Non-equal-precision-based data processing method for multi-position north-seeking of fiber-optic gyroscope total station

Abstract

The application discloses a non-equal-precision-based data processing method for multi-position north-seeking of a fiber-optic gyroscope total station, which comprises the following steps: step 1, arranging the fiber-optic gyroscope total station on a surveying station; step 2, calculating the included angle alpha between adjacent sampling positions; step 3, collecting north-seeking data; step 4, removing gross errors from the north-seeking data of each sampling position; step 5, calculating the mean value and the standard deviation of the north-seeking sampling data at each sampling position; step 6, calculating the weight of the mean value of the sampling data at each sampling position and listing the weight matrix of the observation value; step 7, listing the observation equation; step 8, listing the error equation; and step 9, obtaining the least square solution according to the least square criterion to calculate the optimal estimation of the initial azimuth angle. The application improves the reliability of the north-seeking result as a whole and is suitable for complex and changeable underground engineering environments such as tunnels and mines.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of underground tunnel engineering through directional surveying, and particularly relates to a multi-position north-seeking data processing method for a fiber-optic gyroscope total station based on non-equivalent accuracy. TECHNICAL BACKGROUND

[0002] The fiber-optic gyroscope total station is a kind of device integrating a fiber-optic gyroscope and a total station, which independently measures the true north direction through the Sagnac interference effect of the positive and negative beams of the fiber-optic gyroscope, so as to realize the measurement of the north direction angle of any survey line in the underground tunnel engineering. At present, the gyroscopes / theodolites mainly used in the field of underground engineering through surveying mainly adopt the mechanical suspension type.

[0003] At present, the fiber-optic gyroscope has relatively mature north-seeking technology, such as two-position north-seeking, three-position north-seeking, four-position north-seeking and multi-position north-seeking. However, these north-seeking technologies are mainly used to solve the initial azimuth calibration of inertial navigation. In the information processing, the difference between the sampling data at different positions is used to eliminate the influence of system error, so as to obtain the true north direction information. In this solving process, the output north-seeking data sequence of the fiber-optic gyroscope at different positions is regarded as equivalent accuracy observation, and the corresponding difference calculation model is used for calculation. However, in the process of underground engineering directional surveying, due to the unstable engineering environment and many interference sources, the quality of the sampling data at different positions will be greatly different due to the influence of mechanical vibration, temperature change and other factors. Therefore, for the fiber-optic gyroscope total station applied in the underground engineering, the sampling data at different north-seeking positions are of non-equivalent accuracy observation. The difference calculation model used in the conventional two-position, three-position, four-position and multi-position north-seeking methods will cause data processing distortion, and the directional result cannot objectively and truly reflect the correct azimuth value, so it is not suitable for the directional surveying of the underground engineering. SUMMARY

[0004] The present application aims to provide a multi-position north-seeking data processing method for a fiber-optic gyroscope total station based on non-equivalent accuracy, so as to solve the problem that the existing data processing distortion caused by regarding the sampling data at different positions as equivalent accuracy, the directional result cannot objectively and truly reflect the correct azimuth value, and thus is not suitable for the directional surveying of the underground engineering.

[0005] In order to achieve the above-mentioned purpose, the present application adopts the following technical solutions:

[0006] A multi-position north-seeking data processing method for a fiber-optic gyroscope total station based on non-equivalent accuracy, comprising the following steps:

[0007] Step 1: arranging the fiber-optic gyroscope total station on the surveying station, so that the sensitive axis of the fiber-optic gyroscope is parallel to the level surface of the surveying station;

[0008] Step 2, according to the set number of positions n of the fiber-optic gyroscope total station, the included angle a between adjacent sampling positions is calculated according to the following formula:

[0009]

[0010] Step 3, aiming the fiber-optic gyroscope total station at the direction of the survey line, the north-seeking data at the initial position is collected at a predetermined time; then the fiber-optic gyroscope total station is rotated counterclockwise by an angle a, and the data collection is started at the second position; the data collection is sequentially performed at the third, fourth, …, n positions according to the same method, and after the data collection is completed, the data collection is performed again at the initial position;

[0011] Step 4, the north-seeking data collected at each sampling position is subjected to gross error elimination to obtain the retained data after gross error elimination at each sampling position;

[0012] Step 5, the mean value of the north-seeking sampling data at each sampling position is calculated according to the retained data after gross error elimination obtained in Step 4 and the standard deviation STD i :

[0013]

[0014]

[0015] In the formula, ∑l is the sum of the retained data after gross error elimination of the sampling data at the i-th sampling position, l i is each sampling data at the i-th sampling position, is the mean value of the retained data after gross error elimination of the sampling data at the i-th sampling position, and k is the number of the retained data after gross error elimination output in Step 4;

[0016] Step 6, the weight P i of the mean value of the sampling data at each sampling position is calculated according to the standard deviation of each sampling position obtained in Step 5 i , and the observation weight matrix is listed according to the weight:

[0017]

[0018] Step 7, the observation equation is listed:

[0019]

[0020] In the formula, is the mean value of the retained data after gross error elimination of the sampling data at the i-th position, a i is the angle turned by the fiber-optic gyroscope at the i-th position relative to the initial position, ε is the error term at each position, and X1 and X2 are selected parameters;

[0021] For the above equation, let Then the observation equation is written as a matrix equation:

[0022] L = AX

[0023] Step 8, list the error equation:

[0024] Let the selected parameter The adjustment value is Then the error equation is:

[0025]

[0026] Step 9, for the selected parameter X adjustment value Using the error equation obtained in step 8 And the observation value weight matrix P obtained in step 6, according to the least square criterion V T PV = min, the least square solution is obtained:

[0027]

[0028] Where P is the observation value weight matrix calculated in step 6, A and L are the coefficient matrix and observation value column vector of the observation equation listed in step 7, respectively;

[0029] Finally, the initial azimuth best estimate is calculated according to the following formula

[0030]

[0031] Further, the step 4 includes the following sub-steps:

[0032] Step 41, for the north-seeking data collected at each collection position, the mean error δ of the corresponding collection position is calculated according to the following formula i :

[0033]

[0034] In the formula, i is the difference between each observation value at the i-th collection position and the average of all observation values at the position, and m is the number of observation values;

[0035] Step 42, take twice the mean error as the limit difference Δ1, and remove the sampling data at this position that exceeds the limit difference Δ1;

[0036] Step 43, for the data retained after the first elimination, the mean error of the retained data is recalculated according to the formula in step 41, and the new limit error Δ2 is twice the mean error; if all the data retained after the first elimination is less than the new limit error Δ2, the gross error elimination is completed, otherwise, the data exceeding the new limit error Δ2 is eliminated, and the limit error of the data retained after the second gross error elimination is calculated, and whether the retained data exceeds the limit value is checked; the cycle is repeated until the sampling data after the elimination of the gross error is within twice the mean error of the retained data after the elimination, and the retained data after the elimination of the gross error is obtained.

[0037] Compared with the prior art, the beneficial effects of the present application are as follows:

[0038] 1. For the problem of gross error interference in the sampling data, the present application adopts a cyclic gross error elimination method, calculates the limit error value through the data mean error, and then eliminates the gross error according to the limit error, and recalculates the mean error and the limit error after elimination, and repeats the process until the retained data is within the limit error range;

[0039] 2. When calculating the weight of the north-seeking data at each position, the reciprocal of the mean error of the sampling data after the elimination of the gross error at each position in the present application is taken as the corresponding weight value, so as to form a weight matrix to participate in the calculation, thereby improving the reliability of the result;

[0040] 3. In the northward angle solution, the observation weight matrix is added to the solution model to recalculate the north-seeking result. Under the action of the observation weight matrix, the good quality north-seeking position data is amplified in the calculation of the north-seeking result, and the influence of the poor quality north-seeking data on the north-seeking result is reduced, thereby improving the reliability of the north-seeking result as a whole, and being suitable for complex underground engineering environments such as tunnels and mines. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 It is a schematic diagram of the north-seeking orientation measurement data collection sequence of positions 1-13 in the embodiment of the present application.

[0042] Figure 2 It is a data comparison chart before and after the elimination of the gross error.

[0043] Figure 3 It is a flowchart of the method of the present application.

[0044] The technical solutions of the present application are further explained and described below in combination with the drawings and examples. DETAILED DESCRIPTION

[0045] The theoretical basis of the present application is as follows:

[0046] I. Establishment of the observation equation and error equation of the multi-position north-seeking measurement of the fiber-optic gyro total station

[0047] Assume that the output value of the fiber-optic gyro total station at the i-th position is yi :

[0048] y i = Kω e cosβcos(θ+α i )+ε i (Formula 1)

[0049] In the formula, K is a gyro scale factor, which is different for different gyros; ω e is the earth rotation angular rate, which is a constant; β is the latitude of the station, which is determined according to the station location; θ is the included angle between the initial position and the true north direction, which is a to-be-solved quantity; ε i is the error term of the i-th position, which is determined according to each measurement result and is a to-be-solved quantity; α i is the angle turned by the fiber-optic gyroscope relative to the initial position at the i-th position, which is calculated according to the number of positions measured by the fiber-optic gyroscope;

[0050] Expand Formula 1:

[0051] y i = Kω e cosβcosα i cosθ-Kω e cosβsinα i sinθ+ε i (Formula 2)

[0052] For Formula 2, let X1= Kω e cosβcosθ and X2= Kω e cosβsinθ, then Formula 2 can be written as

[0053]

[0054] Approximately, the error terms ε i of the positions are equal to ε, and the following observation equation is obtained:

[0055]

[0056] In the formula, is the mean value calculated according to the sampling data of the i-th position after the outliers are removed; and ε is the error term of each position, which is a to-be-solved quantity.

[0057] For the above formula, let then the observation equation is written as a matrix equation: Y = AX.

[0058] Let the adjustment value of the selected parameter be then the error equation is:

[0059]

[0060] II. Non-equal-precision-based data processing method for multi-position north-seeking of fiber-optic gyroscope total station

[0061] As shown in Figure 3 the non-equal-precision-based data processing method for multi-position north-seeking of fiber-optic gyroscope total station of the present application comprises the following steps:

[0062] Step 1, setting up the instrument. Set up the fiber-optic gyroscope total station at the survey site so that the fiber-optic gyroscope sensitive axis is parallel to the level surface where the survey site is located;

[0063] Step 2, determining the rotation angle between the collection positions. Specifically, according to the set number n of the collection positions of the fiber-optic gyroscope total station, the included angle α between the adjacent sampling positions is calculated according to the following formula:

[0064]

[0065] Step 3, data collection. Specifically, aim the fiber-optic gyroscope total station at the direction of the survey line, and start collecting the north-seeking data at the initial position (1 position) at the predetermined time; then rotate the fiber-optic gyroscope total station aiming part counterclockwise by an angle α, and start collecting data at the second position, and in the same way, sequentially collect data at the third, fourth, …, n positions, and after the end, collect data at the initial position (1 position) again;

[0066] Step 4, removing the gross errors from the north-seeking data collected at each collection position to obtain the retained data after gross error removal at each collection position. Specifically:

[0067] Step 41, calculate the mean error δ of the corresponding collection position for the north-seeking data collected at each collection position according to the following formula: i :

[0068]

[0069] In the formula, i is the difference between each observation value at the i-th collection position and the mean value of all observation values at the position, and m is the number of observation values.

[0070] Step 42, take twice the mean error as the limit difference Δ1, and remove the sampling data at the position that exceeds the limit difference Δ1.

[0071] Step 43, for the data retained after the first elimination, recalculate the mean error of the retained data according to the formula in step 41, and take twice the mean error as the new limit error Δ2; if all the data retained after the first elimination is less than the new limit error Δ2, the gross error elimination is completed, otherwise, eliminate the data exceeding the new limit error Δ2, and calculate the limit error of the data retained after the second gross error elimination, and check whether the retained data has an out-of-limit value; thus, the cycle is repeated until the sampling data after the elimination of gross error is within twice the mean error of the retained data after the elimination, at which time the retained data after the elimination of gross error is obtained;

[0072] Step 5, according to the retained data after the elimination of gross error obtained in step 4, calculate the mean value of the north-seeking sampling data at each collection position and the standard deviation STD i .

[0073]

[0074] In the formula, ∑L is the sum of the retained data after the elimination of gross error of the sampling data at the i-th collection position, and k is the number of the retained data after the elimination of gross error output in step 4.

[0075]

[0076] In the formula, L i is each sampling data at the i-th collection position, is the mean value of the retained data after the elimination of gross error of the sampling data at the i-th collection position, and k is the number of the retained data after the elimination of gross error output in step 4.

[0077] Step 6, calculate the weight of each collection position. Specifically, according to the standard deviation of each collection position obtained in step 5, calculate the weight P i = 1 / STD i of the mean value of the sampling data at each collection position, and list the observation value weight matrix according to it:

[0078]

[0079] Step 7, list the observation equation:

[0080]

[0081] In the formula, is the mean value of the retained data after the elimination of gross error of the sampling data at the i-th position, α i is the angle turned by the fiber optic gyroscope at the i-th position relative to the initial position, ε is the error term of each position, and X1, X2 are selected parameters.

[0082] For the above formula, let then the observation equation is written as a matrix equation:

[0083] L = AX

[0084] Step 8, column error equation:

[0085] Let the selected parameter X be adjusted to The error equation is:

[0086]

[0087] Step 9, calculate the north-seeking result. For the selected parameter X adjustment value Using the error equation obtained in step 8 and the observation value weight matrix P obtained in step 6, according to the least square criterion V T PV = min, the least square solution is obtained:

[0088]

[0089] Wherein, P is the observation value weight matrix obtained in step 6, A and L are the coefficient matrix and observation value column vector of the observation equation listed in step 7.

[0090] According to the setting of the parameters X1 and X2 in the foregoing, it can be known that:

[0091]

[0092] Then the final north-seeking result, that is, the best initial azimuth estimation is:

[0093]

[0094] An embodiment of the present application is given below, and it should be noted that the embodiment is to make the implementation of the technical scheme of the present application easier to understand, and the scope of the technical scheme to be protected by the present application is not limited to the embodiment.

[0095] Embodiment

[0096] Firstly, the instrument is erected at the survey station so that the sensitive axis of the fiber-optic gyroscope is parallel to the level surface where the survey station is located.

[0097] Secondly, the number of north-seeking positions is selected to be 12, and the rotation angle α between each collection position is 30 degrees.

[0098] ​Third step, data collection. The fiber-optic gyroscope total station instrument is aimed at the direction of the survey line, and the north-seeking data of the initial position (1 position) is collected. The collection time is three minutes. After the initial position data collection is completed, the total station instrument is rotated by an angle of a in the counterclockwise direction, and the data collection is started at the second position. In the same way, the data collection is performed at the third, fourth, …, twelfth positions, respectively, and then the data collection is repeated at the initial position (1 position) again. Finally, the north-seeking data of 13 positions is collected. Figure 1 The figure is a schematic diagram of the collection sequence.

[0099] Fourth step, the output data of 13 positions is subjected to the coarse error elimination processing, and the mean value and the standard deviation of the north-seeking sampling data of each collection position after the coarse error elimination are calculated. The data arrangement is shown in the following table.

[0100] Table 1: Gyro output data arrangement

[0101]

[0102] Table 1: continuation

[0103]

[0104] Figure 2 The figure is a comparison diagram of the output data before and after the coarse error elimination. As can be obviously seen from the figure, after the cyclic coarse error elimination, a large amount of observation noise is eliminated, the data fluctuation is effectively reduced, and the stability of the sampling data is greatly improved.

[0105] Fifth step, the weight is calculated according to the standard deviation of the output data of 13 positions in Table 1 after the coarse error elimination, and an observation value weight array P is established according to the weight.

[0106]

[0107] Sixth step, the observation equation is listed as follows.

[0108]

[0109] Let Then the observation equation is written as a matrix equation.

[0110] L = AX

[0111] Seventh step, the error equation is listed as follows.

[0112]

[0113] Eighth step, the north-seeking result is calculated. The least square solution is obtained as follows.

[0114]

[0115] The initial azimuth angle optimal estimation is:

[0116]

[0117] The north-seeking result obtained by the method of the present application is evaluated in precision as follows:

[0118] The unit weight mean error estimation δ0 is:

[0119]

[0120] The correlation factor propagation rate is:

[0121]

[0122] The correlation factor matrix of the adjustment value of the parameters X1 and X2 to be solved is: The correlation factor matrix of the adjustment value of the parameters X1 and X2 to be solved is: The elements in the 1st and 2nd rows and in the 1st and 2nd columns. Then, The covariance matrix of the adjustment value of the parameters X1 and X2 to be solved is:

[0123]

[0124] If the method of the present application is not used to weight each north-seeking position before solving, the covariance matrix of the north-seeking result is:

[0125]

[0126] From the data of the above two covariance matrices, it can be seen that the variance of the selected parameter X1 is reduced from 0.8487 to 0.6247 before and after weighting, and the variance of the parameter X2 is reduced from 0.9793 to 0.9246 before and after weighting. Thus, after adding the observation weight matrix during solving, the precision of the north-seeking result is effectively improved.

Claims

1. A non-equal-precision-based data processing method for multi-position north-seeking of a fiber-optic gyroscope total station, characterized in that, It comprises the following steps: Step 1, disposing the fiber-optic gyro total station on the survey station so that the fiber-optic gyro sensitive axis is parallel to the level surface where the survey station is located; Step 2, according to the set number n of the fiber-optic gyro total station acquisition positions, calculating the included angle α between adjacent sampling positions according to the following formula: Step 3, aiming the fiber-optic gyro total station at the direction of the survey line, starting to collect the north-seeking data at the initial position at a predetermined time; then rotating the fiber-optic gyro total station aiming part α degrees counterclockwise, and starting to collect data at the second position, and sequentially collecting data at the third, fourth, …, n positions according to the same method, and after finishing, collecting data at the initial position again; Step 4, performing gross error elimination on the north-seeking data collected at each acquisition position to obtain the retained data after gross error elimination at each acquisition position; Step 5, according to the retained data after the rough error elimination obtained in step 4, the mean value of the north-seeking sampling data at each collection position is calculated and the standard deviation STD i : wherein ∑L is the sum of the retained data of the sampling data of the i-th collection position after the gross error is eliminated, L i is each sampling data of the i-th collection position, is the mean of the retained data of the sampling data of the i-th collection position after the gross error is eliminated, and k is the number of the retained data after the gross error is eliminated in step 4. Step 6, according to the standard deviation of each collection position obtained in step 5, the weight P of the mean value of the sampling data of each collection position is calculated i = 1 / STD i , and the observation value weight matrix is listed as follows: Step 7, listing the observation equation: In the formula, is the mean value of the reserved data of the sampling data of the i th position after the gross error is eliminated, and α i is the angle turned by the fiber-optic gyroscope at the i th position relative to the initial position, ε is the error term of each position, and X1 and X2 are selected parameters. For the above equation, let The observation equation is then written as a matrix equation: L = AX Step 8, listing the error equation: The selected parameters are adjusted by the adjustment values The error equation is: Step 9. Adjustment of selected parameters X Using the error equation from Step 8 and the weight matrix P from Step 6, the least squares solution is found by minimizing the criterion V T PV = min Wherein, P is the observation value weight matrix obtained in step 6, A and L are respectively the coefficient matrix and the observation value column vector of the observation equation listed in step 7; Finally, the initial azimuth best estimate is calculated according to the following formula 2. The non-equal-precision based fiber-optic gyroscope total station multiple position north-seeking data processing method according to claim 1, characterized in that, The step 4 comprises the following sub-steps: Step 41, the mean error δ of the corresponding collecting position is calculated according to the following formula for the north-seeking data collected at each collecting position i : wherein i is the difference between each observation at the ith collection location and the mean of all observations at that location, and m is the number of observations. Step 42, taking twice the mean error as the limit difference Δ1, and eliminating the sampling data of this position exceeding the limit difference Δ1; Step 43, for the data retained after the first elimination, recalculating the mean error of the retained data according to the formula in step 41, and taking twice the mean error as the new limit difference Δ2; If the retained data after the first elimination is less than the new limit difference Δ2, the gross error elimination is completed, otherwise, the data exceeding the new limit difference Δ2 is eliminated, and the limit difference of the data retained after the second gross error elimination is calculated to check whether the retained data has an out-of-limit value; so on and so forth until the sampling data after eliminating the gross error is within twice the mean error of the retained data after elimination, and at this time, the retained data after gross error elimination is obtained.

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