1k d_2k d_3k … d_nk) Is an evanescent factor matrix, is a diagonal matrix, the diagonal elements are evanescent factors given to different state quantities, when d_iWhen 1 is equal to or less than i and equal to or less than n, the i-th state quantity is not faded away. Since the amount of disturbance in the equation is only applied to east and north velocity errors, D_k＝diag([ones(1,3) d_k4 d_k5 1 ones(1,9)])。

Fading factor d in fading memory Kalman filtering_kThe choice of (c) affects the filtering effect. d_kIf the selection is not proper, the filtering estimation result deviates from the reality, and even filtering divergence occurs. How to select the fading factor d_4kAnd d_5kIs there a The invention provides a method for screening an evanescent factor by taking the minimum error of pure inertial solution as an objective function, which is shown in figure 10. The initial value of the fading factor is 1, and the step length is 0.01. Performing fading memory Kalman filtering once every time an fading factor is traversed, judging whether the filtering is diverged, and if so, terminating the algorithm; if not, a pair of horizontal misalignment angles is estimatedThen, Fourier transform is carried out on the horizontal misalignment angle estimated by the filter, and whether the frequency spectrum is in omega or not is judged_inIf the peak exists, the filtering result is not accurate, and the loop is ended; if so, the filtering result meets the prior condition, and then the vertical deviation is calculated, and the calculation flow of the vertical deviation is shown in fig. 11. And (3) compensating and correcting the gravity term in the pure inertia calculation by using the calculated vertical deviation eta (i) and xi (i), calculating the sum of speed calculation errors, and observing a curve of the sum of the speed errors. And the vertical deviation corresponding to the minimum sum of the speed errors is the recovered vertical deviation, and the fading factor of the cycle is the optimal fading factor.

The calculation process of the vertical deviation is shown in fig. 11. First using theta_EAnd theta_NThe compensated SINS calculation model is subjected to pure inertia calculation, then the error model represented by the formula (2) is subjected to open-loop fading memory Kalman filtering, and the estimated misalignment angle is usedAnd correcting the attitude angle calculated by the pure inertia solution, wherein the corrected attitude angle does not contain the vertical deviation. And the attitude angle is taken as a reference and is subtracted from the attitude angle calculated by the SINS/GNSS combined navigation model which does not perform the vertical deviation compensation, so that the vertical deviation on the track can be recovered.

The SINS attitude measured by the combination of the gyro assembly Gyroso and the GNSS in the SINS is not influenced by the vertical deviation and is only influenced by the Gyroso/GNSS attitude error, and the characteristic is clear. And the attitude measured by the Gyroso/GNSS combination is differed from the attitude measured by the SINS/GNSS, so that the real attitude can be eliminated, and the attitude difference comprises a vertical deviation, a constant error item, a slowly varying error item and a periodic error item. And vertical deviation compensation is carried out on the gravity term in SINS inertial solution by using the attitude difference, and a constant error, a slowly varying error and a periodic error with clear characteristics are introduced while the vertical deviation error is eliminated. Modeling the slowly-varying error into a first-order Gaussian Markov process, taking the periodic error as input, establishing an SINS/GNSS combined navigation equation after vertical deviation compensation, aiming at the problem of system noise change, using fading memory Kalman filtering for state estimation, wherein the estimated attitude is not influenced by the vertical deviation, taking the attitude as an attitude reference, and making a difference with the attitude solved by the SINS/GNSS combination when the vertical deviation is not compensated, wherein the difference result is the vertical deviation. In order to find out the optimal fading factor, the recovered vertical line deviation is used for vertical line deviation compensation in pure inertia calculation, the corresponding fading factor when the sum of the speed errors is minimum is the optimal fading factor, and the corresponding vertical line deviation is the vertical line deviation along the track.

Appendix one:

H＝[0_3×6 I_3×3 0_3×10]。

the technical effects of the present invention will be further described with reference to specific simulation experiments.

Calculation example: the invention uses a section of simulation test data to verify the method. A section of ocean test flight line is simulated, as shown in figure 1(a), and the deviation of the perpendicular line on the flight line is shown in figure 1 (b). The sailing speed of the ship is set to be 10m/s, and SINS and GNSS error parameters used in measurement are shown in a table 1.

TABLE 1 SINS and GNSS error parameters

When normal gravity is used in the resolving process, SINS/GNSS combined navigation and Gyroso/GNSS attitude resolving are respectively carried out, the horizontal attitude resolved by the two methods is shown as figure 2, and the horizontal attitude error is shown as figure 3. From fig. 2, it can be seen that in the SINS/GNSS integrated navigation solution, the true attitude of inertial navigation is coupled with the vertical deviation, which is difficult to distinguish. The gyro/GNSS attitude calculation is not influenced by vertical deviation, and on the basis of the real attitude, periodic oscillation and slow drift with the period of approximately 24h are shown.

The SINS/GNSS attitude is differentiated from the Gyroso/GNSS attitude, so that the shared real attitude can be eliminated, and the difference result shown in FIG. 4 not only contains vertical deviation, but also contains Gyroso/GNSS horizontal attitude error.

The gravity used in SINS calculation is compensated by the attitude difference result, so that the influence of the vertical deviation on the SINS attitude calculation result can be eliminated theoretically, but the Gyross/GNSS attitude error can be introduced into the SINS calculation process while the vertical deviation is compensated, and becomes a new error source. In the SINS/GNSS combined navigation mode, this error will be reflected in the horizontal attitude error with little attenuation. Therefore, after the vertical deviation compensation is performed by using the attitude difference result, ω is certainly included in the horizontal attitude error of the SINS_inThe period term, as shown in FIG. 5.

As shown in fig. 6, there is an offset between the estimated north attitude error and the true north attitude error, which causes the SINS horizontal attitude error and ultimately the solution error of the vertical bias.

After correcting the SINS attitude error caused by the Gyros/GNSS error, the SINS horizontal attitude contains neither vertical deviation nor Gyros/GNSS attitude error, as shown in fig. 7. After the filtering is stabilized, the SINS horizontal attitude error is almost near zero, but due to the constant error of the north component of Gyross/GNSS attitude solution, the error causes a constant offset error of the SINS roll direction. The attitude without vertical deviation is taken as the reference and then is differed from the SINS/GNSS attitude without vertical deviation compensation, and the difference result is shown in fig. 8. It can be seen that the method for measuring the plumb line deviation based on attitude difference compensation can recover the plumb line deviation on the flight path. However, since the north attitude error has a constant offset, a recovery result of the vertical deviation of the prime plane finally has a constant error, but the error can be better corrected through end point matching, and fig. 8(a) also shows the corrected vertical deviation of the prime plane. The out-of-line deviation conforming accuracy of the corrected prime plane is 3.04%, and the out-of-line deviation conforming accuracy of the meridian plane is 3.86%. The error is mainly in the first 10 hours, and in the time period, the algorithm is in the convergence process and has large overshoot. Except for this process, the exo-coincidence accuracies for η and ξ were 1.06 "and 1.17", respectively, for the last 62 hours.

In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, is implemented in a computer program product that includes one or more computer instructions. The procedures or functions described in accordance with the embodiments of the invention may be generated in whole or in part when the computer program instructions are loaded or executed on a computer. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.

The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any modification, equivalent replacement, and improvement made by those skilled in the art within the technical scope of the present invention disclosed in the present invention should be covered within the scope of the present invention.