Platform attitude measurement method for separated electromagnetic vector sensor array of reference wave structure

Abstract

The invention discloses a method for measuring the attitude of a separated electromagnetic vector sensor array platform of a reference wave structure, belongs to the technical field of navigation, and is suitable for measuring the attitude of an aircraft-borne array aerospace platform. The electromagnetic vector sensor is separated in space, engineering realization is facilitated, cross polarization is avoided, and attitude measurement precision is improved. And according to the change rule between the attitude position of the airborne electromagnetic vector sensor and the received signal, an array steering vector of the airborne electromagnetic vector sensor is established. According to a relationship between a three-dimensional information structure of signal time, polarization and space-frequency phase delay and an attitude, signal data is received by arranging all electromagnetic vector sensors, and a parallel factor (PARAFAC) trilinear data model can be obtained. By popularizing the traditional parallel factor alternating least square algorithm, the platform attitude is calculated with high precision under the orthogonal constraint condition when the separated electromagnetic vector sensor is possibly incomplete.

Description

Technical Field

[0001] The present invention relates to the fields of signal detection and estimation, and reconnaissance and navigation technology, and in particular to a platform attitude measurement method based on wave structure information. Background Art

[0002] Manned spaceflight projects require frequent transport of personnel and cargo, as well as docking with space stations, placing higher demands on the accuracy and reliability of vehicle attitude measurement. The widespread use of satellites, rockets, missiles, and other spacecraft has increased the demand for attitude measurement. The uniqueness of the Parallel Factor (PARAFAC) data model decomposition has important application value. By generalizing the traditional Parallel Factor Alternating Least Squares algorithm, we decompose trilinear data to obtain the load matrix. This method has demonstrated excellent results in areas such as CDMA and OFDM.

[0003] Existing aircraft attitude measurement reference points are insufficient, requiring improvements in accuracy, stability, and cost-effectiveness. Estimating the direction of arrival (DOA) from aircraft-mounted arrays is hampered by unknown attitude. Electromagnetic vector sensors are subject to cross-polarization, resulting in complex manufacturing and demanding installation, making them difficult to implement in conformal engineering applications. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortage of existing aircraft attitude measurement reference objects and improve accuracy, stability and economy; to overcome the problems that the accuracy of existing electromagnetic vector sensors is affected by cross-polarization, the manufacturing is complex, the installation requirements are high, and it is difficult to conformalize engineering applications, and to provide a separate electromagnetic vector sensor array platform attitude measurement method with a reference wave structure.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] Step 1: Install a separate electromagnetic vector sensor array with receiving units in the same position and attitude on the aircraft platform and measure the coordinates of each unit within each sensor relative to the reference point of the sensor. Confirm that the direction of arrival and polarization parameters of the navigation signal are known. Based on the change pattern between the attitude position of the missing electromagnetic vector sensor on the aircraft and the received signal, the parallel factor (PARAFAC) is established by arranging the received signal data of all electromagnetic vector sensors.

[0007] Trilinear data corresponds to the three-dimensional linearity of signal time, polarization, and space-frequency phase delay.

[0008] Step 2: Under a certain accuracy threshold, use the trilinear alternating least squares (TALS) method to obtain the polarization domain steering matrix containing the array platform attitude information

[0009] Step 3: Implement attitude matrix orthogonal solution. When the sensor data is complete, according to the relationship between the polarization domain steering array element mode and the zero attitude polarization domain steering array element mode, the attitude matrix is ​​calculated using the Lagrange multiplier method under the attitude matrix orthogonality constraint and the minimum mean square error principle; when the sensor data is incomplete, according to the minimum mean square error principle, the missing attitude matrix is ​​calculated, the attitude matrix is ​​completed using the cross multiplication method, and the Lagrange multiplier method under the attitude matrix orthogonality constraint is used.

[0010] According to the minimum mean square error principle, the attitude matrix under orthogonal constraints is calculated.

[0011] Step 4: Determine whether the accuracy of the attitude matrix can be improved. If so, return to step 2 and perform the next loop at a higher accuracy threshold. If the attitude matrix has reached the desired accuracy, end the loop.

[0012] Compared with the prior art, the present invention adopts the above technical solution and has the following beneficial effects:

[0013] 1) Install a separate electromagnetic vector sensor array with receiving units in the same position and orientation on the aircraft platform and measure the coordinates of each unit within each sensor relative to a reference point. Based on the relationship between the attitude and position of the missing electromagnetic vector sensor and the received signal, the received signal data from all electromagnetic vector sensors are arranged to establish a three-dimensional linear data structure of the parallel factor (PARAFAC), corresponding to the three-dimensional linearity of the signal time, polarization, and space-frequency phase delay.

[0014] 2) By generalizing the traditional parallel factor alternating least squares algorithm, the PARAFAC trilinear data is decomposed to obtain the polarization domain steering matrix. The computational efficiency is superior to the multi-dimensional matching search algorithm;

[0015] 3) Make up for the lack of reference objects for spatial attitude measurement;

[0016] 4) Reduce the requirements for attitude measurement signal sources;

[0017] 5) When the sensor data is complete, the attitude array is calculated based on the relationship between the polarization domain steering array element mode and the zero-attitude polarization domain steering array element mode, using the Lagrange multiplier method under the attitude array orthogonality constraint and the minimum mean square error principle;

[0018] 6) When the sensor data is incomplete, the incomplete attitude matrix is ​​calculated according to the minimum mean square error principle, and the attitude matrix is ​​completed by the cross multiplication method. The Lagrange multiplier method under the orthogonality constraint of the attitude matrix is ​​used to calculate the attitude matrix under the orthogonality constraint according to the minimum mean square error principle.

[0019] 7) The receiving unit of the separate electromagnetic vector sensor can be separated, which is easy to manufacture, reduces cross-polarization interference, and has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Schematic diagram of electromagnetic wave signal propagation;

[0021] Figure 2 It is the elliptically rotating electric field of polarized electromagnetic wave;

[0022] Figure 3 Schematic diagram of the zero rotation attitude electromagnetic vector sensor in the geodetic coordinate system. DETAILED DESCRIPTION

[0023] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0024] (1) Model of electromagnetic vector sensor receiving fully polarized signal

[0025] The propagation direction of electromagnetic wave signal is as follows Figure 1 As shown, in the geodetic coordinate system, the direction of arrival of electromagnetic waves in space is expressed by the parameter Indicates, respectively represents the azimuth and elevation angles, where -π / 2<θ<π / 2, The arrival vector is:

[0026]

[0027] The polarization properties of electromagnetic waves are expressed by the polarization ellipse descriptor (γ,η), the polarization angle is -π / 2<γ≤π / 2, the polarization ellipticity is -π / 4≤η≤π / 4, and the elliptical rotating electric field of the polarized electromagnetic wave is as follows: Figure 2 As shown, are respectively the major and minor axis direction vectors of the electric field polarization ellipse, the electromagnetic wave structure vector u, The wave structure vector is orthogonal to each other and can be used as a reference for attitude measurement. The rectangular coordinate system composed of the wave structure vector as the three coordinate axes is called the wave structure coordinate system. The reference attitude of the three independent orthogonal dipoles at the origin is as follows: Figure 3 As shown, Figure 3 The coordinate system is the earth coordinate system. The present invention uses the dipole array as an example to illustrate the effectiveness of the algorithm. The attitude measurement method of the electromagnetic vector sensor can be derived by analogy. At this time, the ideal steering vector of the independent three orthogonal dipole sensors is in:

[0028]

[0029] The ideal steering vector of three independent orthogonal dipoles at the origin can be further expressed as:

[0030]

[0031] In the formula

[0032]

[0033] d(n)=[0 cosn isinn 0 -isinn cosn] T .

[0034] Reference Figure 1 Know, It reflects the rotation relationship between the earth coordinate system and the wave structure coordinate system. When there is a rotation difference between the attitude of the electromagnetic vector sensor and the earth coordinate system, it is manifested as The difference in rotation matrix Expressed as b R .

[0035] (2) Model of receiving fully polarized signals by an aircraft-borne electromagnetic vector sensor array

[0036] The attitude of the electromagnetic vector sensor and the rotation difference matrix of the earth coordinate system b R The present invention sets the installation posture as the positive posture, and the posture difference caused by the movement of the aircraft platform is a time-varying difference. According to the three-dimensional space rotation theory, the three-dimensional rotation matrix can be represented by a single rotation vector Description, where [φ1 φ2 φ3] is the rotation vector In the coordinate system, the attitude error rotation matrix is ​​equal to: N defective electromagnetic vector sensors, serial number: n = 1, ..., N, are installed at the position coordinates (x no ,y no ,z no ) T , can be accurately measured; without changing the origin of the fuselage, the position coordinates of the electromagnetic vector sensor in the geodetic coordinate system are: (x n ,y n ,z n ) T =b R (x no ,y no ,z no ) T The steering vector expression of electromagnetic vector sensor No. n on the aircraft is:

[0037]

[0038] Where C is a selection matrix composed of partial row vectors of a three-dimensional unit matrix, representing the selection of partial units from three orthogonal dipoles to form a defective electromagnetic vector sensor. When C is a unit matrix, the received data fully reflects the wave structure information, and the single-point received information is said to be complete. When C is composed of partial row vectors of a three-dimensional unit matrix, the receiving sensor unit is missing, and the received data incompletely reflects the wave structure information. The present invention uses iterative operations to repair the missing receiving sensor unit data based on the incomplete wave structure information, allowing the attitude matrix structural constraints to be incorporated into linear iterative operations to solve the attitude matrix. The present invention assumes that the selection matrix of each electromagnetic vector sensor is identical, and selects p = 1,…,P units to form the defective electromagnetic vector sensor.

[0039]

[0040] is the phase delay, Θ represents the frequency drift phase delay caused by aircraft sampling, and the phase delay of N electromagnetic vector sensors is represented by vector express.

[0041] (3) Model of aircraft-borne separated orthogonal dipole array receiving fully polarized signals

[0042] The present invention uses separated three-orthogonal dipole and double-orthogonal dipole arrays as examples to estimate the platform attitude. Figure 3 Dipoles 1, 2, and 3 along the X and Y axes are used as three orthogonal dipoles. All sensors use dipole position 1 as a reference. Dipoles 2 and 3 are translated by 1 unit along the Y and Z axes in the fuselage coordinate system. The serial numbers are: n = 1, ..., N. Dipole 1 of the sensor is not moved. The coordinates (x no ,y no ,z no ) T ; The coordinates of dipole 2 in the fuselage coordinate system after translation (x no ,y no ,z no ) T +(0,1,0) T , the coordinates of dipole 3 in the fuselage coordinate system are translated (x no ,y no ,z no ) T +(0,0,1) T Without changing the origin, the position coordinates of the electromagnetic vector sensor dipole 1 in the geodetic coordinate system are: (x n ,y n ,z n ) T =b R (x no ,y no ,z no) T ; The position coordinates of the electromagnetic vector sensor dipole 2 in the geodetic coordinate system are: (x n ,y n ,z n ) T =b R (x no ,y no ,z no ) T +b R (0,1,0) T ; The position coordinates of the electromagnetic vector sensor dipole 3 in the geodetic coordinate system are: (x n ,y n ,z n ) T =b R (x no ,y no ,z no ) T +b R (0,0,1) T .

[0043] The steering vector expression of electromagnetic vector sensor No. n on the aircraft is:

[0044]

[0045] in:

[0046] and

[0047] (3) Signal receiving model of aircraft-borne electromagnetic vector sensor array

[0048] A separate electromagnetic vector sensor array with receiving units in the same distribution position and orientation is installed on the aircraft platform. The installation coordinates of each sensor in the aircraft coordinate system are measured. The direction of arrival of the navigation signal is confirmed to be known. Based on the variation between the orientation position of the defective electromagnetic vector sensor and the received signal, a guidance vector for the electromagnetic vector sensor is established. Assume that the array receives k = 1, ..., K superimposed signals. The present invention requires that K ≥ 3.

[0049] definition:

[0050]

[0051] is a 3×K matrix.

[0052] is an N×K matrix.

[0053] S=[s1 … s k … sK ], is a T×K matrix, where s k =[s k (1),s k (2),...,s k (T)] T , s k (t) represents the quick sort waveform value at time t, t = 1, 2, ..., T.

[0054] The symbol ⊙ represents the Khatri-Rao product.

[0055] By arranging the signal data received by all electromagnetic vector sensors, a parallel factor (PARAFAC) trilinear data is established, corresponding to the three-dimensional linearity of signal time, polarization, and space-frequency phase delay. The electromagnetic vector sensor array with sequence number n receives k = 1, ..., K superimposed signals as follows:

[0056] X n =GD n (Q)S T +e n (5)

[0057] This is a 3×T matrix, where D n (·) extracts the nth row of the matrix and arranges it into a diagonal matrix.

[0058] Arrange the receiving signals of all N three orthogonal dipoles in the array. When the array platform attitude changes, the receiving model of the three orthogonal dipole array for the superposition signal from K navigation signals is expressed as:

[0059]

[0060] Among them E X is the noise matrix, The received data that satisfies the trilinear model can be arranged into a third-order tensor:

[0061] X=I K ×1G×2Q×3S T +E(7)

[0062] in E represents the noise third-order tensor, is a third-order tensor of received data, containing the signal reception data of all navigation signals received by all three orthogonal dipole antennas in the array within a period of time. Specifically, the element x in X n,p,t Corresponding to x in formula (5) n The pth row and tth column element of n,p,t =x n(p, t), where p is the unit number of the three orthogonal dipoles, p = 1, 2, 3, then the problem of solving the G matrix is ​​expressed as minimizing the following cost function:

[0063]

[0064] Tensor X Perform the slice operation to obtain the section matrices Y and Z:

[0065]

[0066] in Noise Profile Matrix Noise Profile Matrix

[0067] The optimization problem of formula (8) is transformed into the problem of alternately solving the following three cost function minimization problems:

[0068]

[0069]

[0070] (4) According to the signal model, the posture measurement of the present invention is as follows:

[0071] Step 1: Install a separate electromagnetic vector sensor array with identical receiving units in the same position and orientation on the aircraft platform. Measure the coordinates of each sensor unit relative to a reference point within that sensor. Verify that the navigation signal's direction of arrival and polarization parameters are known. Based on the relationship between the attitude and position of the missing electromagnetic vector sensor and the received signal, construct a three-dimensional linear model of the Parallel Factor (PARAFAC) by aligning the received signal data from all electromagnetic vector sensors. This corresponds to the three-dimensional linear model of the signal's time, polarization, and space-frequency phase delay.

[0072] Step 2: Under a certain accuracy threshold, use the trilinear alternating least squares (TALS) method to obtain the polarization domain steering matrix containing the array platform attitude information

[0073] The update expressions for the three factor matrices during the iteration process are:

[0074]

[0075] in Represents S T ,Q,G estimation values,During the iteration process, the cost function is expressed as follows:

[0076]

[0077] ε of the current iteration(k-1) and the ε of this iteration (k) When the difference Δε is less than a very small preset value tol:

[0078] Δε=ε (k-1) -ε (k) <tol (15)

[0079] End the iterative process of PARAFAC decomposition and obtain the polarization domain steering matrix containing the array platform attitude information

[0080] Step 3: Implement attitude matrix orthogonal solution. When the sensor data is complete, the attitude matrix is ​​calculated using the Lagrange multiplier method under attitude matrix orthogonality constraints, based on the relationship between the polarization domain steering array element modulus and the zero-attitude polarization domain steering array element modulus, according to the minimum mean square error principle. When the sensor data is incomplete, the incomplete attitude matrix is ​​calculated according to the minimum mean square error principle, and the cross multiplication method is used to complete the attitude matrix. The Lagrange multiplier method under attitude matrix orthogonality constraints is used to calculate the attitude matrix under orthogonality constraints according to the minimum mean square error principle.

[0081] Take the array as a separated three-orthogonal dipole array as an example of sensor data completeness. Take the modulus of each element of the matrix G, denoted as G || , and compare the definition of G to know G || =b R G 0|| . Among them: G 0|| Represents the polarization domain steering vector matrix with zero attitude Since the arrival parameters and polarization parameters of each navigation signal are known, The modulus of each element is also known, that is, G 0|| is a known real constant matrix. According to G || =b R G 0|| ,exist Under the constraints of R , the problem is transformed into a posture matrix The orthogonal solution process minimizes the cost function, that is, Use the Lagrange multiplier method to solve this problem. Constraints There are six constraints on the element relationship, so that b R The matrix can be described by at most three independent parameters, i.e., only three degrees of freedom.

[0082] Let λ be a real constant symmetric matrix, and define:

[0083]

[0084] This constrained least squares problem can be expressed as the following equation for bR Take the derivative and set it to 0:

[0085]

[0086] have to:

[0087] b R =U[λ+G 0|| G 0|| T ] -1 (16)

[0088] Note that [λ+G 0|| G 0|| T ] -1 Real symmetry, from (16) we get:

[0089] That is: [λ+G 0|| G 0|| T ] 2 =U T U

[0090] So: [λ+G 0|| G 0|| T ]=(U T U) -0.5 , substituting into (16) we get:

[0091] b R =U(U T U) -0.5 (17)

[0092] (17) Formula b R Is an orthogonal matrix, so far b R Matrix orthogonal solver.

[0093] Take the array as a separated orthogonal dipole array as an example of incomplete sensor data. Modulo the two-row matrix G: We can get: At this point, it is explained that according to the two rows of estimated value matrix G, the first two rows of attitude matrix estimates can be calculated. The two rows of attitude estimation values ​​are cross-multiplied to obtain the third row of attitude matrix values, which are divided by the respective row vector moduli to achieve modulus normalization. In this way, the three rows of attitude matrix are obtained, which are recorded as exist Under the constraints of oR , the problem is transformed into a posture matrix The orthogonal solution process minimizes the cost function, that is, Use the Lagrange multiplier method to solve this problem. Constraints There are six constraints on the element relationship, so that b oR The matrix can be described by only three independent parameters at most, i.e., it has only three degrees of freedom. Let λ be a real constant symmetric matrix,

[0094] definition:

[0095]

[0096] This constrained least squares problem can be expressed as the following equation for b oR Take the derivative and set it to 0:

[0097]

[0098] have to:

[0099]

[0100] Note [λ+I] -1 Real symmetry, from (18) we get:

[0101] Right now:

[0102] then: Substituting into (18) we get:

[0103]

[0104] Formula b oR It is an orthogonal matrix, and the orthogonal solution is achieved.

[0105] Step 4: Determine whether the accuracy of the attitude matrix can be improved. If so, return to step 2 and perform the next loop at a higher accuracy threshold. If the attitude matrix has reached the desired accuracy, end the loop.

[0106] Substitute the orthogonal solution of the attitude matrix into step 2, appropriately reduce the preset value tol, and continue to use the trilinear alternating least squares (TALS) method to obtain the polarization domain steering matrix containing the array platform attitude information If the cost function value can be further reduced, it means that the attitude matrix needs to be recalculated through step 3, and step 4 continues the loop judgment; if the cost function value cannot be further reduced, it means that the attitude matrix has reached the ideal accuracy, the loop ends, and the attitude data is output.

[0107] Finally, it should be understood that the above embodiments are merely exemplary embodiments for illustrating the principles of the present invention, and the present invention is not limited thereto. Those skilled in the art will be able to make various modifications and improvements without departing from the principles and essence of the present invention, and such modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A method for measuring the attitude of a separated electromagnetic vector sensor array platform using a reference wave structure, characterized in that: The following steps are involved: Step 1: Install a separate electromagnetic vector sensor array with receiving units in the same position and attitude on the aircraft platform, and measure the coordinates of each unit within each sensor relative to the sensor reference point. Confirm that the direction of arrival and polarization parameters of the navigation signal are known. Based on the change pattern between the attitude position of the missing electromagnetic vector sensor on the airborne aircraft and the received signal, arrange the received signal data of all electromagnetic vector sensors to establish parallel factor trilinear data corresponding to the three-dimensional linearity of signal time, polarization, and space-frequency phase delay. Step 2: Under a certain accuracy threshold, use the trilinear alternating least squares method to obtain the polarization domain steering matrix containing the array platform attitude information Step 3: Implement attitude matrix orthogonal solution: When the sensor data is complete, the attitude matrix is ​​calculated based on the relationship between the polarization domain steering array element modulus and the zero attitude polarization domain steering array element modulus using the Lagrange multiplier method under the attitude matrix orthogonality constraint and the minimum mean square error principle. When the sensor data is incomplete, the missing attitude matrix is ​​calculated based on the minimum mean square error principle, the attitude matrix is ​​completed using the cross multiplication method, and the attitude matrix is ​​calculated based on the Lagrange multiplier method under the attitude matrix orthogonality constraint and the minimum mean square error principle. Step 4: Determine whether the accuracy of the attitude array can be improved. If so, return to step 2 and perform the next cycle at a higher accuracy threshold. If the attitude array has reached the ideal accuracy, end the cycle.

2. The measuring method according to claim 1, wherein In step 1, separate electromagnetic vector sensors with the same receiving units, the same distribution positions, and the same installation posture are installed on the aircraft platform, and the relative coordinates of each unit in each sensor and the reference point of this sensor are measured to establish a parallel factor trilinear data model and realize trilinear data decomposition calculation; confirm that the direction of arrival and polarization parameters of the navigation signal are known; according to the change law between the posture position of the airborne defective electromagnetic vector sensor and the received signal, by arranging the received signal data of all electromagnetic vector sensors, parallel factor trilinear data is established, corresponding to the three-dimensional linearity of signal time, polarization, and space-frequency phase delay, to realize aircraft attitude measurement.

3. The measuring method according to claim 1, wherein In step 2, the polarization domain steering matrix is ​​obtained The method is: Iterate the three factor matrices, and the iterative update expression is: Where, Represents S T , estimated values ​​of Q and G; The cost function in the iterative process is expressed as: ε of the current iteration (k-1) and the ε of this iteration (k) When the difference Δε is less than the preset value tol, the iterative process of PARAFAC decomposition ends and the polarization domain steering matrix containing the array platform attitude information is obtained.

4. The measuring method according to claim 1, wherein In step 3, when the sensor data is complete, the modulus of each element of the matrix G is taken, denoted as G || , G||=b R G 0|| , where G 0|| Represents the polarization domain steering vector matrix with zero attitude Each element modulus is a known real constant matrix; according to G || =b R G 0|| ,exist Under the constraints of R , the problem is transformed into a posture matrix The orthogonal solution process minimizes the cost function, that is, Solve b using the Lagrange multiplier method R =U(U T U) -0.5 , 5. The measuring method according to claim 1, wherein: In step 3, when the sensor data is incomplete, the two rows of the matrix G are modulo: According to the two rows of estimated value matrix G, the first two rows of attitude matrix are calculated by modulus, and the two rows of attitude estimation values ​​are cross-multiplied to obtain the third row of attitude matrix values, which are divided by the respective row vector modulus to achieve modulus normalization and obtain the three rows of attitude matrix. exist Under the constraints of oR , the problem is transformed into a posture matrix The orthogonal solution process minimizes the cost function, that is, Using the Lagrange multiplier method, we can get 6. The measuring method according to claim 1, characterized in that In step 4, substitute the orthogonal solution of the attitude matrix into step 2, reduce the preset value tol, and continue to use the trilinear alternating least squares method to obtain the polarization domain steering matrix containing the array platform attitude information If the cost function value can be further reduced, it means that the attitude matrix needs to be recalculated through step 3, and step 4 continues the loop judgment; if the cost function value cannot be further reduced, it means that the attitude matrix has reached the ideal accuracy, the loop ends, and the attitude data is output.

Images