Strapdown sustainable gravity measurement method

Abstract

The invention discloses a strapdown sustainable gravity measurement method which comprises the following steps: S1, on the basis of Huber-M estimation, providing fast robust Kalman filtering which only needs to traverse a measurement vector, and taking the fast robust Kalman filtering as a data fusion algorithm of integrated navigation; s2, detecting the satellite number or displacement information of the GNSS to judge whether the receiver fails or not; s3, determining the number gt of satellites; 4, when the displacement information is not all zero, considering that the GNSS has no fault, and performing robust all-parameter combination measurement at the moment; s4, when the number of satellites is 1t; 4, performing gravity measurement by using the speed, the position and the attitude provided by the SINS. According to the method, robust filtering and state switching are introduced into a traditional measurement framework, the precision and reliability of open sea gravity measurement are effectively improved, the problem that measurement results jump due to interference of a GNSS during strapdown gravity measurement is solved, the problem that gravity measurement cannot be continuously carried out when the GNSS breaks down is also avoided, and in the open sea gravity measurement period, the measurement accuracy is improved. The research of the gravity measurement precision improvement method has reference significance.

Description

Technical Field

[0001] The present invention relates to the technical field of gravity measurement, and in particular to a strap-down sustainable gravity measurement method. Background Art

[0002] Due to the irregular shape of the earth and the uneven distribution of the mass inside the earth, there are always differences between the earth's gravity field and the normal gravity field. The difference in the vertical direction is called gravity anomaly. Gravity anomaly can be used for gravity matching with SINS to form a passive integrated navigation system, improving the navigation accuracy for long endurance. It can also be used for constructing the gravity background field to enrich the national basic information resource library and promote the research on topics such as geodynamics and oceanography. Gravity anomaly can reflect the vertical difference and can also be used for terrain exploration, resource detection, etc. The ocean occupies 71% of the global area. Measuring the ocean gravity anomaly can further enrich the gravity field data. It is of great significance for promoting the construction of the ocean gravity background field, accelerating the research process of the long-endurance passive navigation system, developing ocean science, and consolidating the modern ocean military status, etc.

[0003] Shipborne gravity measurement has become one of the main technical means to obtain ocean gravity anomaly. Spring gravimeters, strap-down gravimeters, atomic gravimeters, etc. are often used for shipborne gravity measurement. Spring gravimeters are easily affected by temperature, air pressure, magnetic field, etc., and the measurement accuracy fluctuates greatly. Atomic gravimeters are based on optics, using magneto-optical trap to cool and trap atoms, making them fall freely. Then, atomic interference is realized by using matter waves, and gravity information is extracted from the interference fringes. It has the advantages of no drift and strong static stability. However, when performing atomic gravity measurement, it is necessary to always maintain the preparation and vertical fall of the atomic cloud. Atomic gravimeters have extremely high requirements for the environment and must rely on the assistance of temperature control systems, stable platforms, and vibration isolation systems, with relatively high experimental costs. Strap-down gravimeters are based on Newton's laws of motion, using the specific force, attitude, displacement, etc. data provided by GNSS (or other devices that can provide position information) and SINS to extract relative gravity. Strap-down gravimeters have drift due to their inherent properties. However, the related technologies such as integration, miniaturization, temperature control, and gravity extraction are relatively mature, and the zero drift and measurement error are getting smaller and smaller. In addition, strap-down gravimeters do not require the assistance of stable platforms, vibration isolation systems, etc., and have a high degree of integration, and can perform shipborne gravity measurement under any sea conditions. Their stability and sustainable measurement performance are better than those of atomic gravimeters.

[0004] Among them, SINS and GNSS are the main devices for shipborne gravity measurement at sea. Generally speaking, parameters such as position and speed required for gravity measurement are all from GNSS. However, when sailing at sea, it is very easy to have the situation that the wetness causes the wiring of the equipment to malfunction, and typhoons, storms and other situations will also occur. At this time, GNSS will lose lock due to the failure and cannot continue to provide speed and position information, making it difficult to continuously carry out gravity measurement.

[0005] In order to ensure that the gravity measurement equipment can still continuously measure reliable gravity information when GNSS is interfered or fails, we propose a strapdown sustainable gravity measurement method to solve the above problems. Summary of the Invention

[0006] The purpose of the present invention is to solve the deficiencies existing in the prior art and propose a strapdown sustainable gravity measurement method.

[0007] In order to achieve the above purpose, the present invention adopts the following technical solutions:

[0008] A strapdown sustainable gravity measurement method includes the following steps:

[0009] S1. Based on Huber-M estimation, a fast robust Kalman filter that only needs to traverse the measurement vector is proposed and used as the data fusion algorithm for integrated navigation;

[0010] S2. Detect the number of GNSS satellites or displacement information to determine whether the receiver is faulty;

[0011] S3. When the number of satellites > 4 or the displacement information is not all 0, it is considered that GNSS is fault-free. At this time, robust full-parameter combined measurement is carried out, and the attitude, speed, and position information output by SINS / GNSS is used as the parameters for gravity measurement, and the speed and position information provided by GNSS alone is not used to calculate the correction term;

[0012] S4. When the number of satellites < 4 or the displacement information output by GNSS is all 0, it is considered that GNSS is faulty, and a state switch is made to make SINS / GNSS become the pure inertial navigation mode. Information such as attitude, speed, and position is provided by SINS. Even when GNSS is faulty, gravity measurement can still be continuously carried out. When the number of satellites < 4, the speed, position, and attitude provided by SINS are used for gravity measurement.

[0013] Preferably, according to step S1,

[0014] The main problem of Huber-M is to solve the regression model formula, which is solved by Huber's generalized cost function.

[0015]

[0016] where, e i,k is the residual e k = y k - g(x k ), and i = 1, 2, 3,..., m + d. m = 15 is the dimension of the state vector, J(x i ) is the generalized cost function, and ρ(e k ) is the function expression i,k

[0017]

[0018] In the formula, γ is the adjustment factor, and generally γ = 1.345

[0019] To minimize the Huber equivalent weight function, it is necessary to take the derivative of ρ(e i,k )

[0020]

[0021] Define α(e i,k ) = β(e i,k ) / e i,k , where α(e i,k ) is the correction factor matrix of the derivative β(e i,k ) of ρ(e i,k ). Furthermore, calculate the correction factor χ = diag[α(e i,k )], where χ is the correction matrix with α(e i,k ) as the elements, and correct the abnormal measurements

[0022]

[0023] In the formula χ = diag[α(e i,k )], and is the corrected measurement value

[0024] From the formula it can be obtained that Huber - M realizes the robustification of the Kalman filter. Traversing 21 dimensions causes a large computational burden

[0025] Observe the residual ek and the regression equation parameter ξ k based on the measurement noise and state error. It can be obtained that

[0026]

[0027] Expand the formula as follows:

[0028] ​

[0029] Among them, P k,k-1 is the error covariance matrix corresponding to the one-step prediction in the Kalman filter

[0030] Actually, since the true state value x k is unknown, usually the one-step predicted value is brought into the regression calculation Thus, in the formula In the Huber-M estimation at this time, the residual e k can be written as:

[0031]

[0032] That is to say, e k the dimension related to the state in it plays a very small role. When the influence of the abnormal measurement on the state vector is extremely small or even non-existent, the only thing that plays a robust role is Based on this, the cost function in the formula can be written as:

[0033]

[0034] In the formula, l = 1, 2, 3,..., d.

[0035] According to formula The formula The total number of dimensions in it also becomes 6,

[0036] Replace the formula with Then according to the formula Perform measurement reconstruction to become a fast robust strategy, and then introduce this strategy into the KF, which is the fast robust Kalman filter.

[0037] Preferably, according to step S3, the full-parameter combination measurement means that the acceleration, velocity, and position information related to are all provided by SINS / GNSS, that is, the Eotovs and the normal gravity value are the same as and both come from SINS / GNSS. The attitude, velocity, and position information provided by SINS / GNSS is more accurate than the parameters provided by GNSS because it is feedback-corrected and is in the n-frame.

[0038] Preferably, according to step S3, the robustness is the fast robust Kalman filter in step S1, which is a data fusion method when the satellite is normal, avoiding the influence of satellite outliers and solving the jump problem of the gravity anomaly measurement result when the satellite is interfered.

[0039] Preferably, in step S4, the accelerometer bias and gyroscope drift are compensated according to the states estimated by SINS / GNSS. Due to the lack of integrated navigation correction, the parameters such as velocity and position provided by pure inertial navigation have errors. However, the accuracy of inertial navigation used for gravity measurement is relatively high, which can support the measurement accuracy requirements for a certain period. This enables gravity measurement to be carried out even when GNSS fails.

[0040] Preferably, in step S4, when the number of satellites < 4, pure SINS solution is adopted.

[0041] The present invention introduces robust filtering and state switching into the traditional measurement framework, effectively improving the accuracy and reliability of deep-sea gravity measurement. Facing the actual situation, it not only solves the problem of measurement result jumps caused by GNSS interference during strapdown gravity measurement, but also avoids the problem that gravity measurement cannot continue when GNSS fails. It has certain reference significance for the research of methods for improving gravity measurement accuracy during deep-sea gravity measurement. Description of the Drawings

[0042] Figure 1 It is the flowchart of the traditional method for strapdown relative gravity measurement.

[0043] Figure 2 It is the result diagram of the traditional measurement method when auxiliary devices such as satellites fail.

[0044] Figure 3 It is the flowchart of the measurement method of the present invention for strapdown sustainable gravity measurement when the number of satellite stars > 4 or the displacement information of GNSS is not all 0.

[0045] Figure 4 It is the flowchart of the measurement method of the present invention for strapdown sustainable gravity measurement when the number of satellite stars < 4 or the displacement information of GNSS is all 0.

[0046] Figure 5 It is the shipborne mooring experiment diagram in the experiment carried out in the present invention.

[0047] Figure 6 It is one of the GNSS partial measurement information diagrams in the mooring experiment carried out in the present invention.

[0048] Figure 7 It is another GNSS partial measurement information diagram in the mooring experiment carried out in the present invention.

[0049] Figure 8 It is the third GNSS partial measurement information diagram in the mooring experiment carried out in the present invention.

[0050] Figure 9 It is one of the result comparison diagrams of each method in the mooring experiment carried out in the present invention.

[0051] Figure 10 The second of the comparison diagrams of the results of each method for the mooring experiment conducted in the present invention.

[0052] Figure 11 The third of the comparison diagrams of the results of each method for the mooring experiment conducted in the present invention.

[0053] Figure 12 The fourth of the comparison diagrams of the results of each method for the mooring experiment conducted in the present invention.

[0054] Figure 13 The first of the comparison diagrams of the results of each method for the sea navigation experiment conducted in the present invention.

[0055] Figure 14 The second of the comparison diagrams of the results of each method for the sea navigation experiment conducted in the present invention.

[0056] Figure 15 The third of the comparison diagrams of the results of each method for the sea navigation experiment conducted in the present invention.

[0057] Figure 16 The fourth of the comparison diagrams of the results of each method for the sea navigation experiment conducted in the present invention.

[0058] Figure 17 The fifth of the comparison diagrams of the results of each method for the sea navigation experiment conducted in the present invention. Detailed implementation manners

[0059] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0060] 1 Shipborne strapdown gravity measurement method and limitation analysis

[0061] The commonly used coordinate systems of strapdown relative gravimeters include the navigation coordinate system (n-system), the carrier coordinate system (b-system), the geodetic coordinate system (c-system), the earth-centered earth-fixed coordinate system (e-system), the inertial coordinate system (i-system), etc. Since people are used to representing the navigation information of the carrier by longitude, latitude and altitude, the geodetic coordinate system with the direction of "east-north-up" is denoted as the navigation coordinate system. Corresponding to the n-system, the direction of the b-system is expressed as "right-front-up". The navigation coordinate system and the carrier coordinate system with calculation errors are respectively called the n'-system and the b'-system. Gravity measurement is carried out in the n-system.

[0062] In strapdown gravity measurement based on SINS / GNSS, the direct difference method is the most commonly used. According to Newton's laws of motion and Einstein's general theory of relativity, the carrier motion acceleration in the specific force information is deducted to obtain the gravity information. The specific measurement principle is as follows.

[0063]

[0064] In the formula, g n represents the earth gravity at a certain point, also known as the true gravity. and respectively represent the triaxial acceleration and velocity of the carrier. is the specific force after the combined navigation compensation of the accelerometer. is the specific force information with errors, measured by the accelerometer. is the angular velocity with errors, measured by the gyroscope. represents the rotation matrix of the n-system relative to the b-system. represents the earth's angular velocity of rotation in the n-system. is the transport angular velocity. ·× represents the inverse of matrix ·.

[0065] The gravity disturbance is the difference between the true gravity and the normal gravity. The disturbing gravity is:

[0066] δg n = g n -γ n (2)

[0067] In the formula, γ n is the normal gravity, which can be calculated from WGS-84, CGCS2000, etc.

[0068] Generally, the so-called gravity is actually the vertical component of Equation (2), that is, the gravity anomaly. Expanding Equation (2) in matrix form, the gravity anomaly is:

[0069]

[0070] In the formula, L and h respectively represent the latitude and altitude of the carrier. R M and R N represent the meridian and prime vertical radii of the earth. ω ie is the earth's angular velocity of rotation is called the Eötvös correction. is the vertical acceleration correction in the celestial direction. is the celestial component of is the specific force in the n-system,

[0071] γ = 978032.53349(1 + 0.00530244sin 2 L - 0.00000582sin 2 L) - 0.3086H (4)

[0072] Where H is the ellipsoidal height of the calculation point.

[0073] If the height at the measurement point cannot be accurately obtained, the corresponding normal gravity formula is as follows.

[0074] γ = 978032.53349(1 + 0.00530244sin 2 L - 0.00000582sin 2 L) (5)

[0075] According to Eqs. (3)-(5), the flow of the SINS / GNSS-based gravity measurement method is shown in Appendix Figure 1 . In the figure, are the carrier velocities measured by SINS and GNSS respectively. are the positions output by SINS and GNSS respectively. It can be considered that the parameters with are calculated from the navigation information provided by SINS and are in the n'-system. After being suppressed by integrated navigation, these parameters are error-free. Generally, it is considered that the velocities and positions provided by GNSS are accurate and error-free. represents the vertical acceleration correction term, which is obtained by taking the first difference of the geodetic velocity. In fact, in the ocean environment, the vibration frequency of the waves in the vertical direction is high and the vibration amplitude is small. After low-pass filtering, it can be basically eliminated and does not need to be compensated. The Eotovs g and γ D,g represent the Eotovs correction value and the normal gravity value calculated based on the velocities and positions provided by GNSS.

[0076] The specific implementation steps are as Figure 1 shown

[0077] 1) Collect the original data output by the gyroscope and accelerometer, perform SINS solution, and obtain the attitude, velocity, and position information output by SINS.

[0078] 2) Use the differences between the velocities and positions output by GNSS and SINS as the measurements of SINS / GNSS, and use the attitude error, velocity error, position error, gyro drift, and accelerometer zero bias as the states of SINS / GNSS to perform integrated navigation. Use the Kalman filter to estimate the state error and perform feedback correction on the navigation information output by SINS to obtain accurate attitude information. Furthermore, the specific force in the n-frame is obtained. Here, it should be added that the reason for using the integrated navigation is because the solution of SINS has calculation errors, that is, in the n'-frame. While the integrated navigation is considered to be in the n-frame.

[0079] 3) Calculate the Eötvös g and γ D,g .

[0080] 4) Calculate the gravity anomaly according to 2) and 3), and perform low-pass filtering on it to eliminate high-frequency noise. Generally, an FIR filter is used.

[0081] 5) Evaluate the accuracy of the low-pass filtered .

[0082] The above is the gravity measurement method based on SINS / GNSS, which we call the traditional SINS / GNSS gravity measurement method (CGM). In fact, CGM has certain deficiencies. Analyzing Figure 1 shows that GNSS has a great proportion in gravity measurement. The Eötvös g and γ D,g are both provided by GNSS. And is also related to GNSS. During the operation of the measurement ship at sea, the antenna is vulnerable to weather, water vapor, or electromagnetic interference from other equipment, which introduces outliers in the GNSS , and then leads to jumps in the measurement results. And during offshore measurements, it is difficult to maintain GNSS and other equipment in a timely manner. Once a failure occurs, the integrated navigation results will have errors. And various correction terms will generate great errors, making it difficult to continue the subsequent measurements. Attached Figure 2 is the gravity measurement data output by a strapdown gravimeter under static conditions. It can be seen that when the satellite is abnormal, the gravity measurement results of the traditional strapdown gravimeter will diverge greatly.

[0083] 2 Strapdown sustainable gravity measurement method

[0084] Aiming at the problem that CGM is difficult to continuously and accurately measure when GNSS is interfered or fails during shipborne gravity measurement, the present invention proposes a strapdown gravity sustainable anomaly measurement method (SFR-FPGM) based on state switching and robust strategies.

[0085] The SFR-FPGM first detects the number of GNSS satellites or displacement information. When the number of satellites > 4 or the displacement information is not all 0, it is considered that the GNSS is fault-free. At this time, robust full-parameter combined measurement is performed. The full-parameter combined measurement means that the acceleration, velocity, and position information related to is provided by SINS / GNSS. That is, both the Eotovs and the normal gravity value are the same as and come from SINS / GNSS. The attitude, velocity, and position information provided by SINS / GNSS is also considered to be in the n-frame due to feedback correction and is even more accurate than the parameters provided by GNSS. Robust means that the fast robust Kalman filter (FRKF) proposed in this paper, which only detects the measurement vector, is used as the data fusion method when the satellite is normal to avoid the influence of satellite outliers and solve the jump problem of the gravity anomaly measurement result when the satellite is interfered.

[0086] When the number of satellites < 4 or the displacement information output by GNSS is all 0, it is considered that the GNSS is faulty. At this time, it switches to the pure inertial navigation mode, that is, the attitude, velocity, position, etc. information are provided by SINS. During this process, the zero bias of the accelerometer and the drift of the gyroscope are compensated according to the state estimated by SINS / GNSS. Due to the lack of combined navigation correction, the parameters such as velocity and position provided by pure inertial navigation all have errors. However, the inertial navigation accuracy for gravity measurement is relatively high and can support the measurement accuracy requirements for a certain period. This enables gravity measurement to be carried out even when GNSS is faulty.

[0087] The specific process of SFR-FPGM is as shown in Figure 3 and Figure 4 . It can ensure that within a relatively long time when GNSS fails, the gravimeter can still output reliable navigation parameters and gravity information, rather than the measurement result becoming immediately untrustworthy after a fault, increasing the continuity of navigation and measurement. It also avoids the jump of the measurement result when GNSS is fault-free but interfered. To a certain extent, it weakens the proportion of GNSS in gravity measurement and improves the robustness of gravity measurement.

[0088] Figure 3 and Figure 4 , in which the Eotovs in , γ D,in refer to the Eotovs and normal gravity value calculated from the parameters provided by SINS / GNSS. refer to the Eotovs and normal gravity value calculated from the parameters provided by SINS. The relevant theory and process of FRKF will be introduced in the next section.

[0089] 3 Fast Robust Kalman Filter

[0090] When the satellite is fault-free, gravity measurement can be carried out continuously. However, there are still various instruments and devices around the location where the GNSS antenna is placed. Their electromagnetic waves are likely to interfere with GNSS, resulting in outliers in GNSS. Huber-M is a commonly used method to solve the outlier problem and has been widely used in various fields. But every time it is used, all dimensions of the state vector and the measurement vector need to be traversed. Especially for a high-dimensional system like SINS / GNSS, it greatly increases the computational cost. In view of this problem, based on the Huber-M estimation method, the present invention proposes a fast and robust Kalman filter that only needs to traverse the measurement vector to improve the reliability of attitude, velocity, position, and gravity measurement results when outliers occur.

[0091] First, review the Huber-M estimation method. The Huber-M estimation constructs a regression equation and establishes a generalized cost function to reconstruct the measurement information. For the SINS / GNSS integrated navigation system, the corresponding regression equation is as follows.

[0092]

[0093] In the formula, represents the one-step state prediction. z k is the measurement vector, H k is the measurement matrix. is the system state. represents the pitch angle, roll angle, and heading angle errors. represents the north-east-down velocity error. δp = [δL δλ δh] T represents the latitude, longitude, and altitude errors. ε b = [ε bx ε by ε bz T represents the three-axis gyroscope drift. represents the zero bias of the three-axis accelerometer. v k is the measurement innovation. δx k,k-1 is the difference between the true value and the predicted value. is the one-step predicted value of the Kalman filter.

[0094] The Huber-M estimation defines the following variables according to formula (7):

[0095]

[0096]

[0097]

[0098] ​

[0099] In the formula, R k is the measurement noise covariance matrix. P k,k-1 represents the mean square error matrix of one-step prediction. D k is the robust factor of Huber-M estimation. y k is the regression equation parameter based on the predicted state and the true measurement in the constructed regression equation. g(x k ) is the regression equation parameter based on the true state and the predicted measurement in the constructed regression equation. ξ k is the regression equation parameter based on the measurement noise and the state error.

[0100] The regression equation can be expressed as:

[0101] y k = g(x k ) + ξ k (11)

[0102] The main problem of Huber-M is to solve the regression model (12), and this regression problem can be solved by Huber's generalized cost function, such as

[0103]

[0104] where, e i,k is the residual e k = y k - g(x k )'s i-th component, i = 1, 2, 3,..., m + d. m = 15 is the dimension of the state vector. J(x k ) is the generalized cost function. ρ(e i,k ) is the function expression.

[0105]

[0106] In the formula, x is the adjustment factor, and generally γ = 1.345 is taken.

[0107] To make the Huber equivalent weight function reach the minimum value, it is necessary to take the derivative of ρ(e i,k ).

[0108]

[0109] Define α(e i,k ) = β(e i，k ) / e i,k , α(e i,k ) is the correction factor matrix of the derivative β(e i,k ) of ρ(e i,k ). Furthermore, calculate the correction factor χ = diag[α(e i,k ), χ is based on α(ei,k ) is the correction matrix for the elements. It corrects the abnormal measurements.

[0110]

[0111] Where, χ = diag[α(e i,k )]. is the corrected measurement value.

[0112] It can be seen from formulas (12)-(15) that although the Huber-M estimation realizes the robustification of the Kalman filter (KF), it traverses all dimensions (21 dimensions), resulting in a large computational burden.

[0113] We observe the residual e k and the regression equation parameter ξ k based on the measurement noise and the state error. It is not difficult to see that:

[0114]

[0115] Expand formula (16):

[0116]

[0117] Among them, P k,k-1 is the error covariance matrix corresponding to the one-step prediction in the Kalman filter.

[0118] In fact, since the true state value x k is unknown, usually the one-step prediction value is brought into the regression calculation. Thus, In the Huber-M estimation at this time, the residual e k can be written as:

[0119]

[0120] That is to say, the dimensions related to the state in e k play a very small role. When the abnormal measurement has little or no influence on the state vector, the only thing that plays a robust role is Based on this, the cost function in formula (18) can be written as:

[0121]

[0122] Where, l = 1, 2, 3,..., d.

[0123] According to formula (19), the total number of dimensions in formulas (13)-(15) also becomes 6.

[0124] Replace formula (19) with (12), and then perform measurement reconstruction according to (13)-(15). This is the fast and robust strategy proposed in this paper that only needs to traverse the measurement vector. Introducing this strategy into the KF gives the fast and robust Kalman filter (FRKF). It can be seen that when the state vector is not affected by abnormal measurements, the theoretical accuracy of FRKF is almost the same as that of the traditional KF based on Huber-M estimation. FRKF only needs to traverse a 6-dimensional measurement vector, while HRKF needs to traverse a 21-dimensional vector.

[0125] 4 Implementation steps of the present invention in shipborne experiments

[0126] The experimental verification method of the combined measurement method of the atomic interferometric absolute gravimeter / strapdown relative gravimeter for the open sea of the present invention specifically includes the following steps.

[0127] 1) Obtain the original data of SINS and GNSS in the strapdown relative gravity measurement system.

[0128] 2) According to Figure 3 and Figure 4 's measurement steps, judge the number of GNSS satellites or the output information, and then judge the state of GNSS at the current moment. When the number of satellites > 4 or the displacement information is not all 0, it is considered that GNSS has no fault, and at this time, perform Figure 3 's measurement. At this time, the acceleration, velocity, and position information related to are all provided by SINS / GNSS. That is, both the Eotovs and the normal gravity value are the same as and both come from SINS / GNSS.

[0129] 3) In 2), the designed fast and robust Kalman filter (FRKF) is used as the data fusion algorithm to avoid the influence of satellite outliers and solve the problem of jumps in the gravity anomaly measurement results during satellite interference.

[0130] 4) When the number of satellites < 4 or the displacement information output by GNSS is all 0, it is considered that GNSS has a fault, and at this time, switch to the pure inertial navigation mode, that is, the attitude, velocity, position, etc. information are provided by SINS. Refer to Figure 4 . In this process, the accelerometer zero bias and gyroscope drift are compensated according to the state estimated by SINS / GNSS. Due to the lack of combined navigation correction, the speed, position, etc. parameters provided by pure inertial navigation all have errors. However, the inertial navigation accuracy for gravity measurement is relatively high and can support the measurement accuracy requirements for a certain period. This enables gravity measurement to be carried out even when GNSS has a fault.

[0131] 5) Experiments. Conduct on - ship mooring and navigation experiments to compare the performance of the method proposed in the present invention and traditional methods. In these experiments, the experimental object is an inertial gravity measurement system composed of an uninterruptible power supply (UPS), high - precision GNSS and SINS, and an industrial computer (IPC). The IPC can collect the original data of SINS and GNSS. Some parameters of SINS and GNSS are shown in Table 1 in the appendix.

[0132] Table 1 Parameters of SINS and GNSS

[0133]

[0134] In these experiments, we use the internal consistency accuracy and external consistency accuracy as the criteria for evaluating the gravity measurement effect.

[0135] The internal consistency accuracy does not require an external gravity reference value, but instead calculates the discrepancy values of multiple repeated traverse measurements to evaluate. The formula for the overall internal consistency accuracy of all traverses is as follows.

[0136]

[0137] In the formula, δ aj represents the difference between the observed value at the ath measurement point on the jth repeated line and the average value of the observed values at this measurement point on each repeated line. r represents the total number of measurement points. q represents the total number of repeated lines. ε is the internal consistency accuracy. The formula for the overall internal consistency accuracy of all traverses is as follows.

[0138] The external consistency accuracy requires external gravity reference information. The gravity data on the traverse can be evaluated by formula (21).

[0139]

[0140] In the formula, w a is the difference between the measured gravity value at the ath measurement point and the external reference value. τ is the external consistency accuracy.

[0141] The shore - side mooring experiment was conducted at the seaside of Zhoushan City, Zhejiang Province. The experimental equipment includes an inertial gravity measurement system and an atomic gravity meter. Among them, the inertial gravity measurement system is the experimental object in this experiment. The atomic gravity meter has a stable platform and a vibration isolation system, and the experimental environment is relatively stable, so it is used as a reference. Its static accuracy in the laboratory reaches the uGal (1 uGal = 10 -6 m / s 2 ) level. During the experiment, the inertial gravity measurement system and the atomic gravity meter were placed at the center of the measurement ship at the same time for mooring gravity measurement. Therefore, the heights of the two gravity meters are the same. The layout of this experiment is as Figure 5 shown.

[0142] It should be noted that since there is only one GNSS device, differential positioning cannot be carried out, and precise point positioning is not performed either. Only single-point positioning mode is adopted, and accurate height information cannot be obtained. Therefore, the atomic gravimeter and the strapdown gravity measurement system do not perform elevation correction, that is, γ D = γ D,0 , assuming that the heights of the two gravimeters are the same during the measurement period.

[0143] The entire experimental process lasted for 8 hours in total. During 20000s - 21000s, GNSS was interfered and outliers occurred. We compared six gravity measurement methods, namely the traditional gravity measurement method (CGM, Figure 1 method), the full parameter measurement method (FPGM, without state switching and robust strategy), the robust full parameter measurement method (FR-FPGM, only Figure 3 method, without state switching), the state switching full parameter measurement method (S-FPGM, without robust strategy), the full parameter measurement method using state switching and traditional Huber method (SHR-FPGM), and the measurement method proposed in this paper (SFR-FPGM). The measurement frequency of the above six methods is 1 Hz, while the atomic gravimeter outputs a gravity data every 0.6 s. To align the data, for the above six methods, we take a gravity measurement data every 3 points. For the atomic gravimeter, we take a measurement data every 5 points. In this way, the number of gravity measurement points is 9600 for all.

[0144] The speed and position provided by GNSS are as Figures 6 - 8 shown. The gravity anomaly curves of the atomic gravimeter and the six methods are as Figures 9 - 12 shown. The corresponding external conformity accuracy is shown in Table 2. The average operation time of SHR-FPGM and SFR-FPGM is shown in Table 3.

[0145] Table 2 External Conformity Accuracy of Mooring Experiment

[0146]

[0147] Table 3 Average Operation of SHR-APGM and SFR-APGM

[0148]

[0149] It can be seen from the experimental results that the introduction of the robust strategy effectively suppresses the influence of GNSS outliers. The effects of SFR-FPGM, SHR-FPGM, and FR-FPGM are the best. CGM is second, while FPGM and S-FPGM are the worst. This is because, in the displacement information of gravity measurement, the proportion of velocity information is very large, and the influence of position information on the measurement accuracy is extremely small. In CGM, although both the velocity and position of GNSS contain outliers, the velocity outliers are small. For FPGM and S-FPGM, the displacement information comes from integrated navigation. Without any anti-outlier measurement measures, the navigation error will be "amplified" due to the combined influence of velocity and position measurements. In other words, CGM is more independent, that is, the position error does not affect the velocity error. The measurement accuracy of FR-FPGM and SFR-FPGM is slightly lower than that of SHR-FPGM because, in actual situations, it is difficult to ensure that the state parameters are not affected by abnormal measurements. FRKF only traverses the dimensions related to measurements, so the accuracy will decrease slightly. However, combined with the results in Table 3, the operation efficiency of FRKF is improved by 57.69% compared with the traditional Huber-KF, and the accuracy only decreases by 0.86%. Therefore, the comprehensive performance of FRKF is relatively good, and SFR-FPGM and FR-FPGM are effective.

[0150] We also conducted an on-board navigation experiment. In this experiment, the experimental object and the measurement ship were the same as Figure 5 before. GNSS worked normally throughout the process without interference. The measurement ship made a total of 1 round trip in the east-west direction, with a total of 2 survey lines. The navigation speed was approximately 11 knots, and the length of a single survey line was approximately 45 km. Similarly, accurate height information could not be obtained during the experiment, and the strapdown gravity measurement system was not corrected for elevation. To evaluate the effectiveness of the proposed method, we simulated the situation of GNSS anomalies during the second survey line.

[0151] We used the internal consistency as the evaluation index to evaluate the reliability of the proposed method. The results of CGM, FPGM, FR-FPGM, S-FPGM, and SFR-FPGM when GNSS was abnormal are as Figures 13 - 17 shown.

[0152] It can be seen from the experimental results that due to the different requirements for the accuracy of position and velocity in gravity measurement, and the velocity error of CGM is not affected by the position error. When outliers occur, the increase in the error of CGM is not obvious. However, when GNSS fails, the measurement results of CGM become unreliable. Since the displacement information of FPGM comes from integrated navigation, and the effect of traditional integrated navigation is affected by the comprehensive influence of GNSS velocity and position, the gravity measurement results are unreliable in the face of GNSS outliers and failures. Since FR-FPGM only introduces a robust strategy, it cannot handle the situation of GNSS failure. Similarly, since S-FPGM only introduces a state switching mechanism, the measurement results jump due to the combined influence of velocity and position outliers when GNSS is abnormal. SFR-FPGM can avoid the influence of outliers through FRKF when facing GNSS interference, and can obtain an effective Eötvös correction term through the displacement information provided by the pure inertial navigation mode when facing GNSS failure, and the measurement results are optimal.

[0153] It can be seen that the method of the present invention can ensure that the gravimeter can still output reliable navigation parameters and gravity information for a long time when GNSS fails, rather than the measurement results becoming immediately unreliable after the failure, which increases the continuity of navigation and measurement. It also avoids the jump of measurement results when GNSS is not faulty but is interfered. To a certain extent, it weakens the proportion of GNSS in gravity measurement and improves the robustness of gravity measurement.

[0154] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

Claims

1. A strapdown sustainable gravity measurement method, characterized in that: The following steps are involved: S1. Based on Huber-M estimation, a fast robust Kalman filter that only needs to traverse the measurement vector is proposed as a data fusion algorithm for integrated navigation. S2. Detect the number of GNSS satellites or displacement information to determine whether the receiver is faulty; S3: When the number of satellites is > 4 or the displacement information is not all zero, it is considered that GNSS is fault-free. At this time, robust full-parameter combined measurement is performed, and the attitude, velocity, and position information output by SINS / GNSS are used as parameters for gravity measurement. The velocity and position information provided by GNSS alone are not used to calculate the correction items. S4: When the number of satellites is less than 4 or the displacement information output by GNSS is all 0, it is considered that GNSS is faulty and the state is switched to make SINS / GNSS into pure inertial navigation mode. The attitude, speed, position and other information are provided by SINS. Even if GNSS fails, gravity measurement can still be continued. When the number of satellites is less than 4, gravity measurement is performed using the speed, position and attitude provided by SINS.

2. A strapdown sustainable gravity measurement method according to claim 1, characterized in that: According to step S1, The main problem of Huber-M is to solve the regression model formula, which is solved by Huber's generalized cost function. Among them, e i,k is the residual e k =y k -g(x k ), i=1,2,3,...,m+d. m=15 is the dimension of the state vector, J(x k ) is the generalized cost function, ρ(e i,k ) is a function expression In the formula, γ is the adjustment factor, which is generally taken as γ = 1.345 In order to minimize the Huber equivalent weight function, it is necessary to i,k ) Define α(e i,k )=β(e i,k ) / e i,k , α(e i,k ) is ρ(e i,k ) derivative β(e i,k ) correction factor matrix, and then calculate the correction factor χ = diag[α(e i,k )], χ is α(e i,k ) is the correction matrix of the elements to correct the abnormal measurement In the formula, χ=diag[α(e i,k )], The corrected measured value From the formula It is concluded that Huber-M realizes the robustness of Kalman filtering, traversing 21 dimensions, resulting in a large computational burden Observe residuals ek and the regression equation parameters based on measurement noise and state error ξk The definition of , we get: The formula Expand: in, Pk,k-1 is the error covariance matrix corresponding to the one-step prediction in Kalman filtering In fact, since the real state value xk Unknown, usually the one-step prediction value is used in the regression calculation Thus, In the Huber-M estimation at this time, the residual ek It can be written as: That is to say, ek The state dimension in plays a small role. When the abnormal measurement has little or no effect on the state vector, the only robust factor is Based on this, the formula The cost function in can be written as: In the formula, l=1,2,3,...,d. According to the formula formula The total number of dimensions in also becomes 6 The formula replace Then according to the formula The measurement reconstruction becomes a fast robust strategy, and then the strategy is introduced into the KF, which is a fast robust Kalman filter.

3. A strapdown sustainable gravity measurement method according to claim 1, characterized in that: According to step S3, the full parameter combination measurement refers to The relevant acceleration, velocity and position information are all provided by SINS / GNSS, that is, Eotovs and normal gravity values ​​are the same. The attitude, velocity and position information provided by SINS / GNSS are all from SINS / GNSS. The attitude, velocity and position information provided by SINS / GNSS are in the n-frame due to feedback correction, and are more accurate than the parameters provided by GNSS.

4. A strapdown sustainable gravity measurement method according to claim 1, characterized in that: According to step S3, the robust method is the fast robust Kalman filter in step S1, which is a data fusion method when the satellite is normal, avoiding the influence of satellite wild values ​​and solving the jump problem of gravity anomaly measurement results when satellite interference occurs.

5. A strapdown sustainable gravity measurement method according to claim 1, characterized in that: In step S4, the accelerometer bias and gyroscope drift are compensated according to the state estimated by SINS / GNSS. Due to the lack of integrated navigation correction, the speed, position and other parameters provided by pure inertial navigation have errors. However, the inertial navigation accuracy used for gravity measurement is relatively high and can support the measurement accuracy requirements of a certain period. This allows gravity measurement to be performed even when GNSS fails.

6. A strapdown sustainable gravity measurement method according to claim 1, characterized in that: In step S4, pure SINS solution is used when the number of satellites is less than 4.

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