A KF filter-based method and system for processing aerial gravity data

Abstract

The present disclosure discloses a method and system for processing airborne gravity data based on K-F filtering, comprising the following steps: acquiring airborne gravity data from a measurement carrier and constructing a first mathematical model of airborne gravity anomalies; introducing an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomalies, wherein the unknown adjustment coefficient is an adjustment coefficient for which a specific value is to be obtained; organizing the second mathematical model into a Kalman filter state equation and a measurement equation to obtain a spatial state model; obtaining a specific value of the unknown adjustment coefficient based on the spatial state model; substituting the specific value into the second mathematical model and solving the second mathematical model to obtain a third mathematical model containing noise; and performing FIR low-pass filtering on the third mathematical model based on a preset cutoff frequency of the FIR low-pass filter. This improves the ability to handle dynamic noise.

Description

Technical Field

[0001] The present disclosure belongs to the technical field of aerial gravity measurement, and relates to a method and system for processing aerial gravity data based on KF filtering. Background Art

[0002] As a key technology for efficiently and environmentally friendly acquisition of the Earth's gravity field, airborne gravity measurement is widely used in complex terrain, such as mountains, swamps, and oceans, where human beings cannot pass through, or when rapid scanning measurements are required. It plays an important role in mineral resource exploration, geophysical research, and military geology. It is a dual-channel measurement performed by an airborne gravimeter and a differential satellite positioning system using an aircraft (such as an airplane or drone). However, during the measurement process, due to interference from multiple sources such as airflow disturbances, high-frequency vibration of the carrier, and sensor noise, the signal-to-noise ratio of the measured gravity data is only a few thousand or even tens of thousands of parts.

[0003] Currently, research on noise suppression methods for airborne gravity data primarily focuses on optimizing single filtering methods. Common methods in practical applications include low-pass filtering and Kalman filtering. Finite Impulse Response (FIR) filters, due to their well-defined frequency-domain cutoff characteristics, are widely used for frequency-domain processing of airborne gravity data. By designing an appropriate cutoff frequency, FIR filters can effectively remove high-frequency noise and retain the key information of the gravity signal. However, although the frequency band of gravity anomaly signals is primarily distributed in the low-frequency band, there is no obvious spectral transition between them and the noise. A single FIR "one-size-fits-all" approach cannot fully adapt to the dynamically changing noise characteristics of flight platforms, potentially resulting in insufficient suppression of non-stationary noise and insufficient separation of gravity signals and noise in overlapping spectral regions. In contrast, the Kalman filter is a time-domain recursive estimation method. Based on the measurement principles and characteristics of airborne gravity measurement systems, it constructs a state equation to achieve separation and estimation of gravity anomaly signals and noise. It exhibits flexible noise suppression capabilities in dynamic environments and is particularly well-suited to addressing interference from the dynamic characteristics of flight platforms on gravity signals. However, since Kalman filtering is performed in the time domain, the cutoff frequency information of the estimated gravity anomaly signal is not clearly given. As a result, when subsequent terrain correction and other methods are performed, data processing personnel are unable to accurately match the terrain data of the corresponding frequency, which limits its application in engineering.

[0004] Therefore, how to effectively suppress noise, ensure the integrity of gravity anomaly signals, and improve measurement accuracy, reliability and practicality remains an important challenge restricting the in-depth development of the field of aviation gravity. Summary of the Invention

[0005] This disclosure section is provided to briefly introduce concepts that will be described in detail in the detailed description section below. This disclosure section is not intended to identify key features or essential features of the claimed technical solution, nor is it intended to limit the scope of the claimed technical solution.

[0006] The purpose of the present disclosure is to overcome the existing technical defects. An embodiment of the present application provides a method for processing aerial gravity data based on KF filtering (i.e., fusion of Kalman and FIR filtering), and the processing method includes the following steps: acquiring aerial gravity data of a measurement carrier and constructing a first mathematical model of aerial gravity anomaly; introducing an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomaly, wherein the unknown adjustment coefficient is an adjustment coefficient for which a specific value is to be obtained; organizing the second mathematical model into the form of a Kalman filter state equation and a measurement equation to obtain a spatial state model; according to the spatial state model, obtaining a specific value of the unknown adjustment coefficient; bringing the specific value into the second mathematical model, and solving the second mathematical model to obtain a third mathematical model containing noise; and performing FIR low-pass filtering on the third mathematical model based on a preset cutoff frequency of the FIR low-pass filter.

[0007] In some embodiments, the first mathematical model is:

[0008]

[0009] Among them, Δg is the gravity anomaly value, f Σ is the corrected gravity value, is the vertical acceleration of the aircraft, q ∑ is the sum of all types of noise.

[0010] In some embodiments, an unknown adjustment coefficient is introduced into the first mathematical model to obtain a second mathematical model of gravity anomaly, comprising: ∑ It is divided into four parts, including the error caused by gravity acceleration in the X-axis direction, the error caused by gravity acceleration in the Y-axis direction, the error caused by gravity acceleration in the Z-axis direction, and other noises. Three adjustment coefficients Sx, Sy, and Sz are introduced to adjust the errors caused by gravity acceleration fx, fy, and fz in the three directions respectively, and the second mathematical model is obtained. The second mathematical model is

[0011]

[0012] In some embodiments, the step of arranging the second mathematical model into a Kalman filter state equation and a measurement equation to obtain a spatial state model includes:

[0013] Rewrite the second mathematical model as formula (1)

[0014]

[0015] h'=H f X f +δh-----Formula (1)

[0016] Where h' is the height of the reference ellipsoid and δh is the measurement error of h';

[0017] X f =(hv u S z S y S x ) T ,

[0018] The gravity anomaly is a random process, modeled using a shaping filter:

[0019]

[0020] Δg=H g X g Formula (2)

[0021] The gravity anomaly Δg is taken as the estimated state, where is the filter state vector, A g , Γ g is a constant matrix, q g To generate a strength of Q g White noise,

[0022] Pick

[0023] H g =(1 0)

[0024] Combining equations (1) and (2), we can obtain the final spatial state model:

[0025]

[0026] Δg=H g X g

[0027] h'=H f X f +δh

[0028] According to the spatial state model, the specific values ​​of the unknown adjustment coefficients Sx, Sy, and Sz are obtained;

[0029] The specific values ​​of Sx, Sy, and Sz are substituted into the second mathematical model to deduct the errors caused by fx, fy, and fz, thereby obtaining a third mathematical model containing noise.

[0030] In some embodiments, the FIR low-pass filter adopts a window function method, and the window function method includes a Hanning window, a Hamming window, and a Blackman window.

[0031] In some embodiments, the corrected gravity values ​​include the following: normal field correction, altitude correction, Erratum correction, zero drift correction, and base point correction difference.

[0032] In a second aspect, an embodiment of the present disclosure provides an airborne gravity data processing system based on KF filtering, comprising: a data acquisition module for acquiring airborne gravity data; a model construction module for constructing a mathematical model of airborne gravity anomalies; a Kalman filter module for obtaining an adjustment coefficient; and an FIR filter module for performing frequency domain cutoff processing on the signal output by the Kalman filter.

[0033] In some embodiments, the data acquisition module includes an airborne gravimeter and a differential satellite positioning system to obtain high-precision measured gravity data and positioning information.

[0034] In some embodiments, the model building module adjusts the parameters of the mathematical model according to different measurement environments to obtain a model that adapts to complex terrain and dynamic noise conditions.

[0035] In some embodiments, the Kalman filter module adjusts the filter parameters in real time to obtain noise data that adapts to dynamic changes, and the FIR filter module performs filtering processing according to a preset cutoff frequency and window function.

[0036] One or more embodiments of the present disclosure, by fusing Kalman filtering and FIR filtering, retain the ability of Kalman filtering to suppress noise in a dynamic environment, and can also utilize the FIR filter's ability to significantly process dynamic noise based on the clear cutoff frequency of the gravity anomaly signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The above and other features, advantages, and aspects of the various embodiments of the present disclosure will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. Throughout the drawings, the same or similar reference numerals represent the same or similar elements. It should be understood that the drawings are schematic and that the originals and elements are not necessarily drawn to scale.

[0038] Figure 1 This is a schematic diagram of a process for obtaining aerial gravity data based on KF filtering provided by one or more embodiments of the present invention;

[0039] Figure 2 This is a schematic diagram of processing aerial gravity data based on KF filtering in Example 1;

[0040] Figure 3It is the result of FIR filtering (filtering time 100s);

[0041] Figure 4 Schematic diagram of the effect of one or more embodiments of the present disclosure, i.e., the result of KF filtering (filtering time 100s);

[0042] Figure 5 It is a schematic diagram of a processing system for airborne gravity data based on KF filtering;

[0043] Figure 6 It is a schematic diagram of the basic structure of an electronic device provided according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0044] The following describes embodiments of the present disclosure in more detail with reference to the accompanying drawings. Although certain embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be construed as limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present disclosure. It should be understood that the drawings and embodiments of the present disclosure are for illustrative purposes only and are not intended to limit the scope of protection of the present disclosure.

[0045] It should be understood that the various steps described in the method embodiments of the present disclosure may be performed in different orders and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present disclosure is not limited in this respect.

[0046] As used herein, the term "including" and its variations are open-ended, i.e., "including but not limited to." The term "based on" means "based, at least in part, on." The term "one embodiment" means "at least one embodiment," the term "another embodiment" means "at least one additional embodiment," and the term "some embodiments" means "at least some embodiments." Other terms are defined in the following description.

[0047] It should be noted that the concepts of "first" and "second" mentioned in this disclosure are only used to distinguish different devices, modules or units, and are not used to limit the order or interdependence of the functions performed by these devices, modules or units.

[0048] It should be noted that the modifications of "one" and "plurality" mentioned in the present disclosure are illustrative rather than restrictive, and those skilled in the art should understand that unless otherwise clearly indicated in the context, they should be understood as "one or more".

[0049] Please refer to Figure 1 , Figure 1 The flow of a method for processing airborne gravity data based on KF filtering is shown.

[0050] Step 101: Acquire airborne gravity data of a measurement carrier and construct a first mathematical model of airborne gravity anomaly.

[0051] Step 102: introducing an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomaly.

[0052] Here, the unknown adjustment coefficient is an adjustment coefficient whose specific value is to be obtained.

[0053] Step 103: Arrange the second mathematical model into the form of a Kalman filter state equation and a measurement equation to obtain a spatial state model;

[0054] Step 104: Obtain a specific value of the unknown adjustment coefficient according to the spatial state model.

[0055] Step 105 , bringing the specific numerical value into the second mathematical model, and solving the second mathematical model to obtain a third mathematical model containing noise.

[0056] Step 106 : performing FIR low-pass filtering on the third mathematical model based on a preset cutoff frequency of the FIR low-pass filter.

[0057] It should be noted that this embodiment provides an aerial gravity data processing method based on KF filtering, which constructs a first mathematical model of aerial gravity anomaly by acquiring aerial gravity data of a measurement carrier; introduces an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomaly, wherein the unknown adjustment coefficient is an adjustment coefficient whose specific value is to be obtained; the second mathematical model is organized into the form of a Kalman filter state equation and a measurement equation to obtain a spatial state model; according to the spatial state model, the specific value of the unknown adjustment coefficient is obtained; the specific value is brought into the second mathematical model, and the second mathematical model is solved to obtain a third mathematical model containing noise; based on the preset cutoff frequency of the FIR low-pass filter, the third mathematical model is subjected to FIR low-pass filtering; Kalman filtering and FIR filtering can be integrated, which not only retains the Kalman filter's ability to suppress noise in a dynamic environment, but also utilizes the FIR filter's ability to significantly process dynamic noise based on the clear cutoff frequency of the gravity anomaly signal.

[0058] In some embodiments, the first mathematical model is:

[0059]

[0060] Where Δg is the gravity anomaly value, f Σ is the corrected gravity value, is the vertical acceleration of the aircraft, q ∑ is the sum of all types of noise.

[0061] In some embodiments, an unknown adjustment coefficient is introduced into the first mathematical model to obtain a second mathematical model of gravity anomaly, including:

[0062] The q in the first mathematical model Σ It is divided into four parts, including the error caused by gravity acceleration in the X-axis direction, the error caused by gravity acceleration in the Y-axis direction, the error caused by gravity acceleration in the Z-axis direction, and other noises. Three adjustment coefficients Sx, Sy, and Sz are introduced to adjust the errors caused by gravity acceleration fx, fy, and fz in the three directions respectively, and the second mathematical model is obtained. The second mathematical model is

[0063]

[0064] In some embodiments, the step of arranging the second mathematical model into a Kalman filter state equation and a measurement equation to obtain a spatial state model includes:

[0065] Rewrite the second mathematical model as formula (1)

[0066]

[0067] h'=H f X f +δh-----Formula (1)

[0068] Where h' is the height of the reference ellipsoid and δh is the measurement error of h';

[0069] X f =(hv u S z S y S x ) T ,

[0070] The gravity anomaly is a random process, modeled using a shaping filter:

[0071]

[0072] Δg=H g X g Formula (2)

[0073] The gravity anomaly Δg is taken as the estimated state, where Xg is the filter state vector, A g , Γ g is a constant matrix, q g To generate a strength of Q g White noise,

[0074] Pick

[0075] H g =(1 0)

[0076] Combining equations (1) and (2), we can obtain the final spatial state model:

[0077]

[0078] Δg=H g X g

[0079] h'=H f X f +δh

[0080] According to the spatial state model, the specific values ​​of the unknown adjustment coefficients Sx, Sy, and Sz are obtained;

[0081] The specific values ​​of Sx, Sy, and Sz are substituted into the second mathematical model to deduct the errors caused by fx, fy, and fz, thereby obtaining a third mathematical model containing noise.

[0082] In some embodiments, the FIR low-pass filter adopts a window function method, and the window function method includes a Hanning window, a Hamming window, and a Blackman window.

[0083] In some embodiments, the corrected gravity values ​​include the following: normal field correction, altitude correction, Erratum correction, zero drift correction, and base point correction difference.

[0084] As an example, Figure 2 As shown in FIG, the airborne gravity data processing method includes obtaining the original measurement signal of the measurement carrier, using Kalman filter data processing and FIR low-pass filter fusion processing. The details are as follows:

[0085] In actual aerial gravity measurements, the force and flight state of the measurement carrier are analyzed according to Newton's second law, and a mathematical model of aerial gravity anomaly can be constructed as follows:

[0086]

[0087] Among them, Δg is the gravity anomaly value, f Σ The gravity values ​​after various corrections, including normal field correction, altitude correction, Erratum correction, zero drift correction, base point correction, etc. is the vertical acceleration of the aircraft, q Σ is the sum of all types of noise. It should be noted that f Σ It can be calculated by using the differential satellite signal and the original gravity measurement signal and regarded as a known quantity.

[0088] In order to achieve dynamic adjustment of aviation gravity anomaly signals, q ∑ The error is divided into four parts: the error caused by gravity acceleration in the X-axis, the error caused by gravity acceleration in the Y-axis, the error caused by gravity acceleration in the Z-axis, and other noise. Three adjustment coefficients, Sx, Sy, and Sz, are introduced into the mathematical model of aviation gravity anomaly to adjust for the errors caused by gravity acceleration fx, fy, and fz in the three directions, respectively.

[0089] The second mathematical model of aviation gravity anomaly can be further rewritten as:

[0090]

[0091] Rewriting the second mathematical model into the form of Kalman filter state equation and measurement equation, we have:

[0092]

[0093] h'=H f X f +δh Formula (1)

[0094] h' is the height of the reference ellipsoid, and δh is the measurement error of h'.

[0095] X f =(hv u S z S y S x ) T ,

[0096] Gravity anomaly is a random process that can be modeled using a shaping filter:

[0097]

[0098] Δg=H g X g Formula (2)

[0099] The gravity anomaly Δg is taken as the estimated state. Here is the filter state vector, A g , Γ g is a constant matrix, q g To generate a strength of Q g of white noise.

[0100] Pick

[0101] H g =(1 0)

[0102] Combining equations (1) and (2), we can obtain the final spatial state model:

[0103]

[0104] Δg=H g X g

[0105] h'=H f X f +δh

[0106] In order to combine the dynamic adjustment ability of Kalman filter and the clear cutoff frequency of FIR low-pass filter, according to the spatial state model, Kalman filter is first used to obtain the adjustment coefficients Sx, Sy, and Sz; the errors caused by fx, fy, and fz are deducted from the corrected total field using the second mathematical model to obtain the third mathematical model containing noise; finally, FIR low-pass filter is used to remove q others This part of the noise.

[0107] In some embodiments, the FIR low-pass filtering method mentioned in the present disclosure is as follows:

[0108] The FIR filter is an all-zero filter. It is a system that can always maintain stability and has a simple design process. The output signal of an N-order FIR filter can be represented by the convolution of the input signal and the filter's impulse response:

[0109]

[0110] Where y(n) is the output signal, h(k) is the filter coefficient, x(n) is the input signal, and N is the filter order.

[0111] Finite impulse response FIR digital filter requires the use of finite length unit impulse response h(k) to approximate the infinite length unit impulse response h of the ideal filter. d (k), the most commonly used and effective method is the window function method. It is usually used to extract aviation gravity anomaly information. That is, a finite length (length N) "window function" sequence w (k) is used to intercept h d (k) Main ingredients:

[0112] h(k)=h d (k)w(k),k=0,1,2,...,N-1

[0113] The window functions used include Hanning window, Hamming window, Blackman window, etc.

[0114] The Kalman filtering method mentioned in this disclosure can be as follows:

[0115] Assume that the estimated state Xk In t k The system noise sequence W is always k-1 and the deterministic input u k-1 The state equation and measurement equation of the driving mechanism are:

[0116] X k =Φ k,k-1 X k-1 +B k-1 u k-1 +Γ k-1 W k-1

[0117] Z k =H k X k +V k

[0118] Where, Φ k,k-1 、B k-1 is a constant matrix; u k-1 is the control item; Γ k-1 is the system noise driving array; H k is the measurement matrix; W k is the system excitation noise sequence, whose variance is Q k ; V k is the measurement noise sequence, whose variance is R k , and W k and V k satisfy:

[0119] E[W k ]=0,

[0120] E[V k ]=0,

[0121]

[0122] Assume that Q k is non-negative definite, R k is positive, Z k and X k Satisfies the linear relationship.

[0123] As an example, the method described in this disclosure was used to test the filtering algorithm using actual measurement data from a certain sea area. The measurement instrument used was a platform-type airborne gravimeter. This gravimeter uses a "three-axis stabilized platform + quartz flexible accelerometer" design.

[0124] The repeated line flight test was carried out at sea. The length of the test line was about 55-70km, the anomaly amplitude was about 50-60mGal, the anomaly shape was an inverted "S" shape, and the edge was basically close to the background field. The flight altitude was a GPS altitude of 600m level flight, and the ground speed was about 220km / h. During the test, the wind speed was relatively large, sometimes reaching 35 knots (about 60km / h), which had a greater impact on maintaining the speed of the survey line. The results of one of the repeated line flights were selected to illustrate the effectiveness of the algorithm proposed in the present invention. Figure 3 and Figure 4 The results of the repeated line coincidence accuracy for FIR 100s filtering and KF filtering using the technical solution of the present invention for 100s are shown. It can be seen that the KF fusion filtering of the technical solution disclosed in the present invention is better than FIR filtering, and the repeated line coincidence accuracy is reduced from 1.847mGal to 0.557mGal, and the ability to handle dynamic noise is significantly improved.

[0125] Please refer to Figure 5 , this embodiment provides a processing system for aerial gravity data based on KF filtering.

[0126] like Figure 5 As shown, the processing system includes:

[0127] Data acquisition module, used to obtain aerial gravity data;

[0128] Model building module, used to build mathematical models of aviation gravity anomalies;

[0129] Kalman filter module, used to obtain the adjustment coefficient;

[0130] The FIR filter module is used to perform frequency domain cutoff processing on the signal output by the Kalman filter.

[0131] The data acquisition module includes an airborne gravimeter and a differential satellite positioning system to obtain high-precision gravity data and positioning information.

[0132] The model building module adjusts the parameters of the mathematical model according to different measurement environments to obtain a model that adapts to complex terrain and dynamic noise conditions.

[0133] The Kalman filter module adjusts the filter parameters in real time to obtain noise data that adapts to dynamic changes, and the FIR filter module performs filtering processing according to a preset cutoff frequency and window function type.

[0134] One or more embodiments provided by the present disclosure can achieve the following technical effects.

[0135] 1. Dynamically adjust the error coefficient through Kalman filtering to effectively suppress non-stationary noise;

[0136] 2. Combined with the frequency domain cutoff characteristics of FIR filtering, it retains clear cutoff frequency information and supports terrain correction;

[0137] 3. The fusion algorithm has been applied in the GIPS-1A airborne gravimeter, improving data processing accuracy by more than 30%.

[0138] At the same time, this disclosure provides the method and results of quality evaluation of the technical solution of this application as follows:

[0139] Airborne gravity measurement internal accuracy evaluates the dynamic accuracy of repeated airborne gravity measurements using repeated line test data. It reflects the degree of consistency of each repeated line test data relative to its mean field data. Because horizontal variations between repeated lines due to instrument operating conditions and flight conditions are largely eliminated, the adjusted internal accuracy generally better reflects the repeatability of the instrument's dynamic measurements, i.e., the actual accuracy or noise index of dynamic measurements. The dynamic performance of the system can be evaluated by statistically analyzing the repeated line consistency of airborne gravity anomalies.

[0140] The mean square error of each repeated line gravity data complies with the accuracy calculation formula:

[0141]

[0142] Where:

[0143] δ ij ——Gravity value F of each point on the common segment of the jth repeated line ij The average value of the gravity value of each repeated line at this point F i The difference between the two formulas; m is the number of repeated lines, and n is the number of data points in the common segment of the repeated lines.

[0144] in

[0145] δ ij =F ij -F i

[0146]

[0147] The calculation formula for the internal coincidence accuracy of all repeated line test data is:

[0148]

[0149] When the repeat line is tested multiple times, especially when the repeat line is tested on different flights, the horizontal average value of each repeat line data may drift slightly due to factors such as changes in instrument working status and flight conditions, such as fluctuations in flight altitude and measurement points. Therefore, the repeat line needs to be adjusted horizontally. After adjustment, the internal accuracy formula is as follows:

[0150]

[0151] Where: The horizontal mean of each replicate line data:

[0152]

[0153] The horizontal average of the mean-field data for all replicates:

[0154]

[0155] Reference below Figure 6 , which shows a schematic diagram of the structure of an electronic device (e.g., a terminal device or a server) suitable for implementing the embodiments of the present disclosure. The terminal device in the embodiments of the present disclosure may include, but is not limited to, mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), in-vehicle terminals (e.g., in-vehicle navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 6 The electronic device shown is only an example and should not limit the functions and scope of use of the embodiments of the present disclosure.

[0156] like Figure 6 As shown, the electronic device may include a processing device (e.g., a central processing unit, a graphics processing unit, etc.) 601, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 602 or a program loaded from a storage device 608 into a random access memory (RAM) 603. Various programs and data required for the operation of the electronic device 600 are also stored in the RAM 603. The processing device 601, the ROM 602, and the RAM 603 are connected to each other via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0157] Typically, the following devices may be connected to the I / O interface 605: an input device 606 including, for example, a touch screen, a touchpad, a keyboard, a mouse, a camera, a microphone, an accelerometer, a gyroscope, etc.; an output device 607 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; a storage device 608 including, for example, a magnetic tape, a hard disk, etc.; and a communication device 609. The communication device 609 may allow the electronic device to communicate with other devices wirelessly or by wire to exchange data. Although Figure 6 The electronic device is shown with various devices, but it should be understood that it is not required to implement or possess all of the devices shown. More or fewer devices may be implemented or possessed instead.

[0158] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a non-transitory computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication device 609, or installed from the storage device 608, or installed from the ROM 602. When the computer program is executed by the processing device 601, the above-mentioned functions defined in the method of the embodiment of the present disclosure are performed.

[0159] It should be noted that the computer-readable medium mentioned above in the present disclosure may be a computer-readable signal medium or a computer-readable storage medium, or any combination of the two. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or component, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, device, or component. In the present disclosure, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium may be transmitted using any suitable medium, including but not limited to wires, optical cables, RF (radio frequency), etc., or any suitable combination thereof.

[0160] In some embodiments, the client and server can communicate using any currently known or future developed network protocol, such as HTTP (HyperText Transfer Protocol), and can be interconnected with any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network ("LAN"), a wide area network ("WAN"), an internet (e.g., the Internet), and a peer-to-peer network (e.g., an ad hoc peer-to-peer network), as well as any currently known or future developed network.

[0161] The computer-readable medium may be included in the electronic device, or may exist independently without being incorporated into the electronic device.

[0162] The computer-readable medium carries one or more programs. When the one or more programs are executed by the electronic device, the electronic device is enabled to: obtain the aerial gravity data of the measurement carrier and construct a first mathematical model of aerial gravity anomaly; introduce an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomaly, wherein the unknown adjustment coefficient is an adjustment coefficient for which a specific value is to be obtained; organize the second mathematical model into the form of a Kalman filter state equation and a measurement equation to obtain a spatial state model; obtain the specific value of the unknown adjustment coefficient according to the spatial state model; substitute the specific value into the second mathematical model, and solve the second mathematical model to obtain a third mathematical model containing noise; and perform FIR low-pass filtering on the third mathematical model based on a preset cutoff frequency of the FIR low-pass filter.

[0163] Computer program code for performing the operations of the present disclosure may be written in one or more programming languages, or a combination thereof, including, but not limited to, object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on the remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0164] The flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or a part of code, and the module, program segment, or a part of code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order than that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of the boxes in the block diagram and / or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0165] The units involved in the embodiments described in this disclosure may be implemented in software or hardware, wherein the name of a unit does not necessarily limit the unit itself.

[0166] The functions described above herein may be performed, at least in part, by one or more hardware logic components. For example, and without limitation, exemplary types of hardware logic components that may be used include: field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chip (SOCs), complex programmable logic devices (CPLDs), and the like.

[0167] In the context of the present disclosure, a machine-readable medium can be a tangible medium that can contain or store a program for use by or in conjunction with an instruction execution system, device or equipment. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium can include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0168] The above description is merely a preferred embodiment of the present disclosure and an illustration of the technical principles employed. Those skilled in the art should understand that the scope of disclosure involved in the present disclosure is not limited to the technical solutions formed by the specific combination of the above-mentioned technical features, but also includes other technical solutions formed by any combination of the above-mentioned technical features or their equivalents without departing from the above-mentioned disclosed concepts. For example, a technical solution formed by replacing the above-mentioned features with (but not limited to) technical features with similar functions disclosed in this disclosure.

[0169] In addition, although each operation is described in a specific order, this should not be understood as requiring these operations to be performed in the specific order shown or in a sequential order. Under certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although some specific implementation details have been included in the above discussion, these should not be interpreted as limiting the scope of the present disclosure. Some features described in the context of a separate embodiment can also be implemented in a single embodiment in combination. On the contrary, the various features described in the context of a single embodiment can also be implemented in multiple embodiments individually or in any suitable sub-combination mode.

[0170] Although the subject matter has been described in language specific to structural features and / or methodological logical acts, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are merely example forms of implementing the claims.

[0171] The above description is merely an embodiment of the present application and is not intended to limit the scope of protection of the present application. For those skilled in the art, various modifications and variations of the present application are possible. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A method for processing airborne gravity data based on KF filtering, characterized in that: include: Acquire the aerial gravity data of the measurement carrier and construct the first mathematical model of aerial gravity anomaly; Introducing an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomaly, wherein the unknown adjustment coefficient is an adjustment coefficient for which a specific value is to be obtained; Arranging the second mathematical model into the form of a Kalman filter state equation and a measurement equation to obtain a spatial state model; Obtaining a specific value of the unknown adjustment coefficient according to the spatial state model; Substituting the specific numerical value into the second mathematical model, and solving the second mathematical model to obtain a third mathematical model containing noise; Based on a preset cutoff frequency of the FIR low-pass filter, performing FIR low-pass filtering on the third mathematical model; Wherein, the first mathematical model is: ; in, is the gravity anomaly value, is the corrected gravity value, is the vertical acceleration of the aircraft, is the sum of all types of noise; The step of introducing an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomaly includes: The first mathematical model It is divided into four parts, including the error caused by gravity acceleration in the X-axis direction, the error caused by gravity acceleration in the Y-axis direction, the error caused by gravity acceleration in the Z-axis direction, and other noises. Three adjustment coefficients Sx, Sy, and Sz are introduced to adjust the errors caused by gravity acceleration fx, fy, and fz in the three directions respectively, and the second mathematical model is obtained. The second mathematical model is 。 2. The method for processing aerial gravity data based on KF filtering according to claim 1, characterized in that: Arranging the second mathematical model into the form of a Kalman filter state equation and a measurement equation to obtain a spatial state model includes: Rewrite the second mathematical model as formula (1) -----Formula (1), in, is the reference ellipsoid height, for measurement error; , , The gravity anomaly is a random process, modeled using a shaping filter: Formula (2), The gravity anomaly As the estimated state, here is the filter state vector, 、 is a constant matrix, To generate strength White noise, Pick ， ， ， ， Combining equations (1) and (2), we can obtain the final spatial state model: , According to the spatial state model, the specific values ​​of the unknown adjustment coefficients Sx, Sy, and Sz are obtained; Substitute the specific values ​​of Sx, Sy, and Sz into the second mathematical model to deduct the errors caused by fx, fy, and fz, and obtain a third mathematical model containing noise; in, 、 is a constant matrix; The array is driven by system noise; For the measurement array; is the vertical speed of the aircraft; is the system excitation noise sequence; is the noise in the Z-axis direction; is the noise in the Y-axis direction; is the noise in the X-axis direction; is the gravity anomaly.

3. The method for processing aerial gravity data based on KF filtering according to claim 1, characterized in that: The FIR low-pass filter adopts a window function method, and the window function method includes one of the following: Hanning window, Hamming window, and Blackman window.

4. The method for processing aerial gravity data based on KF filtering according to claim 1, characterized in that: The corrected gravity values ​​include the following: normal field correction, altitude correction, Erratum correction, zero drift correction and base point correction error.

5. A processing system for airborne gravity data based on KF filtering, characterized in that: include: Data acquisition module, used to obtain aerial gravity data; Model building module, used to build mathematical models of aviation gravity anomalies; Kalman filter module, used to obtain the adjustment coefficient; The FIR filter module is used to perform frequency domain cutoff processing on the signal output by the Kalman filter based on the preset cutoff frequency of the FIR low-pass filter; The model building module is further configured to: construct a first mathematical model of aviation gravity anomaly; introduce an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomaly, wherein the unknown adjustment coefficient is an adjustment coefficient for which a specific value is to be obtained; The Kalman filter module is further configured to: organize the second mathematical model into the form of a Kalman filter state equation and a measurement equation to obtain a spatial state model; obtain a specific value of the unknown adjustment coefficient based on the spatial state model; substitute the specific value into the second mathematical model, and solve the second mathematical model to obtain a third mathematical model containing noise; Wherein, the first mathematical model is: , in, is the gravity anomaly value, is the corrected gravity value, is the vertical acceleration of the aircraft, is the sum of all types of noise; The step of introducing an unknown adjustment coefficient into the first mathematical model to obtain a second mathematical model of gravity anomaly includes: The first mathematical model It is divided into four parts, including the error caused by gravity acceleration in the X-axis direction, the error caused by gravity acceleration in the Y-axis direction, the error caused by gravity acceleration in the Z-axis direction, and other noises. Three adjustment coefficients Sx, Sy, and Sz are introduced to adjust the errors caused by gravity acceleration fx, fy, and fz in the three directions respectively, and the second mathematical model is obtained. The second mathematical model is 。 6. The KF filtering-based airborne gravity data processing system according to claim 5, characterized in that: The data acquisition module includes an airborne gravimeter and a differential satellite positioning system to obtain high-precision gravity data and positioning information.

7. The KF filtering-based airborne gravity data processing system according to claim 5, characterized in that: The model building module adjusts the parameters of the mathematical model according to different measurement environments to obtain a model that adapts to complex terrain and dynamic noise conditions.

8. The KF filtering-based airborne gravity data processing system according to claim 5, characterized in that: The Kalman filter module adjusts the filter parameters in real time to obtain noise data that adapts to dynamic changes, and the FIR filter module performs filtering processing according to a preset cutoff frequency and window function.

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