A method and system for determining aeromagnetic signal

Abstract

The present invention relates to the field of magnetic field signal measurement technology, and in particular to a method and system for determining an aeromagnetic signal, the method comprising: obtaining a comprehensive measurement model of a three-axis magnetometer; the three-axis magnetometer is arranged on an aircraft, and the comprehensive measurement model is a comprehensive measurement model of the error of the three-axis magnetometer and the magnetic field interference field; based on a shaping filter and the maximum angular acceleration of the aircraft, determining the real-time angular acceleration of the aircraft; using the real-time angular acceleration as an input quantity, the roll angle, pitch angle, yaw angle, roll angular velocity, pitch angular velocity and yaw angular velocity of the aircraft as state quantities, and the measured magnetic field intensity of the three-axis magnetometer as an output quantity, constructing a real-time geomagnetic field estimation model of the aircraft; solving the real-time geomagnetic field estimation model using a cubature Kalman filter to determine the state quantity; determining the geomagnetic field intensity and the eddy current magnetic field intensity according to the state quantity. The present invention improves the accuracy of the measurement of the geomagnetic field intensity and the eddy current magnetic field intensity.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic field signal measurement, and in particular to an aeromagnetic signal determination method and system. Background Art

[0002] Magnetometers are widely used in the fields of geomagnetic navigation and guidance as well as magnetic target detection. Recently, three-axis magnetometers have been widely used to measure the magnetic gradient tensor. However, the anomalous field has a great influence on the measurement process and should be compensated before magnetic measurement. The calibration of the anomalous magnetic field includes two steps: the construction of the distortion model and the estimation of the real-time background magnetic field.

[0003] The construction of geomagnetic anomaly fields is not a new problem. Classical methods are mainly based on scalar compensation. Ellipsoid fitting methods have been widely used to compensate magnetic distortion fields. These methods implement calibration adjustments based on the Earth's magnetic field, which is usually measured by optically pumped magnetometers or high-precision proton magnetometers. Only the scalar value of the magnetic field is required in the scalar compensation process. Knowledge of the magnetometer attitude is not required, which leads to some unobservable parts in the scalar measurement.

[0004] Vector compensation methods require knowledge of the magnetometer attitude and the interference of all related components. Pang et al. proposed a vector compensation method that combines a three-axis magnetometer, an inertial system (INS), and a global positioning system (GPS). However, this method is only effective when the measurement conditions are static. In order to solve the problem of dynamic measurement and compensation, some researchers have considered applying the Tolles-Lawson equation to aircraft magnetic field compensation and using the knowledge of the aircraft attitude to calculate the magnetic field strength compensation result. However, effective estimation of measurement parameters is difficult to achieve.

[0005] In addition, in the field of geomagnetic navigation, the influence of eddy current magnetic field when the aircraft moves at high speed cannot be ignored. Therefore, the influence of eddy current magnetic field should be considered when constructing the distortion model. Pang considered a magnetic compensation model that includes not only magnetometer errors but also magnetic distortion, which also includes eddy current magnetic field. However, only the modulus of the abnormal field is calculated to compensate the total field, resulting in the loss of real-time magnetic intensity vector information. Li proposed an abnormal field compensation method based on Rauch-Tung-Striebel (RTS) fixed interval smoothing method and singular value decomposition (SVD), which helps to improve the accuracy of magnetic measurement in dynamic environments. These methods help to build more accurate distortion models under dynamic environmental conditions. However, the eddy current magnetic field is related to the derivative of the magnetic field intensity, especially in the presence of random noise, which is difficult to calculate accurately. Therefore, when considering the eddy current magnetic field in the abnormal field model, it is difficult to obtain the real background magnetic field. Summary of the invention

[0006] The purpose of the present invention is to provide a method and system for determining an aeromagnetic signal, thereby improving the accuracy of measuring the geomagnetic field strength and eddy current magnetic field strength.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A method for determining an aeromagnetic signal, comprising:

[0009] Obtaining a comprehensive measurement model of a three-axis magnetometer; the three-axis magnetometer is arranged on an aircraft, and the comprehensive measurement model is a comprehensive measurement model of the error and magnetic field interference field of the three-axis magnetometer;

[0010] Determining a real-time angular acceleration of the aircraft based on a shaping filter and a maximum angular acceleration of the aircraft;

[0011] Using the real-time angular acceleration as input, the roll angle, pitch angle, yaw angle, roll angular velocity, pitch angular velocity and yaw angular velocity of the aircraft as state quantities, and the measured magnetic field intensity of the three-axis magnetometer as output, a real-time geomagnetic field estimation model of the aircraft is constructed;

[0012] Using cubature Kalman filtering to solve the real-time geomagnetic field estimation model to determine the state quantity;

[0013] The geomagnetic field strength and the eddy current magnetic field strength are determined according to the state quantity.

[0014] Optionally, the shaping filter is expressed as:

[0015]

[0016] Among them, u α,max represents the maximum angular acceleration of the pitch angle, u β,max Indicates the maximum angular acceleration of the roll angle, u γ,max represents the maximum angular acceleration of the yaw angle, v(t) represents a random input signal that obeys a normal distribution, Represents the derivative of the real-time angular acceleration.

[0017] Optionally, the real-time geomagnetic field estimation model is expressed as:

[0018]

[0019] in, u′=[0 1×9 v(t)v(t)v(t)] T , ε1 and ε2 are independent additive process noises, u max =[u α,max u β,max u γ,max ] T, X represents the state quantity, Y represents the output quantity, E3×3 is the third-order unit matrix, E6×6 is the sixth-order unit matrix, and Ω represents the function.

[0020] Optionally, determining the geomagnetic field strength and the eddy current magnetic field strength according to the state quantity specifically includes:

[0021] According to the formula determining the strength of the geomagnetic field;

[0022] Determining the eddy current magnetic field intensity according to the rate of change of the geomagnetic field intensity;

[0023] in, and represents the geomagnetic field strength in the aircraft coordinate system, and Indicates the magnetic field value measured in the earth coordinate system;

[0024]

[0025] α represents the pitch angle, β represents the roll angle, and γ represents the yaw angle.

[0026] The invention discloses an aeromagnetic signal determination system, comprising:

[0027] A comprehensive measurement model acquisition module is used to obtain a comprehensive measurement model of a three-axis magnetometer; the three-axis magnetometer is arranged on the aircraft, and the comprehensive measurement model is a comprehensive measurement model of the error and magnetic field interference field of the three-axis magnetometer;

[0028] A real-time angular acceleration determination module, configured to determine the real-time angular acceleration of the aircraft based on a shaping filter and a maximum angular acceleration of the aircraft;

[0029] A real-time geomagnetic field estimation model building module is used to build a real-time geomagnetic field estimation model for the aircraft using the real-time angular acceleration as input, the roll angle, pitch angle, yaw angle, roll angular velocity, pitch angular velocity and yaw angular velocity of the aircraft as state quantities, and the measured magnetic field intensity of the three-axis magnetometer as output;

[0030] A state quantity determination module, used for solving the real-time geomagnetic field estimation model by using a cubature Kalman filter to determine the state quantity;

[0031] The module for determining the geomagnetic field strength and eddy current magnetic field strength is used to determine the geomagnetic field strength and eddy current magnetic field strength according to the state quantity.

[0032] Optionally, the shaping filter is expressed as:

[0033]

[0034] Among them, u α,max represents the maximum angular acceleration of the pitch angle, u β,max Indicates the maximum angular acceleration of the roll angle, u γ,max represents the maximum angular acceleration of the yaw angle, v(t) represents a random input signal that obeys a normal distribution, Represents the derivative of the real-time angular acceleration.

[0035] Optionally, the real-time geomagnetic field estimation model is expressed as:

[0036]

[0037] in, u′=[0 1×9 v(t) v(t) v(t)] T , ε1 and ε2 are independent additive process noises, u max =[u α,max u β,max u γ,max ] T , X represents the state quantity, Y represents the output quantity, E 3×3 is a third-order unit matrix, E 6×6 is a sixth-order unit matrix, Ω represents function.

[0038] Optionally, the module for determining the geomagnetic field strength and eddy current magnetic field strength specifically includes:

[0039] The geomagnetic field strength determination unit is used to determine the geomagnetic field strength according to the formula determining the strength of the geomagnetic field;

[0040] an eddy current magnetic field strength determination unit, configured to determine the eddy current magnetic field strength according to a rate of change of the geomagnetic field strength;

[0041] in, and represents the geomagnetic field strength in the aircraft coordinate system, and Indicates the magnetic field value measured in the earth coordinate system;

[0042]

[0043] α represents the pitch angle, β represents the roll angle, and γ represents the yaw angle.

[0044] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0045] The present invention discloses an aeromagnetic signal determination method and system, which uses the real-time angular acceleration of an aircraft determined based on a shaping filter as the input of a real-time geomagnetic field estimation model, solves the real-time geomagnetic field estimation model using a cubature Kalman filter, determines the state quantity, thereby determining the geomagnetic field intensity and the eddy current magnetic field intensity, and accurately estimating the eddy current magnetic field component, thereby effectively improving the accuracy of aeromagnetic data, thereby improving the accuracy of geomagnetic navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0047] Figure 1 A schematic diagram of a flow chart of a method for determining an aeromagnetic signal according to the present invention;

[0048] Figure 2 It is a schematic diagram of a linear system with input x(t);

[0049] Figure 3 is a schematic diagram of a linear system excited by a shaping filter;

[0050] Figure 4 The comparison between the actual magnetic field strength and the estimated value of the present invention is shown in FIG. Figure 1 ;

[0051] Figure 5 The comparison between the actual eddy current magnetic field strength and the estimated value of the present invention is shown in FIG. Figure 1 ;

[0052] Figure 6 The comparison between the actual magnetic field strength and the estimated value of the present invention is shown in FIG. Figure 2 ;

[0053] Figure 7 The comparison between the actual eddy current magnetic field strength and the estimated value of the present invention is shown in FIG. Figure 2 ;

[0054] Figure 8 The RMSE value after 100 Monte Carlo experiments in the present invention is shown as follows Figure 1 ;

[0055] Fig. 9 The RMSE value after 100 Monte Carlo experiments in the present invention is shown as follows Figure 2 ;

[0056] Fig.10 The present invention is a schematic diagram of the structure of an aeromagnetic signal determination system. DETAILED DESCRIPTION

[0057] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0058] The purpose of the present invention is to provide a method and system for determining an aeromagnetic signal, thereby improving the accuracy of measuring the geomagnetic field strength and eddy current magnetic field strength.

[0059] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] Figure 1 FIG. 1 is a flow chart of a method for determining an aeromagnetic signal according to the present invention. Figure 1 As shown, a method for determining an aeromagnetic signal comprises:

[0061] Step 101: obtaining a comprehensive measurement model of a three-axis magnetometer; the three-axis magnetometer is arranged on an aircraft, and the comprehensive measurement model is a comprehensive measurement model of the error of the three-axis magnetometer and the magnetic field interference field.

[0062] Wherein, step 101 specifically includes: determining the model parameters of the interference magnetic field error correction model (comprehensive measurement model) according to the structural characteristics of the carrier (aircraft) and the internal error characteristics of the three-axis magnetometer.

[0063] The errors and magnetic interference fields of the three-axis magnetometer are usually modeled uniformly. The calibration model combines the soft magnetic field, hard magnetic field and the real background magnetic field. The eddy current field is also considered in the dynamic environment. The comprehensive measurement model is expressed as:

[0064]

[0065]

[0066] in and is the magnetic field value actually measured by the three-axis magnetometer, and Represents the background magnetic field value in the carrier coordinate system. m ij (i, j = x, y, z) represents the soft magnetic interference coefficient after the soft magnetic interference field in the j direction acts on the i direction. hx 、T hy and T hzRepresents the hard magnetic interference coefficient and does not change over time. ij (i, j = x, y, z) represents the eddy current magnetic field coefficient, and It represents the unit time and The amount of change.

[0067] Step 102: Determine the real-time angular acceleration of the aircraft based on the shaping filter and the maximum angular acceleration of the aircraft.

[0068] Wherein, step 102 specifically includes determining the motion characteristics of the carrier based on the comprehensive measurement model, thereby determining the maximum angular acceleration of the aircraft, which is used to determine the input variable of the shaping filter in the subsequent state equation. The maximum angular acceleration of the aircraft is determined by the motion characteristics of the carrier. Here, the preset value method is used for simulation analysis. The specific application is determined according to the actual situation of the carrier. The maximum angular acceleration of the aircraft includes the maximum angular acceleration of the pitch angle, the maximum angular acceleration of the roll angle, and the maximum angular acceleration of the yaw angle.

[0069] The shaping filter is expressed as:

[0070]

[0071] Among them, u α,max represents the maximum angular acceleration of the pitch angle, u β,max Indicates the maximum angular acceleration of the roll angle, u γ,max represents the maximum angular acceleration of the yaw angle, v(t) represents a random input signal that obeys a normal distribution, Represents the derivative of the real-time angular acceleration.

[0072] Step 103: Using the real-time angular acceleration as input, the aircraft's roll angle, pitch angle, yaw angle, roll angular velocity, pitch angular velocity and yaw angular velocity as state quantities, and the measured magnetic field intensity of the three-axis magnetometer as output, a real-time geomagnetic field estimation model for the aircraft is constructed.

[0073] The real-time geomagnetic field estimation model includes a state equation and a measurement equation. Constructing the real-time geomagnetic field estimation model means constructing the state equation and the measurement equation.

[0074] Step 104: using cubature Kalman filtering to solve the real-time geomagnetic field estimation model and determine the state quantity;

[0075] Step 105: Determine the geomagnetic field strength and the eddy current magnetic field strength according to the state quantity.

[0076] The real-time geomagnetic field estimation model is expressed as:

[0077]

[0078] in, u′=[0 1×9 v(t) v(t) v(t)] T , ε1 and ε2 are independent additive process noises, u max =[u α,max u β,max u γ,max ] T , X represents the state quantity, Y represents the output quantity, E 3×3 is a third-order unit matrix, E 6×6 is a sixth-order unit matrix, Ω represents function.

[0079] Step 105 specifically includes:

[0080] According to the formula Determine the strength of the Earth's magnetic field.

[0081] The eddy current magnetic field strength is determined based on the rate of change of the geomagnetic field strength.

[0082] in, and Represents the background geomagnetic field value (geomagnetic field strength) in the aircraft coordinate system. and Represents the magnetic field value measured in the Earth coordinate system.

[0083]

[0084] α represents the pitch angle, β represents the roll angle, and γ represents the yaw angle.

[0085] The following is a detailed description of the method for determining an aeromagnetic signal of the present invention.

[0086] Step S1: Obtaining a comprehensive measurement model

[0087] The errors and magnetic interference fields of the three-axis magnetometer are usually modeled uniformly. The calibration model combines the soft magnetic field, hard magnetic field and the real background magnetic field. The eddy current field is also considered in the dynamic environment. The comprehensive measurement model can be expressed as:

[0088]

[0089]

[0090] in and is the magnetic field value actually measured by the three-axis magnetometer, and Represents the background magnetic field value in the carrier coordinate system. mij (i, j = x, y, z) represents the soft magnetic interference coefficient after the soft magnetic interference field in the j direction acts on the i direction. hx , T hy and T hz Represents the hard magnetic interference coefficient and does not change over time. ij (i, j = x, y, z) represents the eddy current magnetic field coefficient, and It represents the unit time and The amount of change.

[0091] The relationship between the geomagnetic coordinate system and the carrier coordinate system can be described by a rotation matrix related to the aircraft attitude angle, as shown in equations (3) and (4).

[0092]

[0093]

[0094] Where F is the rotation matrix, α, β, and γ represent the pitch angle, roll angle, and yaw angle, respectively. and Represents the magnetic field value measured in the Earth coordinate system.

[0095] In previous studies, the main focus was on the parameters M, N and [T hx T hy T hz ] T However, after solving the model parameters, how to solve the real background magnetic field value is also an important issue. Especially when considering the influence of eddy current magnetic field, there are the following three problems that need to be solved:

[0096] (1) It is difficult to obtain an accurate eddy current magnetic field model.

[0097] (2) It is difficult to determine the exact time when the eddy current magnetic field is generated.

[0098] (3) Due to the influence of random noise, the change rate of the three components of the magnetic field Difficult to find an accurate solution.

[0099] The present invention solves the above problems by integrating a shaping filter into Kalman filtering.

[0100] Step S2: forming filter

[0101] The shaping filter was originally used in the analysis of physical systems because it allows a system with random inputs to be replaced by an augmented system (the original system plus the shaping filter) excited only by white noise. It is also applicable to systems where the interfering inputs are of known form but occur randomly.

[0102] The system output after being excited by a unit impulse response η(t,τ) is as follows Figure 2 shown.

[0103]

[0104] Among them, equation (5) represents the integration of x from negative infinity to t, τ is the intermediate variable of the integration, and x(t) and y(t) are the input and output of the system respectively. Therefore, the autocorrelation function φ of y(t) yy (t1, t2) can be expressed as:

[0105]

[0106] Among them, τ1 and τ2 are intermediate variables of integration, φ yy (t1, t2) represents the correlation of the random process at two time points t1 and t2.

[0107] From equation (4), we can see that the second-order moment of y(t) is only related to the second-order moment of x(t). Consider the following input:

[0108] x(t)=h(tT) (7)

[0109] Where h(·) is not 0 only when tT≥0, T is the random time when the input signal is generated, and the probability density function of h(·) is assumed to be.

[0110] Figure 3 Where x(t) is the output of a shaping filter, which is excited by white noise υ(t) with autocorrelation function as shown in (8).

[0111] φ υυ (t1, t2) = q(t1)δ(t1-t2) (8)

[0112] If we choose a suitable q(t) so that Figure 3 The shaping filter in can produce the same second-order moment as the output y(t), then Figure 3 The system and Figure 2 The system is equivalent in .

[0113] Step S3, expanding the shaping filter (shaping filter used in the present invention)

[0114] S2 only considers the second-order moment, but in reality, most signal characteristics are difficult to accurately describe by the second-order moment, so it is necessary to consider higher-order statistics. Assume that the state equation of the system is in the following form:

[0115]

[0116] x(t) is a scalar and x(t) is a vector.

[0117] The r-order cumulant of the output y of this system can be expressed by the following formula:

[0118]

[0119] r is the order of the cumulant, ω i are independent random variables in the system input.

[0120] When the autocorrelation function of u(t) is an impulse function, the cumulant sum of u(t) is written as:

[0121]

[0122] At this time, formula (10) can be simplified as:

[0123]

[0124] When x0=0, the moment function can also be written in a form similar to equation (10):

[0125]

[0126] Where φ(t i ,t0) is the state transfer matrix related to A(t), Γ(t,ω)=C(t)φ(t,ω)B(ω), is the r-order cumulant of input u. To construct a shaping filter that can replace input u, the following system is constructed:

[0127]

[0128] Where v(t) is a random input signal that follows a normal distribution. By designing the parameters in model (14), the output u of the system is s The following relations are satisfied:

[0129]

[0130] That is to ensure u s It remains consistent with the r-order cumulant of u.

[0131] Then the input u in equation (9) can be replaced by system (14). The replaced system is:

[0132]

[0133] At this time, we know That is, the output y of the system after replacement s The output y of the initial system has the same r-order cumulant. This method can be used to make a more accurate estimate of the geomagnetic field correction model containing eddy current magnetic fields.

[0134] Step S4: constructing a comprehensive estimation model (real-time geomagnetic field estimation model)

[0135] When the geomagnetic field remains constant, the maneuvering of the aircraft will produce changes in the measured geomagnetic field, thereby generating an eddy current magnetic field. Therefore, in the comprehensive estimation model, the angles and angular velocities of the carrier's pitch, roll, and yaw directions are used as the state quantities of the system, the angular acceleration is used as the input quantity, and the real-time measured magnetic field value is used as the output quantity. The angle, angular velocity, and angular acceleration are respectively denoted as θ = [α, β, γ] T , Then the state quantity is The input is The state equation of the system can be written as:

[0136]

[0137] in E 3×3 It is a third-order unit array.

[0138] The relationship between the output and state quantity of the system can be derived through equation (3). For the convenience of description, the following notation is set:

[0139]

[0140] Therefore, combined with formula (4), we can get

[0141]

[0142] The eddy current magnetic field strength is determined using formula (18).

[0143] Combined with formula (1), the measurement equation can be written as:

[0144]

[0145] Consider the simplest maneuver of the carrier, and regard the upcoming maneuver as a step change in angular acceleration at a random time, that is:

[0146]

[0147] Where U(t) is a unit step function, ξ is a random variable that follows a uniform distribution, and uα,max ,u β,max and u γ,max is the maximum angular acceleration in the three maneuvering directions. The probability distribution function of ξ can be written as:

[0148]

[0149] Then the high-order moment of input u can be written as:

[0150]

[0151] In this case, it is impossible to find a suitable shaping filter whose output has the same high-order cumulant as the input of the system (9)-(11), so the objective condition is changed to

[0152]

[0153] in is the third-order moment of u. According to equations (10) and (13), we know

[0154]

[0155] Therefore, the shaping filter can be designed as:

[0156]

[0157] At this time, the random input v(t) is put into the cumulative amount Combining formula (10), we can get

[0158]

[0159] It is consistent with the result of formula (22), so the designed shaping filter is reasonable.

[0160] Finally, the complete state estimation system can be expressed as:

[0161]

[0162] where u max =[u α,max u β,max u γ,max ] T To facilitate subsequent processing, equation (27) is simplified to:

[0163]

[0164] in u′=[0 1×9 v(t) v(t) v(t)] T, ε1 and ε2 are independent additive process noises, and their covariances are Q and R respectively, where Q and R are constant matrices. The system state equation in equation (28) is linear, and the measurement equation is nonlinear, so the cubature Kalman filter is used in principle to estimate the state quantity.

[0165] The final state equations of the real-time geomagnetic field estimation model are equations (17) and (19). Equation (17) is the state equation of the system, and equation (19) is the measurement equation of the system. The two together constitute the geomagnetic field estimation model, which uses the state quantity and input quantity to estimate the output quantity, and the output quantity is the magnetic field strength measured by the magnetometer.

[0166] In the case where the angular acceleration model and generation time are unknown, a shaping filter is designed to replace the angular acceleration input, that is, the output of the designed shaping filter is used as the input of the model.

[0167] Since the input u (i.e. angular acceleration) in the state equation (17) is unknown, it is necessary to construct a shaping filter to replace this input. The specific process is as follows: (20)-(25), and the designed shaping filter is as follows: (25). That is, using the output u in the shaping filter (25) s Replace the input u in the original state equation (17).

[0168] The input of the shaping filter is determined according to the maximum angular acceleration, and the input is a uniformly distributed random quantity with the maximum acceleration as the mean square error and 0 as the mean.

[0169] Determine the parameters in equation (20), that is, determine the probability distribution of the input u in equation (17) through equation (20), and determine the parameters of the shaping filter according to this probability distribution, thereby completing the construction of the overall model (real-time geomagnetic field estimation).

[0170] The final model of the real-time geomagnetic field estimation model is formula (28).

[0171] The cubature Kalman filter is used to estimate the real-time geomagnetic field strength and eddy current magnetic field components.

[0172] The following simulation experiment is used to illustrate the technical effect of the method for determining an aeromagnetic signal of the present invention.

[0173] In the simulation experiment, the parameters in formula (1) are set as follows:

[0174]

[0175] To verify the proposed method, the geomagnetic field strength is set as follows:

[0176]

[0177] The aircraft is assumed to maintain a fixed attitude. Therefore, the measured geomagnetic field value can be obtained by formula (1): The measurement noise is added to the output via equation (30).

[0178]

[0179] Where ξ is Gaussian white noise with a mean of 0 and a standard deviation of 100 nT. Then, the state variable X can be estimated by equation (28) and cubature Kalman filtering.

[0180] Figure 4 The comparison between the estimated value of the geomagnetic field and the true value in the X direction is shown. The estimated result of the method proposed in the present invention is consistent with the true geomagnetic field. Figure 5 As shown, the results in the X direction are also given. There is a time delay between the estimated value of the eddy current magnetic field and the true value, which is a disadvantage of the shaping filter. However, the influence of this phenomenon in the estimation of the geomagnetic field value can be ignored.

[0181] In order to simulate the geomagnetic measurement process during aircraft maneuvers, the angular accelerations of pitch, yaw, and roll maneuvers are set to π / 1200, π / 2400, and π / 1200, respectively. Other parameters are set the same as above. The real geomagnetic field is a constant vector The performance of the method proposed in the present invention is evaluated by the root mean square error (RMSE), and the calculation process is shown in the following formula:

[0182]

[0183] Where P is the true value, is the estimated value, and n is the number of measurement points. The estimated results of the geomagnetic field and eddy current magnetic field are as follows: Figure 6 and Figure 7 shown.

[0184] The estimates of the calibration model without eddy current magnetic field are also added for comparison. Different angular velocities are simulated and 100 Monte Carlo simulations are performed. Figure 8 The angular accelerations for pitch, yaw, and roll maneuvers are set to π / 1200, π / 2400, and π / 1200, respectively. Figure 8 (a) shows the error of the magnetic field component in the X direction, (b) shows the error of the magnetic field component in the Y direction, (c) shows the error of the magnetic field component in the Z direction, and (d) shows the error of the total field. Fig. 9 The angular accelerations for pitch, yaw, and roll maneuvers in are set to π / 960, π / 960, and π / 960, respectively. Fig. 9(a) shows the error of the X-direction component magnetic field, (b) shows the error of the Y-direction component magnetic field, (c) shows the error of the Z-direction component magnetic field, and (d) shows the error of the total field. Compared with the calibration model without eddy current magnetic field, this method can accurately estimate the eddy current magnetic field value with smaller magnetic error. The faster the aircraft maneuvers, the more obvious the advantage of the proposed method.

[0185] In the process of geomagnetic navigation, the actual magnetic survey data will be interfered by various noises and seriously affect the navigation positioning accuracy. Especially in the process of high-speed movement of the aircraft, the influence of the eddy current magnetic field on the measurement data cannot be ignored. However, the eddy current magnetic field is difficult to measure directly, and the time of its generation is also difficult to determine. Therefore, the present invention proposes a method for estimating aeromagnetic data based on a shaping filter. The simulation results show that this method can effectively estimate the eddy current magnetic field component accurately, thereby effectively improving the accuracy of aeromagnetic data, thereby improving the accuracy of geomagnetic navigation.

[0186] Fig.10 FIG. 1 is a schematic diagram of the structure of an aeromagnetic signal determination system of the present invention, as shown in FIG. Fig.10 An aeromagnetic signal determination system is shown, comprising:

[0187] The comprehensive measurement model acquisition module 201 is used to obtain a comprehensive measurement model of a three-axis magnetometer; the three-axis magnetometer is set on the aircraft, and the comprehensive measurement model is a comprehensive measurement model of the error and magnetic field interference field of the three-axis magnetometer;

[0188] A real-time angular acceleration determination module 202, configured to determine the real-time angular acceleration of the aircraft based on the shaping filter and the maximum angular acceleration of the aircraft;

[0189] A real-time geomagnetic field estimation model building module 203 is used to build a real-time geomagnetic field estimation model for an aircraft using real-time angular acceleration as input, the aircraft's roll angle, pitch angle, yaw angle, roll angular velocity, pitch angular velocity and yaw angular velocity as state quantities, and the measured magnetic field intensity of a three-axis magnetometer as output;

[0190] The state quantity determination module 204 is used to solve the real-time geomagnetic field estimation model using a cubature Kalman filter to determine the state quantity;

[0191] The module 205 for determining the geomagnetic field strength and eddy current magnetic field strength is used to determine the geomagnetic field strength and eddy current magnetic field strength according to the state quantity.

[0192] The shaping filter is expressed as:

[0193]

[0194] Among them, u α,max represents the maximum angular acceleration of the pitch angle, uβ,max Indicates the maximum angular acceleration of the roll angle, u γ,max represents the maximum angular acceleration of the yaw angle, v(t) represents a random input signal that obeys a normal distribution, Represents the derivative of the real-time angular acceleration.

[0195] The real-time geomagnetic field estimation model is expressed as:

[0196]

[0197] in, u′=[0 1×9 v(t) v(t) v(t)] T , ε1 and ε2 are independent additive process noises, u max =[u α,max u β,max u γ,max ] T , X represents the state quantity, Y represents the output quantity, E 3×3 is a third-order unit matrix, E 6×6 is a sixth-order unit matrix, Ω represents function.

[0198] The module for determining the geomagnetic field strength and eddy current magnetic field strength specifically includes:

[0199] The geomagnetic field strength determination unit is used to determine the geomagnetic field strength according to the formula Determine the strength of the Earth's magnetic field;

[0200] An eddy current magnetic field strength determination unit, used to determine the eddy current magnetic field strength according to the rate of change of the geomagnetic field strength;

[0201] in, and Represents the background geomagnetic field value (geomagnetic field strength) in the aircraft coordinate system. and Indicates the magnetic field value measured in the earth coordinate system;

[0202]

[0203] α represents the pitch angle, β represents the roll angle, and γ represents the yaw angle.

[0204] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0205] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for determining an aeromagnetic signal, characterized in that: include: Obtaining a comprehensive measurement model of a three-axis magnetometer; the three-axis magnetometer is arranged on an aircraft, and the comprehensive measurement model is a comprehensive measurement model of the error and magnetic field interference field of the three-axis magnetometer; Determining a real-time angular acceleration of the aircraft based on a shaping filter and a maximum angular acceleration of the aircraft; Using the real-time angular acceleration as input, the roll angle, pitch angle, yaw angle, roll angular velocity, pitch angular velocity and yaw angular velocity of the aircraft as state quantities, and the measured magnetic field intensity of the three-axis magnetometer as output, a real-time geomagnetic field estimation model of the aircraft is constructed; Using cubature Kalman filtering to solve the real-time geomagnetic field estimation model to determine the state quantity; Determine the geomagnetic field intensity and the eddy current magnetic field intensity according to the state quantity; The shaping filter is expressed as: Among them, u α,max represents the maximum angular acceleration of the pitch angle, u β,max Indicates the maximum angular acceleration of the roll angle, u γ,max represents the maximum angular acceleration of the yaw angle, v(t) represents a random input signal that obeys a normal distribution, represents the derivative of the real-time angular acceleration; The real-time geomagnetic field estimation model is expressed as: in, u′=[0 1×9 v(t) v(t) v(t)] T , ε1 and ε2 are independent additive process noises, u max =[u α,max u β,max u γ,max ] T , X represents the state quantity, Y represents the output quantity, E 3×3 is a third-order unit matrix, E 6×6 is a sixth-order unit matrix, Ω represents Function of Determining the geomagnetic field strength and the eddy current magnetic field strength according to the state quantity specifically includes: According to the formula determining the strength of the geomagnetic field; Determining the eddy current magnetic field intensity according to the rate of change of the geomagnetic field intensity; in, and represents the geomagnetic field strength in the aircraft coordinate system, and Indicates the magnetic field value measured in the earth coordinate system; α represents the pitch angle, β represents the roll angle, and γ represents the yaw angle.

2. An aeromagnetic signal determination system, characterized in that: include: A comprehensive measurement model acquisition module is used to obtain a comprehensive measurement model of a three-axis magnetometer; the three-axis magnetometer is arranged on the aircraft, and the comprehensive measurement model is a comprehensive measurement model of the error and magnetic field interference field of the three-axis magnetometer; A real-time angular acceleration determination module, configured to determine the real-time angular acceleration of the aircraft based on a shaping filter and a maximum angular acceleration of the aircraft; A real-time geomagnetic field estimation model building module is used to build a real-time geomagnetic field estimation model for the aircraft using the real-time angular acceleration as input, the roll angle, pitch angle, yaw angle, roll angular velocity, pitch angular velocity and yaw angular velocity of the aircraft as state quantities, and the measured magnetic field intensity of the three-axis magnetometer as output; A state quantity determination module, used for solving the real-time geomagnetic field estimation model by using a cubature Kalman filter to determine the state quantity; A module for determining the geomagnetic field strength and eddy current magnetic field strength, used for determining the geomagnetic field strength and eddy current magnetic field strength according to the state quantity; The shaping filter is expressed as: Among them, u α,max represents the maximum angular acceleration of the pitch angle, u β,max Indicates the maximum angular acceleration of the roll angle, u γ,max represents the maximum angular acceleration of the yaw angle, v(t) represents a random input signal that obeys a normal distribution, represents the derivative of the real-time angular acceleration; The real-time geomagnetic field estimation model is expressed as: in, u′=[0 1×9 v(t) v(t) v(t)] T , ε1 and ε2 are independent additive process noises, u max =[u α,max u β,max u γ,max ] T , X represents the state quantity, Y represents the output quantity, E 3×3 is a third-order unit matrix, E 6×6 is a sixth-order unit matrix, Ω represents Function of The module for determining the geomagnetic field strength and eddy current magnetic field strength specifically comprises: The geomagnetic field strength determination unit is used to determine the geomagnetic field strength according to the formula determining the strength of the geomagnetic field; an eddy current magnetic field strength determination unit, configured to determine the eddy current magnetic field strength according to a rate of change of the geomagnetic field strength; in, and represents the geomagnetic field strength in the aircraft coordinate system, and Indicates the magnetic field value measured in the earth coordinate system; α represents the pitch angle, β represents the roll angle, and γ represents the yaw angle.

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