Phase interferometer DOA and polarization parameter joint estimation method based on multiple linearly polarized antennas

Abstract

The invention discloses a phase interferometer DOA and polarization parameter joint estimation method based on multiple linearly polarized antennas, and belongs to the technical field of radar signal processing. According to the method, the problems of low ambiguity resolution probability and low signal DOA and polarization parameter estimation precision of an existing method are solved. Noise variance and signal power estimation is carried out by adopting a method of receiving data covariance matrix high-order power, and the complexity is reduced. Aiming at the problem that the defuzzification probability is limited due to polarization mismatch, the method firstly adopts a method of solving a short base line by a long base line to reduce a phase difference error, then utilizes a multi-base-line phase weighted defuzzification method, and utilizes phase differences and amplitude information of all base lines to perform polarization domain phase difference and spatial domain phase difference decoupling, so that the defuzzification probability is limited. And the power estimation error is reduced through the LMMSE method, and the precision of signal DOA and signal polarization parameter estimation is improved. The method can be applied to joint estimation of DOA and polarization parameters of the phase interferometer.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a phase interferometer DOA and polarization parameter joint estimation method based on multiple linearly polarized antennas. Background Art

[0002] With the expansion of the frequency coverage of passive radar direction finding systems, it is a severe challenge to obtain the DOA and polarization parameters of electromagnetic wave signals in a wide frequency band (0.8 GHz to 18 GHz). Compared with the DOA estimation method based on scalar interferometer, the DOA estimation method based on phase interferometer composed of multiple linearly polarized antennas can have better DOA estimation performance and deambiguation performance for wide-band signals under low signal-to-noise ratio.

[0003] Scalar interferometers perform unambiguous DOA estimation by measuring the spatial phase difference. Among them, the LBI (Long-Baseline Interferometer) algorithm proposes a fast and robust DOA estimation method based on the principle of short baseline to resolve long baseline ambiguity. However, the method of resolving long baseline by short baseline will increase the phase difference error, which leads to a decrease in the accuracy of DOA estimation. At the same time, this method does not use the polarization information of the electromagnetic wave signal and cannot obtain the polarization parameters.

[0004] Compared with scalar interferometer, the phase difference between antennas of phase interferometer includes not only spatial phase difference but also polarization phase difference, so the polarization parameters of electromagnetic wave signals can be estimated. Among them, the Im-MPI (Improved Multi-baseline Polarized Interferometer method) algorithm realizes the polarization parameter estimation of electromagnetic wave signals by decoupling the polarization phase difference and spatial phase difference. However, since the phase difference and amplitude information of all baselines are not fully utilized in the deambiguation process, the decoupling of polarization phase difference and spatial phase difference is affected by polarization mismatch, which will lead to the limitation of deambiguation probability. In addition, in the process of signal polarization parameter estimation, due to the limited number of snapshots and the possible small correlation between signal and noise, there are errors in power estimation, which limits the accuracy of signal DOA and polarization parameter estimation.

[0005] Therefore, in the estimation of DOA and polarization parameters of wideband signals, it is necessary to study how to make full use of the phase difference and amplitude information of all baselines to decouple the polarization domain phase difference and the spatial domain phase difference to improve the deambiguation probability, and how to reduce the power estimation error to solve the problem of low accuracy of signal DOA and polarization parameter estimation. Summary of the invention

[0006] The purpose of the present invention is to solve the problems of low deambiguation probability and low estimation accuracy of signal DOA and polarization parameters in existing methods, and propose a phase interferometer DOA and polarization parameter joint estimation method based on multiple linearly polarized antennas.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a phase interferometer DOA and polarization parameter joint estimation method based on multiple linearly polarized antennas, the method specifically comprising the following steps:

[0008] Step 1: Calculate the covariance matrix of the received data using the data received by the phase interferometer including N linearly polarized antennas Then according to the covariance matrix of the received data Estimated noise variance

[0009] Step 2: According to the covariance matrix of the received data To estimate the signal power and Phase

[0010] Step 3: Using the estimated noise variance and signal power To estimate the power polarization coefficient;

[0011] Step 4: Use the estimated power polarization coefficient and signal power and Phase And the signal DOA estimation result is obtained based on the multi-baseline phase weighted deambiguation method;

[0012] Step 5: Calculate a power normalization coefficient using the signal DOA estimation result and the estimated power polarization coefficient, and then calculate a polarization parameter estimation value using the power normalization coefficient, the signal DOA estimation result and the power polarization coefficient estimation value;

[0013] The polarization parameters include a polarization auxiliary angle and a polarization phase difference.

[0014] Furthermore, the specific process of step one is:

[0015] Step 1: N linear polarization antennas in the phase interferometer are arranged linearly, and polarization pointing angles of the N linear polarization antennas are not completely the same;

[0016] The received data of the linear polarization antenna array is recorded as X(t), and the covariance matrix of the received data is calculated based on X(t)

[0017]

[0018] Where K is the number of signal sampling snapshots, t = 1, 2, ..., K, XH (t) is the conjugate transpose of X(t);

[0019] Step 1 and 2: Based on the covariance matrix of the received data Estimated noise variance

[0020]

[0021] in, yes is the trace of , and h is a constant.

[0022] Furthermore, the signal power The estimation method is:

[0023] Using the covariance matrix of the received data Approximate signal subspace:

[0024]

[0025] Among them, λ max and v max is an intermediate variable;

[0026]

[0027] Among them, ·1 represents the 1-norm operation, is the covariance matrix The nth column vector of is λ max The estimated value of Substituting into formula (11), we get v max Estimated value of

[0028] According to Estimating signal power

[0029]

[0030] in, Indicates that intermediate variables are calculated separately The square of the magnitude of each element in .

[0031] Furthermore, the phase The estimation method is:

[0032]

[0033] Here, arg(·) represents the complex argument.

[0034] Furthermore, the specific process of step three is:

[0035] Step 3.1: The signal power p received by the nth linear polarization antenna n Polarization pointing angle α with linear polarization antenna n The relationship is:

[0036] p n =a+bcos2α n +CSIN2α n (16)

[0037] Where a, b and c are power polarization coefficients;

[0038] Based on the estimated signal power Solve for the power polarization coefficient:

[0039]

[0040] in, is a pseudo-inverse operation, Q is a matrix composed of trigonometric functions of the polarization pointing angle of the linear polarization antenna, and are the estimated values ​​of the power polarization coefficients a, b and c, respectively, are the estimated signal powers received by the first linear polarization antenna, ..., the nth linear polarization antenna, ..., the Nth linear polarization antenna, α2 is the polarization pointing angle of the second linear polarization antenna, α3 is the polarization pointing angle of the third linear polarization antenna, α N is the polarization pointing angle of the Nth linearly polarized antenna;

[0041] Step 3.2: Estimated value of power polarization coefficient and It is expressed as:

[0042]

[0043] Among them, the superscript T represents the transpose, and -1 represents the inverse of the matrix;

[0044] Then use the estimated noise variance and signal power The power polarization coefficient estimate and It is expressed as:

[0045]

[0046] Among them, ρ is the adjustment coefficient of signal power; R s =E{S(t)S H (t)}, E{·} denotes expectation, S(t) is the spatial signal vector; I3 is the unit matrix.

[0047] Furthermore, the specific process of step 4 is as follows:

[0048] Step 4: Take the first linear polarization antenna in the linear polarization antenna array as the reference linear polarization antenna, and use the estimated power polarization coefficient and phase Calculate the test spatial phase difference between the nth linear polarization antenna and the reference linear polarization antenna

[0049] Step 42: Calculate the spatial phase difference φ between the nth linear polarization antenna and the reference linear polarization antenna at the i-th ambiguity angle n1 (i);

[0050] Step 43: Obtain the DOA estimation result according to the calculation results of step 41 and step 42.

[0051] Furthermore, the specific process of step 41 is as follows:

[0052] Using the estimated power polarization coefficient and Calculate the polarization domain phase difference between the nth linearly polarized antenna and the reference linearly polarized antenna

[0053]

[0054] Among them, α n is the polarization pointing angle of the nth linear polarization antenna n, α1 is the polarization pointing angle of the reference linear polarization antenna; using the estimated phase Calculate the phase difference between the nth linearly polarized antenna and the reference linearly polarized antenna

[0055]

[0056] in, yes The phase corresponding to the nth linearly polarized antenna in is, yes The phase corresponding to the reference linear polarization antenna;

[0057] The test spatial phase difference between the nth linear polarization antenna and the reference linear polarization antenna is for:

[0058]

[0059] Furthermore, the specific process of step 42 is as follows:

[0060] Step 421: Calculate all fuzzy numbers k based on the two linear polarization antennas corresponding to the longest baseline i and blur angle θ i :

[0061]

[0062] Among them, d N1 is the antenna spacing between the two linearly polarized antennas corresponding to the longest baseline, is the test spatial phase difference of the two linearly polarized antennas corresponding to the longest baseline;

[0063] Step 422: At the i-th ambiguity angle, the spatial phase difference φ between the n-th linear polarization antenna and the reference linear polarization antenna n1 (i) is:

[0064] φ n1 (i) = mod(2πd n1 sinθ i / λ,2π) (24)

[0065] Among them, d n1 represents the antenna spacing between the nth linearly polarized antenna and the reference linearly polarized antenna, mod(·) represents the modulo operation, and λ is the wavelength of the incident signal.

[0066] Furthermore, the specific process of step 43 is as follows:

[0067] Calculate the spatial phase difference φ n1 (i) and test spatial phase difference The difference:

[0068]

[0069] in, is the blur angle θ i Corresponding to the difference between the spatial phase difference and the test spatial phase difference, the set of differences corresponding to each blur angle is recorded as Δψ, and Δψ is weighted as follows:

[0070]

[0071] Among them, mean(·) represents the operation of calculating the mean of all elements in the set Δψ, for l n The reciprocal of l n is the position coordinate vector of the nth linearly polarized antenna, ξ i is the blur angle θ i The corresponding weighted Euclidean distance;

[0072] The smallest ξ i The corresponding blur angle θ i As the signal DOA estimation result

[0073] Furthermore, the specific process of step five is as follows:

[0074] Step 51: Based on the estimated power polarization coefficient and And the signal DOA estimation results Calculate the power normalization coefficient

[0075]

[0076] Step 52: Use power normalization coefficient Power polarization coefficient And the signal DOA estimation results Get the polarization parameter estimates:

[0077]

[0078] in, is the polarization auxiliary angle estimate, is the estimated polarization phase difference.

[0079] The beneficial effects of the present invention are:

[0080] The present invention adopts the method of receiving data covariance matrix high-order power to estimate noise variance and signal power, which reduces complexity. In view of the problem of limited deambiguation probability caused by polarization mismatch, the present invention first adopts the method of long baseline to deambiguate short baseline to reduce the phase difference error, and then uses the multi-baseline phase weighted deambiguation method to use the phase difference and amplitude information of all baselines to decouple the polarization domain phase difference and the spatial domain phase difference, thereby improving the deambiguation probability, and uses the LMMSE (Linear Minimum Mean Squared Error) method to reduce the power estimation error and improve the accuracy of signal DOA and signal polarization parameter estimation.

[0081] Compared with the Im-MPI algorithm and the LBI algorithm, the deambiguation probability of the method of the present invention is increased by about 29% and 39% respectively; the root mean square error of the polarization parameters of the method of the present invention is smaller than that of the Im-MPI algorithm; compared with the Im-MPI algorithm and the LBI algorithm, the DOA estimation accuracy of the method of the present invention is also improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a flow chart of a method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas of the present invention;

[0083] Figure 2 It is a curve diagram of the variation of defuzzification probability with signal-to-noise ratio;

[0084] Figure 3 is the curve diagram of the change of DOA estimation and polarization parameter root mean square error with signal-to-noise ratio SNR;

[0085] Figure 4 This is the DOA estimation result diagram in the microwave darkroom. DETAILED DESCRIPTION

[0086] Specific implementation method 1: Combination Figure 1 This embodiment describes a method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas, and the method specifically includes the following steps:

[0087] Step 1: Calculate the covariance matrix of the received data using the data received by the phase interferometer including N linearly polarized antennas Then according to the covariance matrix of the received data Estimated noise variance

[0088] Step 2: According to the covariance matrix of the received data To estimate the signal power and Phase

[0089] Step 3: Using the estimated noise variance and signal power To estimate the power polarization coefficient;

[0090] Step 4: Use the estimated power polarization coefficient and signal power and Phase And the signal DOA estimation result is obtained based on the multi-baseline phase weighted deambiguation method;

[0091] Step 5: Calculate a power normalization coefficient using the signal DOA estimation result and the estimated power polarization coefficient, and then calculate a polarization parameter estimation value using the power normalization coefficient, the signal DOA estimation result and the power polarization coefficient estimation value;

[0092] The polarization parameters include a polarization auxiliary angle and a polarization phase difference.

[0093] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the specific process of step 1 is as follows:

[0094] Step 1: N linear polarization antennas in the phase interferometer are arranged linearly, and the polarization pointing angles of the N linear polarization antennas are not completely the same (that is, there may be linear polarization antennas with the same polarization pointing angle among the N linear polarization antennas, but the polarization pointing angles of the N linear polarization antennas cannot be the same value);

[0095] The received data of the linear polarization antenna array is recorded as X(t), and the covariance matrix of the received data is calculated based on X(t)

[0096]

[0097] Where K is the number of signal sampling snapshots, t = 1, 2, ..., K, X H (t) is the conjugate transpose of X(t);

[0098] Step 1 and 2: Based on the covariance matrix of the received data Estimated noise variance

[0099]

[0100] in, yes The trace of , h is a constant. When the value of h is infinite, it satisfies the theoretical situation. In practice, when the value of h is greater than or equal to 6, it can meet the noise variance estimation condition.

[0101] The other steps and parameters are the same as those in the first embodiment.

[0102] Consider the noise to be zero mean and with variance σ 2 The complex additive Gaussian white noise, and the noise and signal are statistically independent. Considering one signal, the received data of the linear polarization antenna array is as follows:

[0103] X(t)=AS(t)+N(t) (3)

[0104]

[0105] Where X(t) is the N×K dimensional received data received by the linearly polarized antenna, A is the steering vector of the incident signal, S(t) is the spatial signal vector, and N(t) is the noise data vector of the phase interferometer of multiple linearly polarized antennas. K is the number of signal sampling snapshots, t∈[1,K]. n is the polarization pointing angle of the nth linearly polarized antenna, n∈[1,N]. θ is the incident azimuth of the incident signal, γ is the polarization auxiliary angle, η is the polarization phase difference, j is the imaginary unit, and u n is the spatial phase shift factor for linearly polarized antenna n, is the unit direction vector of the incident signal, l n is the position coordinate vector of the linearly polarized antenna n, and λ is the wavelength of the incident signal. Therefore, the covariance matrix of the received data is:

[0106] R = E{X(t)X H (t)}=AR s A H +σ 2 I N (7)

[0107] Among them, R s =E{S(t)S H (t)},I N is the N×N identity matrix, (·) Η denotes conjugate transpose, and E(·) denotes mathematical expectation.

[0108]

[0109] Among them, λ n For AR s A H The nth eigenvalue of n For AR s A H The nth eigenvector of max For AR s A H The maximum eigenvalue, v max For AR s A H The eigenvector corresponding to the maximum eigenvalue of n ,...,v N ],Λ=diag{σ 2 (λ max +σ 2 ) -1 ,1,…,1}.

[0110] Due to σ 2 (λ max +σ 2 ) -1 <1

[0111]

[0112] When h is large enough,

[0113]

[0114] Therefore, we can get

[0115] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that the signal power The estimation method is:

[0116] Using the covariance matrix of the received data Approximate signal subspace:

[0117]

[0118] When m→∞, the signal subspace can be obtained. In practical applications, when m=6, satisfactory convergence performance can be obtained. max and v max is an intermediate variable;

[0119]

[0120] Among them, ·1 represents the 1-norm operation, is the covariance matrix The nth column vector of is λ max The estimated value of Substituting into formula (11), we get v max Estimated value of

[0121] According to Estimating signal power

[0122]

[0123] in, Indicates that intermediate variables are calculated separately The square of the modulus of each element in , diag(·) means extracting the diagonal elements.

[0124] The other steps and parameters are the same as those in the first or second embodiment.

[0125] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the phase The estimation method is:

[0126]

[0127] Here, arg(·) represents the complex argument.

[0128] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0129] AR s A H The eigenvectors of s A H v n =λ n v n , we can get:

[0130]

[0131] It can be seen that AR s A H The eigenvector v corresponding to the maximum eigenvalue of R is the same as Rmax Zhang Cheng's space sapn{v max}=sapn{A}. Therefore, the principal component analysis method is used to obtain |v max | 2 Equivalent to the received signal power P, arg(v max ) is equivalent to the received phase difference ψ. Where sapn(·) represents the spanned space, |·| 2 Represents the square of the modulus.

[0132] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the specific process of step 3 is as follows:

[0133] Step 3.1: The signal power p received by the nth linear polarization antenna n Polarization pointing angle α with linear polarization antenna n The relationship is:

[0134] p n =a+bcos2α n +CSIN2α n (16)

[0135] Where a, b and c are power polarization coefficients;

[0136] Based on the estimated signal power Solve for the power polarization coefficient:

[0137]

[0138] in, is a pseudo-inverse operation, Q is a matrix composed of trigonometric functions of the polarization pointing angle of the linear polarization antenna, and are the estimated values ​​of the power polarization coefficients a, b and c, respectively, are the estimated signal powers received by the first linear polarization antenna, ..., the nth linear polarization antenna, ..., the Nth linear polarization antenna, α2 is the polarization pointing angle of the second linear polarization antenna, α3 is the polarization pointing angle of the third linear polarization antenna, α N is the polarization pointing angle of the Nth linearly polarized antenna;

[0139] Step 3.2: Estimated value of power polarization coefficient and It is expressed as:

[0140]

[0141] Among them, the superscript T represents the transpose, and -1 represents the inverse of the matrix;

[0142] Since the number of snapshots in the actual environment is limited, the covariance matrix of the noise is not a strictly diagonal matrix; there may be a small correlation between the signal and the noise. For the power estimation error caused by these two factors, LMMSE can be used to reduce the power polarization parameter estimation error caused by the power error;

[0143] Based on the LMMSE method, the estimated noise variance is used and signal power The power polarization coefficient estimate and It is expressed as:

[0144]

[0145] Where, ρ is the signal power adjustment coefficient, which is used to balance the power of each linear polarization antenna; R s =E{S(t)S H (t)}, E{·} denotes expectation, S(t) is the spatial signal vector; I3 is the unit matrix.

[0146] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0147] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the specific process of step 4 is as follows:

[0148] Step 41. Use the first linear polarized antenna in the linear polarized antenna array as the reference linear polarized antenna (here, any linear polarized antenna located at the two end points of the linear array can be used as the reference linear polarized antenna, and the reference linear polarized antenna is used as the first linear polarized antenna. According to the distance from each linear polarized antenna in the array to the first linear polarized antenna from small to large, each linear polarized antenna is numbered from the second linear polarized antenna to the Nth linear polarized antenna in sequence). According to the estimated power polarization coefficient and phase Calculate the test spatial phase difference between the nth linearly polarized antenna and the reference linearly polarized antenna (n can be any linearly polarized antenna in the array)

[0149] Step 42: Calculate the spatial phase difference φ between the nth linear polarization antenna and the reference linear polarization antenna at the i-th ambiguity angle n1 (i);

[0150] Step 43: Obtain the DOA estimation result according to the calculation results of step 41 and step 42.

[0151] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0152] Specific implementation method 7: This implementation method is different from specific implementation methods 1 to 6 in that the specific process of step 41 is as follows:

[0153] Using the estimated power polarization coefficient and Calculate the polarization domain phase difference between the nth linearly polarized antenna and the reference linearly polarized antenna

[0154]

[0155] Among them, α n is the polarization pointing angle of the nth linear polarization antenna, α1 is the polarization pointing angle of the reference linear polarization antenna;

[0156] Using the estimated phase Calculate the phase difference between the nth linearly polarized antenna and the reference linearly polarized antenna

[0157]

[0158] in, yes The phase corresponding to the nth linearly polarized antenna in is, yes The phase corresponding to the reference linear polarization antenna;

[0159] The test spatial phase difference between the nth linear polarization antenna and the reference linear polarization antenna is for:

[0160]

[0161] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0162] Specific implementation eight: This implementation differs from specific implementations one to seven in that the specific process of step four-two is as follows:

[0163] Step 421: Calculate all fuzzy numbers k based on the two linear polarization antennas corresponding to the longest baseline i and blur angle θ i :

[0164]

[0165] Among them, d N1 is the antenna spacing between the two linearly polarized antennas corresponding to the longest baseline (i.e., the antenna spacing between the Nth linearly polarized antenna and the first linearly polarized antenna), is the test spatial phase difference of the two linearly polarized antennas corresponding to the longest baseline; according to formula (23), multiple groups of fuzzy numbers and fuzzy angles satisfying formula (23) can be obtained;

[0166] Step 422: At the i-th ambiguity angle, the spatial phase difference φ between the n-th linear polarization antenna and the reference linear polarization antenna n1 (i) is:

[0167] φ n1 (i) = mod(2πd n1 sinθ i / λ,2π) (24)

[0168] Among them, d n1 represents the antenna spacing between the nth linearly polarized antenna and the reference linearly polarized antenna, mod(·) represents the modulo operation, and λ is the wavelength of the incident signal.

[0169] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0170] Specific implementation method 9: This implementation method is different from specific implementation methods 1 to 8 in that the specific process of step 43 is as follows:

[0171] Calculate the spatial phase difference φ n1 (i) and test spatial phase difference The difference:

[0172]

[0173] in, is the blur angle θ i Corresponding to the difference between the spatial phase difference and the test spatial phase difference, the set of differences corresponding to each blur angle is recorded as Δψ, and Δψ is weighted as follows:

[0174]

[0175] Among them, mean(·) represents the operation of calculating the mean of all elements in the set Δψ, for l n The reciprocal of l n is the position coordinate vector of the nth linearly polarized antenna, ξ i is the blur angle θ i The corresponding weighted Euclidean distance;

[0176] The smallest ξ i The corresponding blur angle θ i As the signal DOA estimation result

[0177] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0178] Specific implementation method 10: This implementation method is different from the specific implementation methods 1 to 9 in that the specific process of step 5 is as follows:

[0179] Step 51: Based on the estimated power polarization coefficient and And the signal DOA estimation results Calculate the power normalization coefficient

[0180]

[0181] Step 52: Use power normalization coefficient Power polarization coefficient And the signal DOA estimation results Get the polarization parameter estimates:

[0182]

[0183] in, is the polarization auxiliary angle estimate, is the estimated polarization phase difference.

[0184] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0185] Formula (28) and Formula (29) are obtained according to the following relationship between the power polarization coefficient and the incident signal polarization parameter:

[0186]

[0187] Experimental Section

[0188] In order to verify the effect of the method of the present invention, the influence of the signal-to-noise ratio and signal frequency on the DOA estimation accuracy, deambiguation probability and polarization parameter estimation of the present invention is analyzed, and the effectiveness of the present invention in a microwave darkroom is verified.

[0189] Experiment 1: Analysis of the impact of signal-to-noise ratio on DOA estimation accuracy, deambiguation probability and polarization parameter estimation.

[0190] Five linear polarization antennas are used to form a phase interferometer. The intervals of the linear polarization antennas are 0mm, 170mm, 316mm, 586mm, and 821mm, and the polarization pointing angles of the linear polarization antennas are -67.5°, -22.5°, 22.5°, 67.5°, and -67.5°. The frequency of the signal is 4GHz or 18GHz, the direction of the incoming wave is randomly located at (-0.5° to 0.5°), the polarization state is circular polarization, and the corresponding polarization parameters are (45°, 90°). The signal-to-noise ratio ranges from -10dB to 20dB, the step size is 1dB, and the number of snapshots is set to 64.

[0191] from Figure 2 It can be seen that the proposed method has the best deambiguation probability performance. Specifically, when the signal-to-noise ratio is -5dB and the frequency is 4GHz, the deambiguation probability of the proposed method is increased by about 29% and 39% compared with the Im-MPI algorithm and the LBI algorithm, respectively.

[0192] from Figure 3 It can be seen that at 4 GHz and 18 GHz, the root mean square error of DOA estimation of the method proposed in the present invention is smaller than that of the Im-MPI algorithm, and the error of polarization parameter estimation is also smaller than that of the Im-MPI algorithm. In particular, when the signal-to-noise ratio is lower than 0 dB, the root mean square error of polarization parameters of the method proposed in the present invention is significantly smaller than that of the Im-MPI algorithm, and the polarization parameter estimation performance is better.

[0193] Experiment 2: Analysis of the impact of signal frequency on the deambiguation probability and polarization parameter estimation.

[0194] Set the signal-to-noise ratio to 0dB and the signal frequency to 0.8GHz to 18GHz. The other conditions are consistent with Experiment 1. The deambiguation probability at each frequency is shown in Table 1;

[0195] Table 1 Deambiguation probability (%) of three algorithms at different frequencies (GHz) at 0 dB

[0196]

[0197] It can be seen from Table 1 that when the signal-to-noise ratio is 0 dB, in the range of 0.8 GHz to 18 GHz, the deambiguation probability of the method of the present invention is greater than that of the Im-MPI algorithm and the LBI algorithm. In particular, in the range of 4 GHz to 18 GHz, the deambiguation probability of the method of the present invention is greater than 98%.

[0198] The RMS errors of polarization parameters at each frequency are shown in Table 2;

[0199] Table 2 RMS error of polarization parameters at different frequencies (GHz) at 0 dB

[0200]

[0201] It can be seen from Table 2 that when the signal-to-noise ratio is 0 dB, in the range of 0.8 GHz to 18 GHz, the root mean square error of the polarization parameters of the method of the present invention is smaller than that of the Im-MPI algorithm, and the polarization parameter estimation performance is improved.

[0202] Experiment 3: The effectiveness of the present invention in a microwave darkroom.

[0203] Experimental conditions: A double-ridged conical horn antenna is used as the transmitting signal source to generate a horizontally polarized signal. The phase interferometer of multiple linearly polarized antennas is rotated by a turntable so that the angle between the incident signal and the receiving array varies within the range of ±30°. The signal source frequency is 6GHz and the power is set to 30dBm.

[0204] from Figure 4 It can be seen that the deambiguation probabilities of the method proposed in the present invention and Im-MPI are higher than those of LBI, and the DOA estimation results are more accurate.

[0205] Experiment 4: Deambiguation probability analysis of the present invention in a microwave darkroom.

[0206] The signal source frequency is 2GHz~6GHz, and the power is set to 30dBm. The other conditions are consistent with Experiment 2. The deambiguation probability of the three algorithms varies with the signal as shown in Table 3:

[0207] Table 3 Deambiguation probability (%) of three algorithms at different frequencies (GHz)

[0208]

[0209] It can be seen from Table 3 that with the increase of frequency, the unambiguous probabilities of the three algorithms decrease to a certain extent, but the deambiguation probability of the method of the present invention is higher than that of the Im-MPI algorithm and the LBI algorithm, and is still greater than 98% when the signal frequency is 6 GHz.

[0210] In summary, the present invention proposes a joint estimation method of DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas. The present invention estimates the noise variance and signal power according to the high-order powers of the sample covariance matrix. Then, the LMMSE method is used to reduce the estimation error of the power polarization parameter caused by the power error, thereby improving the estimation accuracy of the power polarization parameter. In addition, the present invention uses the phase difference and amplitude information of all baselines, and weights the Euclidean distance of the difference between all baseline fuzzy phase differences and actual phase differences through a multi-baseline phase weighted deambiguation method. The fuzzy angle corresponding to the minimum value of the weighted Euclidean distance is the actual angle, thereby improving the accuracy of deambiguation. Under experimental conditions, the method of the present invention achieves the improvement of the accuracy of DOA estimation and polarization parameter estimation, and the probability of successful deambiguation exceeds 98%.

[0211] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A phase interferometer DOA and polarization parameter joint estimation method based on multiple linearly polarized antennas, characterized in that: The method specifically comprises the following steps: Step 1: Calculate the covariance matrix of the received data using the data received by the phase interferometer including N linearly polarized antennas Then according to the covariance matrix of the received data Estimated noise variance Step 2: According to the covariance matrix of the received data To estimate the signal power and Phase Step 3: Using the estimated noise variance and signal power To estimate the power polarization coefficient; Step 4: Use the estimated power polarization coefficient and signal power and Phase And the signal DOA estimation result is obtained based on the multi-baseline phase weighted deambiguation method; Step 5: Calculate a power normalization coefficient using the signal DOA estimation result and the estimated power polarization coefficient, and then calculate a polarization parameter estimation value using the power normalization coefficient, the signal DOA estimation result and the power polarization coefficient estimation value; The polarization parameters include a polarization auxiliary angle and a polarization phase difference.

2. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 1, characterized in that: The specific process of step one is: Step 1: N linear polarization antennas in the phase interferometer are arranged linearly, and polarization pointing angles of the N linear polarization antennas are not completely the same; The received data of the linear polarization antenna array is recorded as X(t), and the covariance matrix of the received data is calculated based on X(t) Where K is the number of signal sampling snapshots, t = 1, 2, ..., K, X H (t) is the conjugate transpose of X(t); Step 1 and 2: Based on the covariance matrix of the received data Estimated noise variance in, yes is the trace of , and h is a constant.

3. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 2, characterized in that: The signal power The estimation method is: Using the covariance matrix of the received data Approximate signal subspace: Among them, λ max and v max is an intermediate variable; Among them, ||·||1 represents the 1-norm operation, is the covariance matrix The nth column vector of is λ max An estimated value of Will Substituting into formula (11), we get v max Estimated value of According to Estimating signal power in, Indicates that intermediate variables are calculated separately The square of the magnitude of each element in .

4. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 3, characterized in that: The phase The estimation method is: Here, arg(·) represents the complex argument.

5. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 4, characterized in that: The specific process of step three is: Step 3.1: The signal power p received by the nth linear polarization antenna n Polarization pointing angle α with linear polarization antenna n The relationship is: p n a+bcos2α n +csin2α n (16) Where a, b and c are power polarization coefficients; Based on the estimated signal power Solve for the power polarization coefficient: in, is a pseudo-inverse operation, Q is a matrix composed of trigonometric functions of the polarization pointing angle of the linear polarization antenna, and are the estimated values ​​of the power polarization coefficients a, b and c, respectively, are the estimated signal powers received by the first linear polarization antenna, ..., the nth linear polarization antenna, ..., the Nth linear polarization antenna, α2 is the polarization pointing angle of the second linear polarization antenna, α3 is the polarization pointing angle of the third linear polarization antenna, α N is the polarization pointing angle of the Nth linearly polarized antenna; Step 3.2: Estimated value of power polarization coefficient and It is expressed as: Among them, the superscript T represents the transpose, and -1 represents the inverse of the matrix; Then use the estimated noise variance and signal power The power polarization coefficient estimate and It is expressed as: Among them, ρ is the adjustment coefficient of signal power; R s =E{S(t)S H (t)}, E{·} denotes expectation, S(t) is the spatial signal vector; I3 is the unit matrix.

6. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 5, characterized in that: The specific process of step 4 is as follows: Step 4: Take the first linear polarization antenna in the linear polarization antenna array as the reference linear polarization antenna, and use the estimated power polarization coefficient and phase Calculate the test spatial phase difference between the nth linear polarization antenna and the reference linear polarization antenna Step 42: Calculate the spatial phase difference φ between the nth linear polarization antenna and the reference linear polarization antenna at the i-th ambiguity angle n1 (i); Step 43: Obtain the DOA estimation result according to the calculation results of step 41 and step 42.

7. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 6, characterized in that: The specific process of step 41 is: Using the estimated power polarization coefficient and Calculate the polarization domain phase difference between the nth linearly polarized antenna and the reference linearly polarized antenna Among them, α n is the polarization pointing angle of the nth linear polarization antenna n, and α1 is the polarization pointing angle of the reference linear polarization antenna; Using the estimated phase Calculate the phase difference between the nth linearly polarized antenna and the reference linearly polarized antenna in, yes The phase corresponding to the nth linearly polarized antenna in is, yes The phase corresponding to the reference linear polarization antenna; The test spatial phase difference between the nth linear polarization antenna and the reference linear polarization antenna is for:

8. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 7, characterized in that: The specific process of step 42 is as follows: Step 421: Calculate all fuzzy numbers k based on the two linear polarization antennas corresponding to the longest baseline i and blur angle θ i : Among them, d N1 is the antenna spacing between the two linearly polarized antennas corresponding to the longest baseline, is the test spatial phase difference of the two linearly polarized antennas corresponding to the longest baseline; Step 422: At the i-th ambiguity angle, the spatial phase difference φ between the n-th linear polarization antenna and the reference linear polarization antenna n1 (i) is: Among them, d n1 represents the antenna spacing between the nth linearly polarized antenna and the reference linearly polarized antenna, mod(·) represents the modulo operation, and λ is the wavelength of the incident signal.

9. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 8, characterized in that: The specific process of step 43 is as follows: Calculate the spatial phase difference φ n1 (i) and test spatial phase difference The difference: in, is the blur angle θ i Corresponding to the difference between the spatial phase difference and the test spatial phase difference, the set of differences corresponding to each blur angle is recorded as Δψ, and Δψ is weighted as follows: Among them, mean(·) represents the operation of calculating the mean of all elements in the set Δψ, for l n The reciprocal of l n is the position coordinate vector of the nth linearly polarized antenna, ξ i is the blur angle θ i The corresponding weighted Euclidean distance; The smallest ξ i The corresponding blur angle θ i As the signal DOA estimation result 10. The method for jointly estimating DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas according to claim 9, characterized in that: The specific process of step five is as follows: Step 51: Based on the estimated power polarization coefficient and And the signal DOA estimation results Calculate the power normalization coefficient Step 52: Use power normalization coefficient Power polarization coefficient And the signal DOA estimation results Get the polarization parameter estimates: in, is the polarization auxiliary angle estimate, is the estimated polarization phase difference.

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