Joint estimation method of doa and polarization parameters based on phase interferometer of multiple linear polarization antennas

Abstract

The application discloses a phase interferometer DOA and polarization parameter joint estimation method based on multiple linear polarization antennas, and belongs to the technical field of radar signal processing.The application solves the problems of low demodulation probability, low signal DOA and polarization parameter estimation precision of the existing method.The application adopts a high-order power method of a received data covariance matrix to estimate noise variance and signal power, and reduces the complexity.Aiming at the problem that polarization mismatch leads to limited demodulation probability, the application first adopts a long-baseline demodulation short-baseline method to reduce phase difference error, and then adopts a multi-baseline phase weighting demodulation method to utilize phase difference and amplitude information of all baselines to demodulate polarization domain phase difference and space domain phase difference, so that the demodulation probability is improved, and the LMMSE method is used to reduce power estimation error, and the signal DOA and signal polarization parameter estimation precision is improved.The method can be applied to joint estimation of phase interferometer DOA and polarization parameter.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal processing, and particularly relates to a phase interferometer DOA and polarization parameter joint estimation method based on multiple linear polarization antennas. BACKGROUND

[0002] With the expansion of the frequency coverage range of the passive radar direction finding system, it faces severe challenges to obtain the DOA and polarization parameters of the electromagnetic wave signal in the wide frequency band (0.8GHz-18GHz). Compared with the DOA estimation method of the scalar interferometer, the DOA estimation method of the phase interferometer composed of multiple linear polarization antennas can have better DOA estimation performance and de-aliasing performance for the wide frequency band signal in the case of low signal-to-noise ratio.

[0003] The scalar interferometer performs unambiguous DOA estimation through the measurement value of the spatial phase difference. The LBI (Long-Baseline Interferometer) algorithm uses the principle of short baseline to solve the long baseline ambiguity to propose a fast and robust DOA estimation method, but the method of solving the long baseline through the short baseline will increase the phase difference error, which leads to the reduction of the DOA estimation accuracy. At the same time, this method does not make use of the polarization information of the electromagnetic wave signal, and the polarization parameter cannot be obtained.

[0004] Compared with the scalar interferometer, the phase difference between the antennas of the phase interferometer not only contains the spatial phase difference, but also contains the polarization domain phase difference, so the polarization parameter of the electromagnetic wave signal can be estimated. The Im-MPI (Improved Multi-baseline Polarized Interferometer method) algorithm realizes the polarization parameter estimation of the electromagnetic wave signal by decoupling the polarization domain phase difference and the spatial phase difference. However, since the phase difference and amplitude information of all baselines are not fully utilized in the de-aliasing process, the decoupling of the polarization domain phase difference and the spatial phase difference is affected by the polarization mismatch, which will limit the de-aliasing probability. And in the process of signal polarization parameter estimation, due to the limited number of shots and the possible small correlation between the signal and the noise, the power estimation error exists, so that the signal DOA and polarization parameter estimation accuracy is limited.

[0005] Therefore, in the DOA and polarization parameter estimation of the wide frequency band signal, it is necessary to study how to fully utilize the phase difference and amplitude information of all baselines to decouple the polarization domain phase difference and the spatial phase difference to improve the de-aliasing probability, and how to reduce the power estimation error to solve the problem of low signal DOA and polarization parameter estimation accuracy. SUMMARY

[0006] The application aims to solve the problems of low deblurring probability, low signal DOA and polarization parameter estimation accuracy of the existing method, and proposes a phase interferometer DOA and polarization parameter joint estimation method based on multiple linear polarization antennas.

[0007] The technical scheme adopted by the application to solve the above technical problems is: a phase interferometer DOA and polarization parameter joint estimation method based on multiple linear polarization antennas, which specifically comprises the following steps:

[0008] Step one, using the data received by the phase interferometer including N linear polarization antennas to calculate the covariance matrix of the received data Then, according to the covariance matrix of the received data Estimate the noise variance

[0009] Step two, according to the covariance matrix of the received data Estimate the signal power And the phase

[0010] Step three, using the estimated noise variance And the signal power Estimate the power polarization coefficient

[0011] Step four, using the estimated power polarization coefficient, signal power And the phase And based on the multi-baseline phase weighting deblurring method, the signal DOA estimation result is obtained

[0012] Step five, using the signal DOA estimation result and the estimated power polarization coefficient to calculate the power normalization coefficient, and using the power normalization coefficient, the signal DOA estimation result and the power polarization coefficient estimation value to calculate the polarization parameter estimation value

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

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

[0015] Step one, the N linear polarization antennas in the phase interferometer are linearly arranged, and the 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 denoted as X(t), and the covariance matrix of the received data is calculated according to X(t)

[0017]

[0018] Wherein, K is the number of signal sampling snaps, 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 The trace of , 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] Based on Estimated 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 three one, the signal power p received by the nth linearly polarized antenna n and the polarization pointing angle α of the linearly polarized antenna n is:

[0036] p n = a + b cos 2α n + c sin 2α n (16)

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

[0038] According to the estimated signal power the power polarization coefficients are solved:

[0039]

[0040] wherein is a pseudo-inverse operation, Q is a matrix composed of trigonometric functions of the polarization pointing angle of the linearly polarized 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 linearly polarized antenna, …, the nth linearly polarized antenna, …, the Nth linearly polarized antenna respectively, α2 is the polarization pointing angle of the second linearly polarized antenna, α3 is the polarization pointing angle of the third linearly polarized antenna, and α N is the polarization pointing angle of the Nth linearly polarized antenna;

[0041] Step three two, the power polarization coefficient estimated values and are expressed as:

[0042]

[0043] wherein the upper index T represents transposition, and -1 represents the inverse of a matrix;

[0044] Then, the power polarization coefficient estimated values and are expressed as:

[0045]

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

[0047] Further, the specific process of the step four is:​​

[0048] Step four one, taking the first linearly polarized antenna in the linearly polarized antenna array as a reference linearly polarized antenna, calculating the test spatial phase difference between the n-th linearly polarized antenna and the reference linearly polarized antenna according to the estimated power polarization coefficient and phase

[0049] Step four two, calculating the spatial phase difference between the n-th linearly polarized antenna and the reference linearly polarized antenna at the i-th ambiguous angle n1 (i);

[0050] Step four three, obtaining the DOA estimation result according to the calculation results of step four one and step four two.

[0051] Further, the specific process of step four one is:

[0052] using the estimated power polarization coefficient and calculating the polarization domain phase difference between the n-th linearly polarized antenna and the reference linearly polarized antenna

[0053]

[0054] wherein, α n is the polarization pointing angle of the n-th linearly polarized antenna n, and α1 is the polarization pointing angle of the reference linearly polarized antenna; using the estimated phase calculating the phase difference between the n-th linearly polarized antenna and the reference linearly polarized antenna

[0055]

[0056] wherein, is the phase corresponding to the n-th linearly polarized antenna in , and is the phase corresponding to the reference linearly polarized antenna in ;

[0057] then the test spatial phase difference between the n-th linearly polarized antenna and the reference linearly polarized antenna is:

[0058]

[0059] Further, the specific process of step four two is:

[0060] Step four two one, calculating all ambiguous numbers k i and ambiguous angles θ i according to the two linearly polarized antennas corresponding to the longest baseline:

[0061] ​

[0062] where d N1 is the antenna separation of the two linear polarized antennas corresponding to the longest baseline, is the test spatial phase difference between the two linear polarized antennas corresponding to the longest baseline;

[0063] Step four two, calculating the spatial phase difference φ n1 (i) between the n-th linear polarized antenna and the reference linear polarized antenna under the i-th ambiguous angle:

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

[0065] where d n1 is the antenna separation between the n-th linear polarized antenna and the reference linear polarized antenna, mod(·) is the modulo operation, and λ is the wavelength of the incident signal.

[0066] Further, the specific process of step four three is as follows:

[0067] calculating the difference between the spatial phase difference φ n1 (i) and the test spatial phase difference :

[0068]

[0069] where Δψ is the difference between the spatial phase difference and the test spatial phase difference corresponding to the ambiguous angle θ i , and the set composed of the difference values corresponding to each ambiguous angle is denoted as Δψ, and the weighted sum of Δψ is:

[0070]

[0071] where mean(·) is an operation for calculating the mean value of all elements in the set Δψ, is the reciprocal of l n , and l n is the position coordinate vector of the n-th linear polarized antenna, and ξ i is the weighted Euclidean distance corresponding to the ambiguous angle θ i ;

[0072] the ambiguous angle θ i corresponding to the smallest ξ i is taken as the signal DOA estimation result

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

[0074] Step five one, according to the estimated power polarization coefficient and and the signal DOA estimation result Calculate the power normalization coefficient

[0075]

[0076] Step five two, using the power normalization coefficient Power polarization coefficient and the signal DOA estimation result Get the polarization parameter estimation value:

[0077]

[0078] Wherein, is the polarization auxiliary angle estimation value, is the polarization phase difference estimation value.

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

[0080] The present application adopts the method of high order power of received data covariance matrix to estimate noise variance and signal power, which reduces the complexity. In view of the problem that polarization mismatch leads to limited ambiguity resolution probability, the present application first adopts the method of long baseline resolving short baseline to reduce the phase difference error, and then uses the multi baseline phase weighted ambiguity resolution method to decouple the polarization domain phase difference and the spatial domain phase difference by using the phase difference and amplitude information of all baselines, so as to improve the ambiguity resolution probability, and through 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 Im-MPI algorithm and LBI algorithm, the ambiguity resolution probability of the method of the present application is improved by about 29% and 39% respectively; the root mean square error of the polarization parameter of the method of the present application is less than that of Im-MPI algorithm; compared with Im-MPI algorithm and LBI algorithm, the DOA estimation accuracy of the method of the present application is also improved. BRIEF DESCRIPTION OF DRAWINGS

[0082] Figure 1 is a flow chart of a phase interferometer DOA and polarization parameter joint estimation method based on multiple linear polarization antennas of the present application;

[0083] Figure 2 is a curve graph of the change of ambiguity resolution probability with signal to noise ratio;

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

[0085] Figure 4 DOA estimation result chart for microwave darkroom. DETAILED DESCRIPTION

[0086] Embodiment I: combination Figure 1 This embodiment describes a method for joint estimation of DOA and polarization parameters based on a phase interferometer with multiple linearly polarized antennas. The method specifically includes the following steps:

[0087] Step one: use the data received by the phase interferometer with N linearly polarized antennas to calculate the covariance matrix of the received data Then, according to the covariance matrix of the received data estimate the noise variance

[0088] Step two: estimate the signal power and phase based on the covariance matrix of the received data

[0089] Step three: use the estimated noise variance and signal power to estimate the power polarization coefficient

[0090] Step four: use the estimated power polarization coefficient, signal power and phase and the multi-baseline phase weighting deambiguity method to obtain the signal DOA estimation result

[0091] Step five: use the signal DOA estimation result and the estimated power polarization coefficient to calculate the power normalization coefficient, and then use the power normalization coefficient, signal DOA estimation result and power polarization coefficient estimate to calculate the polarization parameter estimate

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

[0093] Embodiment II: The difference between this embodiment and embodiment I is that the specific process of step one is as follows:

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

[0095] Let the received data of the linearly polarized antenna array be X(t), and calculate the covariance matrix of the received data according to X(t)

[0096]

[0097] where K is the number of signal samples, t = 1, 2, …, K, X H (t) is the conjugate transpose of X(t) ;

[0098] Step two, estimate the noise variance according to the covariance matrix of the received data

[0099]

[0100] where, is the trace of , h is a constant. When the value of h is infinite, it meets the theoretical case. In practice, when the value of h is greater than or equal to 6, the noise variance estimation condition can be met.

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

[0102] Consider that the noise is a complex additive Gaussian white noise with a mean of zero and a variance of σ 2 , and the noise and the signal are statistically independent. Considering a signal case, the received data of the linearly polarized antenna array is as follows:

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

[0104]

[0105] where X(t) is the N x K-dimensional received data of the linearly polarized antenna, A is the steering vector of the incident signal, S(t) is the spatial signal vector, N(t) is the noise data vector of the phase interferometer of the multiple linearly polarized antennas. K is the number of signal samples, t ∈ [1, K]. α n is the polarization pointing angle of the nth linearly polarized antenna, n ∈ [1, N]. θ is the incident azimuth angle of the incident signal, γ is the polarization auxiliary angle, η is the polarization phase difference, j is the imaginary unit, u n is the spatial phase shift factor of the 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] where R s = E{S(t)S H (t)}, I N is the N x N identity matrix, (·) Η denotes conjugate transpose, and E(·) denotes mathematical expectation.

[0108]

[0109] where λ n is the n-th eigenvalue of AR s A H , v n is the n-th eigenvector of AR s A H , λ max is the largest eigenvalue of AR s A H , v max is the eigenvector corresponding to the largest eigenvalue of AR s A H , V = [v1,..., v n ,..., v N ], and Λ = diag{σ 2 (λ max + σ 2 ) -1 ,1,...,1}.

[0110] Since σ 2 (λ max + σ 2 ) -1 < 1

[0111]

[0112] When h is large enough,

[0113]

[0114] Therefore, we have

[0115] Specific Implementation Three: This implementation is different from the first or second implementation in that the estimation method of the signal power is as follows:

[0116] The covariance matrix of the received data is used to approximate the signal subspace:

[0117]

[0118] ​When m→∞, the signal subspace can be obtained. In practical applications, when m=6, satisfactory convergence performance can be obtained. Wherein, λ max and v max are intermediate variables;

[0119]

[0120] Wherein, ·1 represents the 1-norm operation, is the nth column vector of the covariance matrix , and is the estimated value of λ max ; by substituting into equation (11), the estimated value of v max is obtained

[0121] Then, according to , the signal power

[0122]

[0123] Wherein, represents the square of the modulus of each element in the intermediate variable , and diag(·) represents extracting the diagonal elements.

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

[0125] Embodiment four: the difference between this embodiment and one of embodiments one to three is that the estimation method of the phase is as follows:

[0126]

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

[0128] The other steps and parameters are the same as those in one of embodiments one to three.

[0129] The eigenvector of AR s A H satisfies AR s A H v n = λ n v n , and the following can be obtained:

[0130]

[0131] It can be seen that the eigenvector of AR s A H is the same as that of R, and the eigenvector vmax The spatial span sapn{v max} = sapn{A}. Thus, |v max | 2 is equivalent to the received signal power P, and arg(v max ) is equivalent to the received phase difference ψ. Wherein, sapn(·) represents the span space, |·| 2 represents the square of the module.

[0132] Specific implementation five: this embodiment is different from one of the first to fourth specific implementations, and a specific process of the step three is:

[0133] Step three one, the relationship between the signal power p n received by the nth linearly polarized antenna and the polarization pointing angle α n of the linearly polarized antenna is:

[0134] p n = a + b cos 2α n + c sin 2α n (16)

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

[0136] According to the estimated signal power , the power polarization coefficients are solved:

[0137]

[0138] Wherein, is a pseudo-inverse operation, Q is a matrix composed of trigonometric functions of the polarization pointing angle of the linearly polarized 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 linearly polarized antenna, …, the nth linearly polarized antenna, …, the Nth linearly polarized antenna respectively, α2 is the polarization pointing angle of the second linearly polarized antenna, α3 is the polarization pointing angle of the third linearly polarized antenna, and α N is the polarization pointing angle of the Nth linearly polarized antenna;

[0139] Step three two, the power polarization coefficient estimated values and are expressed as:

[0140]

[0141] Wherein, the upper index T represents transposition, 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 strict diagonal matrix; there can be a small correlation between the signal and the noise, and for the power estimation error caused by these two factors, the LMMSE can be used to reduce the power error caused by the power polarization parameter estimation error;

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

[0144]

[0145] Wherein, ρ is the adjustment coefficient of the signal power, used to balance the power of each linearly polarized antenna; R s = E{S(t)S H (t)}, E{·} represents the expectation, and S(t) is the spatial signal vector; I3 is the unit matrix.

[0146] The other steps and parameters are the same as one of the first to fourth embodiments.

[0147] The sixth embodiment is different from one of the first to fifth embodiments in that the specific process of the fourth step is:

[0148] Step four one, taking the first linearly polarized antenna in the linearly polarized antenna array as the reference linearly polarized antenna (here, any one of the linearly polarized antennas at the two ends of the linear array can be taken as the reference linearly polarized antenna, and the reference linearly polarized antenna is taken as the first linearly polarized antenna, and each linearly polarized antenna is numbered as the second linearly polarized antenna to the Nth linearly polarized antenna in the order of the distance from the first linearly polarized antenna), 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 four two, calculate the spatial phase difference φ n1 (i) between the nth linearly polarized antenna and the reference linearly polarized antenna at the ith ambiguous angle.

[0150] Step four three, obtain the DOA estimation result according to the calculation results of step four one and step four two.

[0151] The other steps and parameters are the same as one of the first to fifth embodiments.

[0152] Specific implementation seven: the difference between this implementation and one of the specific implementations one to six is that the specific process of step four one is:

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

[0154]

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

[0156] Using the estimated phase Calculate the phase difference between the nth linear polarization antenna and the reference linear polarization antenna

[0157]

[0158] Wherein, is the phase corresponding to the nth linear polarization antenna in , and is the phase corresponding to the reference linear polarization antenna in ;

[0159] Then the test space phase difference between the nth linear polarization antenna and the reference linear polarization antenna is:

[0160]

[0161] The other steps and parameters are the same as one of the specific implementations one to six.

[0162] Specific implementation eight: the difference between this implementation and one of the specific implementations one to seven is that the specific process of step four two is:

[0163] Step four two one, calculate all ambiguity numbers k i And ambiguity angle θ i According to the two linear polarization antennas corresponding to the longest baseline:

[0164]

[0165] Wherein, d N1 is the antenna spacing of the two linear polarization antennas corresponding to the longest baseline (i.e. the antenna spacing of the nth linear polarization antenna and the first linear polarization antenna), the spatial phase difference between the two linear polarization antennas corresponding to the longest baseline; according to formula (23), a plurality of sets of ambiguous numbers and ambiguous angles satisfying formula (23) can be obtained;

[0166] Step four two, the spatial phase difference φ n1 (i) between the nth linear polarization antenna and the reference linear polarization antenna at the ith ambiguous angle

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

[0168] wherein d n1 represents the antenna interval between the nth linear polarization antenna and the reference linear polarization 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 one of the first to seventh embodiments.

[0170] The ninth embodiment is different from one of the first to eighth embodiments in that the specific process of the step four three is as follows:

[0171] calculating the difference between the spatial phase difference φ n1 (i) and the test spatial phase difference

[0172]

[0173] wherein is the ambiguous angle θ i corresponding to the spatial phase difference and the test spatial phase difference, a set composed of the difference values corresponding to each ambiguous angle is denoted as Δψ, and the weighted sum of Δψ is:

[0174]

[0175] wherein mean(·) represents an operation of calculating the mean value of all elements in the set Δψ, is the reciprocal of l n , l n is the position coordinate vector of the nth linear polarization antenna, and ξ i is the weighted Euclidean distance corresponding to the ambiguous angle θ i .

[0176] the ambiguous angle θ i corresponding to the smallest ξ i is taken as the signal DOA estimation result

[0177] ​The other steps and parameters are the same as one of embodiments 1-8.

[0178] Embodiment 10 is different from one of embodiments 1-9 in that the specific process of step five is as follows:

[0179] Step five one, according to the estimated power polarization coefficient and and the signal DOA estimation result calculate the power normalization coefficient

[0180]

[0181] Step five two, using the power normalization coefficient power polarization coefficient and the signal DOA estimation result get the polarization parameter estimation value:

[0182]

[0183] wherein, is the polarization auxiliary angle estimation value, is the polarization phase difference estimation value.

[0184] The other steps and parameters are the same as one of embodiments 1-9.

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

[0186]

[0187] Experimental part

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

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

[0190] The phase interferometer is composed of five linearly polarized antennas. The interval of the linearly polarized antennas is 0mm, 170mm, 316mm, 586mm and 821mm, and the polarization pointing angle of the linearly polarized antennas is -67.5°, -22.5°, 22.5°, 67.5° and -67.5°. The frequency of the signal is 4GHz or 18GHz, the incoming wave direction is randomly located in (-0.5°-0.5°), and the polarization state is circular polarization, and the corresponding polarization parameter is (45°, 90°). The signal-to-noise ratio changes in the range of -10dB-20dB with a step of 1dB, and the number of snaps is set to 64.

[0191] From Figure 2 It can be seen that the method proposed in the application has the best probability of ambiguity resolution. Specifically, when the signal-to-noise ratio is -5dB and the frequency is 4GHz, the probability of ambiguity resolution of the method proposed in the application 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 in the cases of 4GHz and 18GHz, the root mean square error of DOA estimation of the method proposed in the application is smaller than that of the Im-MPI algorithm, and the polarization parameter estimation error is also smaller than that of the Im-MPI algorithm. Especially when the signal-to-noise ratio is lower than 0dB, the root mean square error of the polarization parameter of the method proposed in the application is significantly smaller than that of the Im-MPI algorithm, and the polarization parameter estimation performance is better.

[0193] Experiment two: analysis of the influence of signal frequency on the probability of ambiguity resolution and polarization parameter estimation.

[0194] The signal-to-noise ratio is set to 0dB, and the signal frequency is 0.8GHz-18GHz. The remaining conditions remain the same as in experiment one. The probability of ambiguity resolution under each frequency is shown in Table 1.

[0195] Table 1: Probability of ambiguity resolution (%) of three algorithms under different frequencies (GHz) at 0dB

[0196]

[0197] From Table 1, it can be seen that when the signal-to-noise ratio is 0dB, in the range of 0.8GHz-18GHz, the probability of ambiguity resolution of the method proposed in the application is greater than that of the Im-MPI algorithm and the LBI algorithm. Especially in the range of 4GHz-18GHz, the probability of ambiguity resolution of the method proposed in the application is greater than 98%.

[0198] The root mean square error of the polarization parameter under each frequency is shown in Table 2.

[0199] Table 2: Root mean square error of polarization parameter under different frequencies (GHz) at 0dB

[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 was used as the transmitting signal source, generating a horizontally polarized signal. A phase interferometer with multiple linearly polarized antennas was rotated on a turntable, allowing the angle between the incident signal and the receiving array to vary within a ±30° range. The signal source frequency was 6 GHz, and the power was set to 30 dBm.

[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: Defuzzification probability analysis of the present invention in a microwave darkroom.

[0206] The signal source frequency ranged from 2 GHz to 6 GHz, and the power was set to 30 dBm. All other conditions remained the same as in Experiment 2. The deambiguation probabilities of the three algorithms as they varied with the signal are shown in Table 3:

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

[0208]

[0209] As can be seen from Table 3, as the frequency increases, the unambiguous probabilities of the three algorithms decrease to a certain extent. However, the deambiguous 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 for DOA and polarization parameters of a phase interferometer based on multiple linearly polarized antennas. The present invention estimates the noise variance and signal power based on 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 utilizes 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 an improvement in the accuracy of DOA estimation and polarization parameter estimation, and the probability of successful deambiguation exceeds 98%.

[0211] The above examples of the present application are only to illustrate the calculation model and calculation process of the present application, and are not intended to limit the embodiments of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art, and it is impossible to enumerate all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present application are still within the protection scope of the present application.

Claims

1. A joint estimation method of DOA and polarization parameters based on a phase interferometer of 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 Sum signal power To estimate the power polarization coefficient; Step 4: Use the estimated power polarization coefficient and signal power and phase 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 estimate using the power normalization coefficient, the signal DOA estimation result, and the estimated power polarization coefficient. 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 linearly polarized antennas in the phase interferometer are arranged linearly, and the polarization pointing angles of the N linearly polarized antennas are not exactly the same; The received data of the linearly polarized 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 The trace of , 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, wherein: 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 estimated value of; Will Substituting into formula (11), we get v max Estimated value of Based on Estimated 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 linearly polarized antenna n Polarization pointing angle α of linearly polarized antenna n The relationship is: p n a+bcos2α n +csin2α n (16) Where a, b, and c are power polarization coefficients; According to 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 Expressed as: Among them, the superscript T represents the transpose, and -1 represents the inverse of the matrix; Then use the estimated noise variance Sum signal power The power polarization coefficient estimate and Expressed as: Among them, ρ is the adjustment coefficient of signal power; R s =E{S(t)S H (t)}, E{·} represents expectation, S(t) is the spatial signal vector; I3 is the identity 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 linearly polarized antenna in the linearly polarized antenna array as the reference linearly polarized antenna, and use 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 Step 4.2: Calculate the spatial phase difference φ between the nth linearly polarized antenna and the reference linearly polarized antenna at the i-th ambiguity angle n1 (i); Step 43: Obtain the DOA estimation result based on 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 linearly polarized antenna n, and α1 is the polarization pointing angle of the reference linearly polarized 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 linearly polarized antenna and the reference linearly polarized 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 linearly polarized 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 between 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 linearly polarized antenna and the reference linearly polarized 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 The difference between the corresponding spatial phase difference and the test spatial phase difference is recorded as Δψ, and the weighted Δψ is: Here, mean(·) represents the operation of calculating the mean of all elements in the set Δψ. 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: Step 5.1: 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-aided angle estimate, is the estimated polarization phase difference.

Images