Platform attitude tracking PARAFAC decomposition measurement method of reference wave structure

Abstract

The invention provides a PARAFAC decomposition measurement method for platform attitude tracking of a reference wave structure, and the method comprises the steps: building an array steering vector of an airborne electromagnetic vector sensor according to a change rule between the attitude position of the airborne electromagnetic vector sensor and a received signal; according to a three-dimensional information structure and attitude relation of signal time, polarization and space-frequency phase delay, all electromagnetic vector sensors are arranged to receive signal data, and a parallel factor trilinear data model can be obtained. An observation matrix is windowed, a tracking algorithm is used for replacing tradition, and complexity is prevented from being increased along with time. By popularizing a traditional parallel factor alternating least square algorithm, platform attitude data of a reference wave structure is tracked under the orthogonal constraint condition, and then the platform attitude is calculated.

Description

Technical Field

[0001] The invention belongs to the field of navigation technology, and in particular relates to a PARAFAC decomposition measurement method for platform attitude tracking with reference to a wave structure. Background Art

[0002] Surveying and mapping technology requires accurate data on the platform's attitude. Manned spaceflight projects require frequent transportation of personnel and cargo and docking with space stations, which places higher demands on the accuracy and reliability of the aircraft's attitude measurement. Satellites, rockets, missiles, and other aircraft are widely used, and the demand for attitude measurement has increased. The uniqueness of the decomposition of the Parallel Factor (PARAFAC) data model has important application value. By promoting the traditional Parallel Factor Alternating Least Squares algorithm, the trilinear data (Parallel Factor, PARAFAC) is decomposed to obtain the load matrix. Good results have been achieved in the CDMA, OFDM and other neighborhoods.

[0003] The existing aircraft attitude measurement reference objects are insufficient and need to be improved in accuracy, stability and economy; the aircraft-borne array estimation of the direction of arrival is troubled by unknown attitude. Summary of the invention

[0004] Purpose of the invention: The technical problem to be solved by the present invention is to overcome the lack of existing aircraft attitude measurement reference objects, improve accuracy, stability, refresh rate and economy; overcome the existing aircraft-borne array estimated attitude tracking performance problems, and provide a platform attitude tracking PARAFAC decomposition measurement method with reference wave structure, which is suitable for aircraft-borne array aerospace detection.

[0005] The method of the present invention comprises the following steps:

[0006] Step 1, establish a tracking attitude measurement system: install an electromagnetic vector sensor array with the same receiving unit and the same attitude on the aircraft platform, and measure the installation coordinates of each sensor in the fuselage coordinate system. The output data of the sensor array forms a trilinear structure, and the parallel factor alternating least squares algorithm is used to perform PARAFAC decomposition to obtain the spatial domain and polarization domain guidance factors of each signal. According to the navigation system, the wave direction is set, and the polarization domain guidance factor under zero attitude is calculated. According to the relationship between the polarization guidance factor and the attitude, the platform attitude is solved to realize the attitude measurement based on the wave structure information. The present invention provides a fast attitude tracking algorithm, and the tracking condition requires the acquisition of initial attitude data, and the initial attitude data is close to the real-time attitude value. The initial attitude can be provided by other sensors, or by an attitude estimation algorithm with reference to the wave structure. The attitude tracking algorithm provided by the present invention is faster than the general attitude estimation algorithm with reference to the wave structure, which can effectively improve the attitude measurement refresh rate. The existing public signals of satellites such as Beidou and GPS can be used to realize the attitude measurement of aircraft, and the signal wave arrival and polarization parameters can be calculated and obtained by the navigation system in real time.

[0007] Step 2. Depending on the received information, the received signal can be subjected to attitude tracking and estimation when multiple signals are fully sampled; or attitude tracking and estimation can be performed when multiple signals are incompletely sampled; or attitude tracking and estimation can be performed when a single signal is completely sampled. Attitude tracking when multiple signals are fully sampled refers to the situation where independent three orthogonal dipole signals or three orthogonal magnetic ring signals are realized when multiple satellite signals are received, incomplete sampling of multiple signals refers to the situation where independent non-three orthogonal dipole signals are realized when multiple satellite signals are received, and attitude tracking and estimation when a single signal is fully sampled refers to the situation where independent three orthogonal dipole signals or three orthogonal magnetic ring signals are realized when a single satellite signal is received.

[0008] In step 1, electromagnetic vector sensors with the same receiving units are installed on the aircraft platform to establish a parallel factor trilinear data model; an electromagnetic vector sensor array with the same attitude is installed to realize trilinear data decomposition calculation; and the installation coordinates of each sensor in the fuselage coordinate system are measured to realize the utilization of space wave arrival information; the existing public signals of Beidou, GPS and other satellites, as well as their mixed signals, can be used to realize aircraft attitude measurement, requiring that the signal wave arrival and polarization parameters can be calculated and obtained by the navigation system in real time.

[0009] In step 2, the posture tracking estimation during multi-signal complete sampling includes the following steps:

[0010] Step 2-1-1, input the estimated values ​​of each signal sequence within the initial sliding window time, the initial attitude estimate, and the spatial domain and polarization domain steering factors of each signal.

[0011] Step 2-1-2, calculating the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor, and combining them into a full array steering vector;

[0012] Step 2-1-3, multiply the real-time data received by each sensor by the Moor-Penrose generalized inverse of the unupdated steering vector matrix of the entire array to obtain the first real-time estimate of the signal sequence;

[0013] Step 2-1-4, merging the real-time data received by each sensor with the data received during the old window period; merging the real-time estimation of the signal sequence with the signal sequence during the old window period;

[0014] Step 2-1-5, estimating a real-time update matrix of the full array steering vector based on the combined sensor reception data and signal sequence;

[0015] Step 2-1-6, the real-time update matrix of the steering vector is the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor. Each signal column data is inversely quantized into a matrix, and the matrix is ​​conjugate-transposed and multiplied with the polarization domain steering factor to obtain the real-time update of the corresponding spatial domain factor; the column data inverse quantization matrix is ​​multiplied with the spatial domain factor, and the real-time update of the corresponding polarization domain steering factor is obtained after modulus normalization;

[0016] Step 2-1-7, multiply the real-time update matrix Moor-Penrose generalized inverse of the steering vector by the time-shift update of each sensor receiving data to obtain the real-time signal re-update estimate, which is merged with the historical data;

[0017] Step 2-1-8, updating the zero attitude polarization domain steering factor according to the change of the navigation system conditions, calculating the unorthogonalized attitude array based on the relationship between the zero attitude polarization domain steering factor and the real-time attitude polarization domain steering factor, and orthogonalizing the attitude array before outputting it;

[0018] Step 2-1-9, the time sliding window re-circles the valid data: delete the first column of the data array received by each sensor and the first row of the signal sequence, update the time scale of the remaining parameters, and become the initial conditions for the next round of tracking, and return to step 2-1.

[0019] In step 2, the attitude tracking estimation is performed when the multi-signal incomplete sampling is performed. For an orthogonal dipole array, since the array is selected so that the calculated unorthogonalized attitude array has only two rows, the following steps are performed according to the principle that the tracking attitude change is a slight rotation:

[0020] Step 2-2-1, input the estimated values ​​of each signal sequence within the initial sliding window time, the initial attitude estimate, and the spatial domain and polarization domain steering factors of each signal.

[0021] Step 2-2-2, calculating the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor, and combining them into a full array steering vector;

[0022] Step 2-2-3, multiply the real-time data received by each sensor by the Moor-Penrose generalized inverse of the unupdated steering vector matrix of the entire array to obtain the first real-time estimate of the signal sequence;

[0023] Step 2-2-4, merging the real-time data received by each sensor with the data received during the old window period; merging the real-time estimation of the signal sequence with the signal sequence during the old window period;

[0024] Step 2-2-5, estimating a real-time update matrix of the full array steering vector based on the combined sensor reception data and signal sequence;

[0025] Step 2-2-6, the real-time update matrix of the steering vector is the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor. Each signal column data is inversely quantized into a matrix, and the matrix is ​​conjugate-transposed and multiplied with the polarization domain steering factor to obtain the real-time update of the corresponding spatial domain factor; the column data inverse quantization matrix is ​​multiplied with the spatial domain factor, and the real-time update of the corresponding polarization domain steering factor is obtained after modulus normalization;

[0026] Step 2-2-7, multiply the real-time update matrix Moor-Penrose generalized inverse of the steering vector by the time-shift update of each sensor receiving data to obtain the real-time signal re-update estimate, which is merged with the historical data;

[0027] Step 2-2-8, update the zero attitude polarization domain guidance factor according to the change of navigation system conditions: the relationship between the zero attitude polarization domain guidance factor and the real-time attitude polarization domain guidance factor, as well as the attitude matrix relationship obtained in the last measurement, calculate the two rows of element values ​​of the attitude change matrix, while the micro-rotation matrix represented by the Euler angle has only three unknowns. Therefore, according to the principle of equal corresponding values ​​of elements, the attitude change matrix is ​​obtained, and then the real-time attitude is calculated;

[0028] Step 2-2-9, the time sliding window re-circles the valid data: delete the first column of the data array received by each sensor and the first row of the signal sequence, update the time scale of the remaining parameters, and become the initial conditions for the next round of tracking, and return to step 3-1.

[0029] In step 2, the posture tracking estimation during single signal complete sampling includes the following steps:

[0030] Step 2-3-1, input the estimated values ​​of each signal sequence within the initial sliding window time, the initial attitude estimate, and the spatial domain and polarization domain steering factors of each signal.

[0031] Step 2-3-2, calculate the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor, and combine them into a full array steering vector;

[0032] Step 2-3-3, multiply the real-time data received by each sensor by the Moor-Penrose generalized inverse of the unupdated steering vector matrix of the entire array to obtain the first real-time estimate of the signal sequence;

[0033] Step 2-3-4, merge the real-time data received by each sensor with the data received during the old window period; merge the real-time estimation of the signal sequence with the signal sequence during the old window period;

[0034] Step 2-3-5, estimating a real-time update matrix of the full array steering vector based on the combined sensor received data and signal sequence;

[0035] Step 2-3-6, the real-time update matrix of the steering vector is the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor. Each signal column data is inversely quantized into a matrix, and the matrix is ​​conjugate transposed and multiplied with the polarization domain steering factor to obtain the real-time update of the corresponding spatial domain factor; the column data inverse quantization matrix is ​​multiplied with the spatial domain factor, and the real-time update of the corresponding polarization domain steering factor is obtained after modulus normalization;

[0036] Step 2-3-7, multiply the real-time update matrix Moor-Penrose generalized inverse of the steering vector by the time-shift update of each sensor receiving data to obtain the real-time signal re-update estimate, which is merged with the historical data;

[0037] Step 2-3-8, update the zero attitude polarization domain steering factor according to the change of navigation system conditions: from the relationship between the zero attitude polarization domain steering factor, the real-time attitude polarization domain steering factor, and the attitude array relationship obtained in the last measurement, calculate the linear equations of the three unknowns about the attitude change array, solve the equation to obtain the attitude change array, and then calculate the real-time attitude;

[0038] Step 2-3-9, the time sliding window re-circles the valid data: delete the first column of the data array received by each sensor and the first row of the signal sequence, update the time scale of the remaining parameters, and become the initial conditions for the next round of tracking, and return to step 4-1.

[0039] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the described method.

[0040] The present invention also provides a storage medium storing a computer program or instruction. When the computer program or instruction is run on a computer, the steps of the method described are executed.

[0041] Compared with the prior art, the present invention adopts the above technical solution and has the following beneficial effects:

[0042] 1) Since the electromagnetic vector sensor polarization array receives raw data presenting a three-dimensional data structure of time, polarization and space-frequency phase delay, the electromagnetic vector sensor polarization array can use this data structure to quickly track the aircraft attitude measurement of the reference wave structure vector. The trilinear data structure can be used to perform PARAFAC decomposition to track the aircraft attitude. The present invention integrates the attitude array orthogonal structure into the PARAFAC decomposition to improve the fitting accuracy of the algorithm.

[0043] 2) Decompose PARAFAC trilinear data, track the load matrix in real time, and efficiently refresh the aircraft attitude data. The computing efficiency is better than traditional algorithms.

[0044] 3) Make up for the lack of reference objects for spatial attitude measurement;

[0045] 4) Reduce the requirements for attitude measurement signal sources;

[0046] 5) Improved the stability and reliability of vehicle attitude tracking with reference to the wave structure vector. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0048] Figure 1 Schematic diagram of electromagnetic wave signal propagation.

[0049] Figure 2 It is the elliptically rotating electric field of polarized electromagnetic waves.

[0050] Figure 3 Schematic diagram of the electromagnetic vector sensor with zero rotation attitude in the geodetic coordinate system. DETAILED DESCRIPTION

[0051] In an embodiment of the present invention, a PARAFAC decomposition measurement method for platform attitude tracking with reference to wave structure is provided, comprising the following steps:

[0052] Step 1, establishing a model for an electromagnetic vector sensor to receive a fully polarized signal;

[0053] The propagation direction of electromagnetic wave signal is Figure 1 As shown, in the geodetic coordinate system, the spatial arrival direction of electromagnetic waves is measured by the parameter Indicates, φ, θ represent azimuth and elevation respectively, where -π / 2<θ<π / 2, The arrival vector u is:

[0054]

[0055] The polarization properties of electromagnetic waves are represented by the polarization ellipse descriptor (γ,η), γ represents the polarization angle, -π / 2<γ≤π / 2, η represents the polarization ellipticity, -π / 4≤η≤π / 4, and the elliptically rotating electric field of the polarized electromagnetic wave is as follows: Figure 2 As shown, They are the major axis direction vector and minor axis direction vector of the electric field polarization ellipse, and the electromagnetic wave structure vector The wave structure vector is 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. Figure 3 As shown, Figure 3 The coordinate system in the figure is the earth coordinate system. The present invention uses the dipole array as an example to illustrate the effectiveness of the algorithm, and the attitude measurement method of the electromagnetic vector sensor can be derived by analogy. At this time, the ideal guidance vector of the independent three orthogonal dipole sensors is in:

[0056]

[0057] The ideal steering vector of three independent orthogonal dipoles at the origin is further expressed as:

[0058]

[0059] In the formula d(n)=[0cosn isinn0-isinnncosn] T

[0060] Where T represents the matrix transpose;

[0061] Reference Figure 1 Know, Indicates 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 expressed as The difference is rotated in the geodetic coordinate system. Indicates that the geodetic coordinate system rotation difference matrix Simplified to b R .

[0062] Step 2, establishing a model for receiving fully polarized signals by an electromagnetic vector sensor array carried by an aircraft;

[0063] 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 is ​​a single rotation vector Description, where [φ 1 φ 2 φ 3 ] is the rotation vector Coordinates in the coordinate system, the earth coordinate system rotation difference matrix b R equal:

[0064] Among them, e represents a natural constant;

[0065] The number of electromagnetic vector sensors is N, and the serial number is: n = 1, ..., N. The installation 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 (x n ,y n ,zn ) T is: (x n ,y n ,z n ) T =b R (x no ,y no ,z no ) T

[0066] The guidance vector a of the electromagnetic vector sensor n on the aircraft n The expression of (φ,θ,γ,η) is:

[0067]

[0068] Where C is a selection matrix, which is composed of some row vectors of the three-dimensional unit matrix, indicating that some units are selected from three orthogonal dipoles to form an electromagnetic vector sensor; when C is a unit matrix, the received data fully reflects the wave structure information, and at this time, the single-point received information is called complete; when C is composed of P row vectors of the three-dimensional unit matrix, the receiving sensor unit, the received data incompletely reflects the wave structure information. The present invention uses iterative operations to repair the receiving sensor unit data according to the incomplete wave structure information, so that the attitude array structure constraints can be included in the linear iterative operation to solve the attitude array. The present invention sets the selection matrix of each electromagnetic vector sensor to be the same, and selects p=1,…,P units to form an electromagnetic vector sensor. q n (φ,θ) is the phase delay, expressed as:

[0069]

[0070] Where Θ represents the frequency drift phase delay caused by aircraft sampling, and the phase delay of N electromagnetic vector sensors is represented by vector Indicates that q N (φ k ,θ k ) represents the phase delay vector of the Nth electromagnetic vector sensor, and the subscript k=1,…,K represents the sequence number of the Kth navigation signal. The kth navigation signal s k At time t+1-T,…,t, there are T sampling data, and there are sampling data s k (t).

[0071] Step 3, establishing a trilinear data model for tracking the change of the aircraft attitude over time with reference to the wave structure;

[0072] An electromagnetic vector sensor array with the same receiving unit and the same attitude is installed on the aircraft platform, and the installation coordinates of each sensor in the fuselage coordinate system are measured. When the aircraft is flying, the parameters of the navigation signal and the platform attitude change slowly over time, so the following model needs to introduce a dynamic sampling time marker based on the previous model. During the short period of measurement sampling, the parameters of the navigation signal and the platform attitude remain approximately unchanged. According to the change law between the attitude position of the airborne electromagnetic vector sensor and the received signal, the airborne electromagnetic vector sensor guidance vector is established. According to the three-dimensional information structure relationship of signal time, polarization and space-frequency phase delay, by arranging all electromagnetic vector sensor receiving signal data, a parallel factor (PARAFAC) trilinear data model is established.

[0073] Definition: G(t) is a 3×K polarization domain steering factor real matrix,

[0074] Q(t) is the N×K spatial guidance factor matrix,

[0075] S(t) is a T×K time domain sampling data matrix, S(t)=[s 1 (t)…s k (t)…s K (t)], where the kth column vector s k (t) At time t+1-T,…,t, there are T sampling data in total.

[0076] The electromagnetic vector sensor array with serial number n receives k=1,…,K superimposed signals X n (t) is:

[0077] X n (t) = Cb R (t)G(t)D n (Q(t))S T (t)+e n (4)

[0078] X n (t) is a P×T matrix, where D n (·) extracts the nth row of the matrix and constructs it into a diagonal matrix. n By arranging the signal matrix received by all electromagnetic vector sensors, the received data is arranged into a trilinear model of an N×P×T tensor matrix, and the (n, p, t)th element of the trilinear model is X n The (p, t)th element of . In the presence of noise and error, the modulo-n product of the PARAFAC model is expressed as:

[0079] Z(t)=I K × 1 Q(t)× 2 (Cb R (t))× 3 S(t)+E (5)

[0080] Among them I K is the cubic unit tensor; E represents the noise tensor;

[0081] By solving the following cost function: Estimate the corresponding factor matrix, where ||*|| F represents the Frobenius norm.

[0082] Arrange the front slice model of the tensor matrix Z(t) as follows to obtain the NP×T matrix:

[0083]

[0084] The symbol ⊙ represents the Khatri-Rao product. Continuing with formula (6), the data received by each sensor at time t+1 is vector x(t+1), which is combined with the previous T sampling data to obtain: X(t+1)=[X(t), x(t+1)].

[0085] Step 4, establish a tracking attitude measurement system: install an electromagnetic vector sensor array with the same receiving unit and the same attitude on the aircraft platform, and measure the installation coordinates of each sensor in the fuselage coordinate system. In this way, the output data of the sensor array can form a trilinear structure, and the PARAFAC decomposition is performed using the parallel factor alternating least squares algorithm to obtain the spatial domain and polarization domain guidance factors of each signal. According to the navigation system, the wave direction is set, and the polarization domain guidance factor under zero attitude is calculated. According to the relationship between the polarization guidance factor and the attitude, the platform attitude can be solved to achieve attitude measurement based on wave structure information. The present invention provides a fast attitude tracking algorithm, and the tracking condition requires obtaining initial attitude data, and the initial attitude data is close to the real-time attitude value. The initial attitude can be provided by other sensors or by an attitude estimation algorithm with reference to the wave structure. The attitude tracking algorithm provided by the present invention is faster than the general attitude estimation algorithm with reference to the wave structure, which can effectively improve the attitude measurement refresh rate. The existing public signals of satellites such as Beidou and GPS can be used to realize the attitude measurement of aircraft, and the signal wave arrival and polarization parameters can be calculated and obtained by the navigation system in real time.

[0086] Definition: G b (t) = Cb R (t)G(t),H(t)=Q(t)⊙G b (t). Where G b(t) is the polarization domain arrival factor, G(t) is the zero-attitude polarization domain arrival factor, and H(t) is the full array multi-signal steering vector array. b (t) ：，k Represents G b (t) kth column, use H(t+1) :,k It means taking the kth column of H(t+1), Q(t+1) :,k It means taking the kth column of Q(t+1).

[0087] Formula (6) is simplified to:

[0088] X(t)=(Q(t)⊙G b (t))S T (t)+E x =H(t)S T (t)+E x

[0089] Where E x represents the noise matrix;

[0090] Step 5, performing posture tracking estimation when multiple signals are fully sampled, includes the following steps:

[0091] Sampling at a point in space includes three orthogonal dipole sampling or three orthogonal magnetic ring sampling, and the sampling information of the point is complete, taking three orthogonal dipole array sampling as an example.

[0092] Step 5-1: Input the old estimated value S(t) and b at time t R (t), and calculate Q(t) at this time according to formula (3).

[0093] Step 5-2: Update the direction of arrival according to the navigation system settings, calculate the polarization domain steering vector, and combine them into the matrix G(t) as described above. Then we get G b (t) and H(t).

[0094] Step 5-3: Based on the data input x(t+1) received by each sensor at time t+1, set H(t)=H(t+1) to obtain the next updated estimate s of the estimated value s(t) T (t+1)=H+(t)x(t+1). + (t) denotes the Moor-Penrose generalized inverse;

[0095] Step 5-4: Compose the estimate

[0096] Step 5-5: Estimate H(t+1): H(t+1)=X(t+1)S T (t+1).

[0097] Step 5-6: Estimate Q(t+1) and G from H(t+1) b (t+1).

[0098] k takes a value of 1 to K and performs the following calculation:

[0099] H k (t+1)=unvec(H(t+1) :,k )

[0100] Q * (t+1) ：，k =H H k (t+1)G b (t) ：，k

[0101]

[0102] Among them, unvec() means inverse quantization into a matrix;

[0103] Step 5-7: Time-Shift Update:s T (t+1)=H + (t+1)x(t+1),

[0104] Step 5-8: Update G(t+1) at time t+1 according to the change of navigation system conditions. b (t+1)=b R (t+1)G(t+1), calculated to get U=G b (t+1)G + (t+1), U is the unorthogonalized attitude matrix. Output orthogonalized attitude b R (t+1)=U(U T U) -0.5 .

[0105] Step 5-9: Forget the old data, that is, delete the first column of X(t+1) and the first row of S(t+1), which become X(t) and S(t) of the next round, b R The time stamp of (t+1) is also changed to (t), and the time stamps of other parameters are also changed from (t+1) to (t), and the process returns to step 5-1.

[0106] The special feature of the attitude estimation algorithm based on complete wave structure information is b R is a real number attitude matrix, and the constraint condition b R T b R =I 3 , I 3The present invention integrates the orthogonal structure of the attitude array into the PARAFAC decomposition based on the complete wave structure information to improve the fitting accuracy of the algorithm.

[0107] Step 6: Perform posture tracking estimation when multiple signals are not fully sampled:

[0108] Taking the array as an orthogonal dipole array as an example, steps 6-1 to 6-7, and step 6-9 are the same as steps 5-1 to 5-7, and step 5-9. Step 6-8 needs to be changed to: solve the platform attitude, by formula in It represents the slight change of attitude from t to t+1. If the attitude matrix is ​​expressed in Euler angles but Orthogonal dipole selection array There are only two lines.

[0109] The right side of the above equation is known, so according to the principle of equal values ​​of corresponding elements, we can get the matrix elements Δm1(t+1), Δm2(t+1) and Δm3(t+1) on the left side, that is, According to The attitude is calculated. The remaining steps are the same as the attitude tracking estimation when multiple signals are fully sampled.

[0110] Step 7 is performed, and the attitude tracking estimation is performed when the single signal is fully sampled:

[0111] The attitude cannot be estimated correctly when a single signal is not fully sampled, so we only study the attitude tracking estimation when a single signal is fully sampled. Taking the three-orthogonal dipole array sampling as an example, we choose array C as the unit array, so Since the single signal has no aliasing, G can be obtained from the trilinear relationship of the sampled data. b (t+1), and G(t+1) is measurable, b R (t) is known. So the equation In the equation, except for the three unknowns Δm1(t+1), Δm2(t+1), and Δm3(t+1), the rest are constants. Therefore, steps 7-1 to 7-7 and 7-9 are the same as steps 5-1 to 5-7 and 5-9. Step 7-8 needs to be changed to: Solve this three-variable linear equation to get Δm1(t+1), Δm2(t+1), and Δm3(t+1), and then get

[0112] The present invention provides a PARAFAC decomposition measurement method for platform attitude tracking with reference to wave structure. There are many methods and ways to implement the technical solution. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A PARAFAC decomposition measurement method for platform attitude tracking with reference to wave structures, characterized in that: The following steps are involved: Step 1, establish a tracking attitude measurement system: install an electromagnetic vector sensor array with the same receiving unit and the same attitude on the aircraft platform, and measure the installation coordinates of each sensor in the fuselage coordinate system. The sensor array output data forms a trilinear structure. The parallel factor alternating least squares algorithm is used to perform PARAFAC decomposition to obtain the spatial domain and polarization domain guidance factors of each signal. The wave direction of arrival is set according to the navigation system, and the polarization domain guidance factor under zero attitude is calculated. According to the relationship between the polarization guidance factor and the attitude, the platform attitude is solved to realize attitude measurement based on wave structure information; Step 2: Based on the tracking and attitude measurement system established in step 1, according to the signal reception situation, attitude tracking estimation is performed when multiple signals are fully sampled; or attitude tracking estimation is performed when multiple signals are incompletely sampled; or attitude tracking estimation is performed when a single signal is fully sampled.

2. The platform attitude tracking PARAFAC decomposition measurement method of reference wave structure according to claim 1 is characterized in that: The multi-signal complete sampling in step 2 refers to sampling at a point in space to obtain three orthogonal dipole sampling or three orthogonal magnetic ring sampling containing multiple signals, and the sampling information of the point reaches a complete state; the posture tracking estimation when performing multi-signal complete sampling includes the following steps: Step 2-1-1, input the estimated values ​​of each signal sequence within the initial sliding window time, the initial attitude estimate, and the spatial domain and polarization domain steering factors of each signal; Step 2-1-2, calculating the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor, and combining them into a full array steering vector; Step 2-1-3, multiply the real-time data received by each sensor by the Moor-Penrose generalized inverse of the unupdated steering vector matrix of the entire array to obtain the first real-time estimate of the signal sequence; Step 2-1-4, merging the real-time data received by each sensor with the data received during the old window period; merging the real-time estimation of the signal sequence with the signal sequence during the old window period; Step 2-1-5, estimating a real-time update matrix of the full array steering vector based on the combined sensor reception data and signal sequence; Step 2-1-6, the real-time update matrix of the steering vector is the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor. Each signal column data is inversely quantized into a matrix, and the matrix is ​​conjugate-transposed and multiplied with the polarization domain steering factor to obtain the real-time update of the corresponding spatial domain factor; the column data inverse quantization matrix is ​​multiplied with the spatial domain factor, and the real-time update of the corresponding polarization domain steering factor is obtained after modulus normalization; Step 2-1-7, multiply the real-time update matrix Moor-Penrose generalized inverse of the steering vector by the time-shift update of each sensor receiving data to obtain the real-time signal re-update estimate, which is merged with the historical data; Step 2-1-8, updating the zero attitude polarization domain steering factor according to the change of the navigation system conditions, calculating the unorthogonalized attitude array based on the relationship between the zero attitude polarization domain steering factor and the real-time attitude polarization domain steering factor, and orthogonalizing the attitude array before outputting it; Step 2-1-9, the time sliding window re-circles the valid data: delete the first column of the data array received by each sensor and the first row of the signal sequence, update the time scale of the remaining parameters, and become the initial conditions for the next round of tracking, and return to step 2-1.

3. The platform attitude tracking PARAFAC decomposition measurement method of reference wave structure according to claim 1, characterized in that: The multi-signal incomplete sampling in step 2 refers to non-three-orthogonal dipole sampling or non-three-orthogonal orthogonal magnetic ring sampling of multiple signals obtained by sampling at one point in space. Since the array is selected so that the calculated orthogonalized attitude array has only two rows, according to the principle that the tracking attitude change is a slight rotation, the attitude tracking estimation when the multi-signal is incompletely sampled adopts the following steps: Step 2-2-1, input the estimated values ​​of each signal sequence within the initial sliding window time, the initial attitude estimate, and the spatial domain and polarization domain steering factors of each signal; Step 2-2-2, calculating the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor, and combining them into a full array steering vector; Step 2-2-3, multiply the real-time data received by each sensor by the Moor-Penrose generalized inverse of the unupdated steering vector matrix of the entire array to obtain the first real-time estimate of the signal sequence; Step 2-2-4, merging the real-time data received by each sensor with the data received during the old window; Merge the real-time estimation of the signal sequence with the signal sequence during the old window; Step 2-2-5, estimating a real-time update matrix of the full array steering vector based on the combined sensor reception data and signal sequence; Step 2-2-6, the real-time update matrix of the steering vector is the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor. Each signal column data is inversely quantized into a matrix, and the matrix is ​​conjugate-transposed and multiplied with the polarization domain steering factor to obtain the real-time update of the corresponding spatial domain factor; the column data inverse quantization matrix is ​​multiplied with the spatial domain factor, and the real-time update of the corresponding polarization domain steering factor is obtained after modulus normalization; Step 2-2-7, multiply the real-time update matrix Moor-Penrose generalized inverse of the steering vector by the time-shift update of each sensor receiving data to obtain the real-time signal re-update estimate, which is merged with the historical data; Step 2-2-8, update the zero attitude polarization domain steering factor according to the change of navigation system conditions: calculate the two rows of element values ​​of the attitude change array based on the relationship between the zero attitude polarization domain steering factor and the real-time attitude polarization domain steering factor, and the attitude array relationship obtained in the last measurement, and obtain the attitude change array based on the principle of equal corresponding values ​​of elements, and then calculate the real-time attitude; Step 2-2-9, the time sliding window re-circles the valid data: delete the first column of the data array received by each sensor and the first row of the signal sequence, update the time scale of the remaining parameters, and become the initial conditions for the next round of tracking, and return to step 2-2-1.

4. The platform attitude tracking PARAFAC decomposition measurement method of reference wave structure according to claim 1, characterized in that: The single signal complete sampling in step 2 refers to sampling at a point in space to obtain three orthogonal dipole sampling or three orthogonal magnetic ring sampling containing a single signal, and the sampling information of this point reaches the single signal complete state. The posture tracking estimation when performing single signal complete sampling includes the following steps: Step 2-3-1, input the estimated values ​​of each signal sequence within the initial sliding window time, the initial attitude estimate, and the spatial domain and polarization domain steering factors of each signal. Step 2-3-2, calculate the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor, and combine them into a full array steering vector; Step 2-3-3, multiply the real-time data received by each sensor by the Moor-Penrose generalized inverse of the unupdated steering vector matrix of the entire array to obtain the first real-time estimate of the signal sequence; Step 2-3-4, merging the real-time data received by each sensor with the data received during the old window; Merge the real-time estimation of the signal sequence with the signal sequence during the old window; Step 2-3-5, estimating a real-time update matrix of the full array steering vector based on the combined sensor received data and signal sequence; Step 2-3-6, the real-time update matrix of the steering vector is the Khatri-Rao product of the spatial domain steering factor and the polarization domain steering factor. Each signal column data is inversely quantized into a matrix, and the matrix is ​​conjugate transposed and multiplied with the polarization domain steering factor to obtain the real-time update of the corresponding spatial domain factor; the column data inverse quantization matrix is ​​multiplied with the spatial domain factor, and the real-time update of the corresponding polarization domain steering factor is obtained after modulus normalization; Step 2-3-7, multiply the real-time update matrix Moor-Penrose generalized inverse of the steering vector by the time-shift update of each sensor receiving data to obtain the real-time signal re-update estimate, which is merged with the historical data; Step 2-3-8, update the zero attitude polarization domain steering factor according to the change of navigation system conditions: from the relationship between the zero attitude polarization domain steering factor, the real-time attitude polarization domain steering factor, and the attitude array relationship obtained in the last measurement, calculate the linear equations of the three unknowns about the attitude change array, solve the equation to obtain the attitude change array, and then calculate the real-time attitude; Step 2-3-9, the time sliding window re-circles the valid data: delete the first column of the data array received by each sensor and the first row of the signal sequence, update the time scale of the remaining parameters, and become the initial conditions for the next round of tracking, and return to step 2-3-1.

5. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 4.

6. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 4 are executed.

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