Covariance accumulation-based direction of arrival estimation method for s-mode signal at low signal-to-noise ratio

Abstract

A covariance accumulation-based direction of arrival estimation method for an S-mode signal at a low signal-to-noise ratio, relating to the technical field of information processing. According to the method, a delayed covariance matrix of array output data is comprehensively utilized, a weight is determined by means of a correlation feature of the S-mode signal, and the delayed covariance matrix of array output data is accumulated, so that the direction of arrival estimation precision of a MUSIC method for the S-mode signal in a low signal-to-noise ratio environment is improved, establishing more accurate angle tracking for an S-mode target in the low signal-to-noise ratio environment, effectively reducing the false alarm probability, and expanding the effective working ranges of angle measurement and a tracking system.

Description

A Covariance Accumulation Direction of Arrival Estimation Method for Low SNR Mode S Signals Technical Field

[0001] The present invention belongs to the technical field of information processing, and in particular relates to a covariance accumulation direction of arrival estimation method for a low signal-to-noise ratio S-mode signal. Background Art

[0002] Mode S signals are used in scenarios such as air traffic monitoring, conflict detection, and collision avoidance through interrogation and reply or broadcast modes. Mode S uplink interrogation signals are radiated at 1030 MHz, and Mode S downlink reply or broadcast signals are radiated at 1090 MHz. There are many scenarios where Direction of Arrival (DOA) estimation is required for Mode S downlink reply or broadcast signals, such as:

[0003] 1) In an air traffic surveillance scenario, the ground radar of the air traffic control radar beacon system transmits a Mode S interrogation signal. After receiving the Mode S interrogation, the aircraft transmits a Mode S reply signal through the Mode S transponder. While receiving the signal, the radar measures the range and direction of the signal to achieve aircraft identification, as well as azimuth and distance monitoring.

[0004] 2) In the Traffic Collision Avoidance System (TCAS) operating scenario, the TCAS antenna is also required to transmit a Mode S interrogation signal to the surrounding airspace. Nearby aircraft transmit a Mode S reply signal after receiving the interrogation. The local TCAS system needs to estimate the direction of arrival of the Mode S reply signal to determine the aircraft's position and establish angle tracking to input into the collision avoidance logic.

[0005] 3) Mode S's DF17, DF18, and DF19 downlink signal formats are used for Automatic Dependent Surveillance-Broadcast (ADS-B). Aircraft automatically broadcast situational information, including position and velocity, in this format. Airborne and ground-based participants can receive and decode the signals to determine aircraft status, enabling airspace surveillance. However, ADS-B broadcasts in clear text, making it susceptible to false targets through forgery or delayed forwarding. This deceptive interference can affect participants' situational awareness and threaten airspace security. By estimating the direction of arrival of the ADS-B signal and establishing angle tracking, and verifying its consistency with the position information decoded from the ADS-B message, deceptive interference can be effectively detected.

[0006] Direction of arrival (DOA) estimation requires antenna arrays. Methods for DOA estimation include phase comparison, equal-signal amplitude comparison, equal-signal sum-difference, and spatial spectrum estimation. Spatial spectrum estimation methods are further categorized as traditional beamforming-based, Capon-based, and subspace-based. With the exception of subspace-based methods, traditional methods generally fail to exceed the Rayleigh limit. Subspace-based methods, which typically utilize the eigenvalue decomposition of the covariance matrix of the array output data, exhibit super-resolution properties, surpassing the Rayleigh limit and enabling resolution of multiple targets within a beam. These methods significantly improve DOA estimation accuracy compared to traditional methods and have been widely adopted.

[0007] The Multiple Signal Classification (MUSIC) method is a subspace-based super-resolution direction-of-arrival (DOA) estimation method with high angular accuracy and practical engineering value. Its concept is to perform eigendecomposition using the covariance matrix of the array output data to separate the signal and noise subspaces. The orthogonality of the signal direction vector and the noise subspace is then used to construct a spatial scanning spectrum. This is then used to perform a global spectral peak search, thereby achieving signal parameter estimation.

[0008] The use of the MUSIC method to estimate the direction of arrival of S-mode signals has the following disadvantages:

[0009] The first major drawback is that the MUSIC method has poor accuracy in DOA estimation at low signal-to-noise ratios. When the signal-to-noise ratio drops to a certain level, the estimation accuracy of the MUSIC method drops sharply until it becomes completely ineffective.

[0010] The second major disadvantage is that the traditional subspace method only uses the covariance matrix of the array element received data at zero delay, which essentially only reflects the correlation of the array output data at zero delay, without considering the actual signal characteristics. In fact, compared with noise, the autocorrelation of the S-mode signal is not only reflected at zero delay.

[0011] The third major disadvantage is that even if the signal-to-noise ratio is improved through accumulation, the S-mode signal has its own special form and does not take into account the relevant characteristics of the signal. Accumulation may cause the signal energy to diverge, accumulating the original signal energy into noise, which has a counterproductive effect.

[0012] Summary of the Invention

[0013] In view of this, the present invention provides a covariance accumulation direction-of-arrival (DOA) estimation method for low-SNR S-mode signals. The method comprehensively utilizes the covariance matrix of delayed array output data, determines weights based on the correlation characteristics of the S-mode signals, and accumulates the covariance matrix of the delayed array output data. This improves the DOA estimation accuracy of the MUSIC method for S-mode signals in low-SNR environments, thereby establishing more accurate angle tracking of S-mode targets in low-SNR environments, effectively reducing the false alarm probability, and expanding the effective operating range of the angle measurement and tracking system.

[0014] In order to achieve the above technical objectives, the specific technical solutions adopted by the present invention are:

[0015] A method for estimating the direction of arrival of a low signal-to-noise ratio S-mode signal using covariance accumulation is provided. The method comprises the following steps performed in sequence:

[0016] S1 obtains the S-mode discrete signal after multi-channel sampling from the receiver with array antenna as the S1 stage of array output data;

[0017] S2 multiplies the array output data of the S1 stage with the conjugate transpose of its own time delay to obtain the maximum likelihood estimate of the covariance matrix of the delayed array output data, which is recorded as the S2 stage;

[0018] S3 is the S3 stage where the weights are obtained based on the expectation of the correlation function of the S-mode signal and the sampling interval;

[0019] S4 multiplies the weight obtained in step S3 by the maximum likelihood estimate of the delayed data covariance matrix obtained in step S2, and then accumulates the weighted accumulated data covariance matrix to obtain the S4 stage;

[0020] S5: performing eigenvalue decomposition on the weighted accumulated data covariance matrix obtained in step S4 to obtain the noise subspace eigenvector S5;

[0021] S6 uses the noise subspace eigenvector obtained in step S5 and the constructed direction vector to calculate the spatial spectrum function, perform spectrum peak search, and then obtain the S6 stage of the wave arrival direction.

[0022] Furthermore, the S1 is specifically:

[0023] After down-conversion and sampling, a receiver with an array antenna with M elements obtains M-channel discrete signals. After detecting the header of the S-mode downlink signal, for each channel, starting from the sampling point at the rising edge of the first pulse of the header, the following L-1 consecutive samples are taken, and finally M discrete signal sequences of length L are obtained, forming an M×L order matrix X(l) as the array output data.

[0024] Furthermore, the S2 is specifically as follows: delaying the array output data matrix X(l) obtained in S1 by τ sampling points to obtain X(l-τ), and then performing conjugate transposition on X(l-τ) to obtain X H (l-τ), and finally X(l) and X H Multiply (l-τ) and divide by L to get the covariance matrix R of the array output data at delay τ X Maximum likelihood estimate of (τ) τ is changed from -L+1 to L-1, and finally the maximum likelihood estimate of the covariance matrix of 2L-1 delayed array output data is obtained.

[0025] Furthermore, in S3, the method of obtaining the weights according to the expectation of the correlation function of the S-mode signal and the sampling interval is to examine the autocorrelation and cross-correlation of the two S-mode signals and calculate the expectation of the correlation function. s When the absolute value of the product of is less than or equal to one-third of the symbol width (the symbol width is 1 μs), the autocorrelation value of the S-mode signal is greater than the cross-correlation value, and the covariance matrix of the array output data corresponding to these time delays τ is calculated. The weight value is 1, and the covariance matrix of the delayed array output data corresponding to the remaining delay τ is Assign a weight of 0 and set The weight is 0.

[0026] Furthermore, in S4, the weights obtained in S3 are multiplied by the maximum likelihood estimate of the delayed data covariance matrix obtained in S2, and then accumulated to obtain the weighted accumulated data covariance matrix by multiplying all the τ values ​​obtained in S2 by the maximum likelihood estimate of the delayed data covariance matrix. Multiply the weight w at each τ obtained in S3 respectively τ Then multiply by the complex multiplier Then add up and get the weighted accumulated data covariance matrix

[0027] Furthermore, in S5, the weighted accumulated data covariance matrix obtained in S4 is subjected to eigenvalue decomposition to obtain the noise subspace eigenvector. Perform eigenvalue decomposition to obtain M eigenvalues ​​and corresponding eigenvectors. Arrange the M eigenvalues ​​from large to small, sort the eigenvectors corresponding to each eigenvalue in the same order as the eigenvalues, extract the eigenvectors corresponding to the last MK smaller eigenvalues, and obtain the noise subspace eigenvector U N .

[0028] Furthermore, in S6, the method of calculating the spatial spectrum function using the noise subspace eigenvector obtained in S5 and the constructed direction vector to search for the spectrum peak and then obtain the direction of arrival is to set the search start and end points and the search step size of the direction of arrival, search a total of S times, select the reference point of the array antenna, and search the angle θ current When θ current The phase difference between the incoming wave incident on each element of the array and the reference point forms a steering vector a(θ current ), use U in S5 N and a(θ current ) calculate the value of the spectral function After the search is completed, plot P(θ current ) spectrum, find the θ corresponding to the first K (K is the number of signal sources) highest spectrum peaks current , which is the estimated direction of arrival.

[0029] By adopting the above technical solution, the present invention can bring the following beneficial effects:

[0030] The present invention further sharpens the beam of the spectrum peak in the MUSIC spectrum function, improves the angular resolution, and has higher wave direction of arrival estimation accuracy. It can establish more accurate angle tracking of S-mode targets in a low signal-to-noise ratio environment, effectively reduce the probability of false alarms, expand the effective working range of the angle measurement and tracking system, and reduce the system deployment density and cost when multi-point deployment is required.

[0031] The effectiveness of the covariance accumulation direction-of-arrival estimation method for low-SNR S-mode signals provided by this invention is demonstrated through simulation data. In the experiment, the S-mode signal carrier frequency was 1090 MHz, mixed at 1030 MHz, and then down-converted to an intermediate frequency of 60 MHz. Intermediate frequency bandpass sampling was performed at different sampling rates, with 64 baseband symbols. The simulation used a uniform linear array with an element spacing of half a wavelength, and the experiment was repeated 100 times under each condition.

[0032] Scenario 1) Single Mode S signal incident, SNR -20dB:

[0033] At a 33MHz sampling rate, this method reduces the root mean square error (RMSE) of the direction of arrival estimation from 30 degrees to 2 degrees (with 5 array elements), an improvement of 93%, and from 10 degrees to 0.5 degrees (with 10 array elements), an improvement of 95%.

[0034] At a sampling rate of 44MHz, the RMSE of the DOA estimation of this method is reduced from 20 degrees to 1.5 degrees (with 5 array elements), an improvement of 92.5%; and from 4 degrees to 0.4 degrees (with 10 array elements), an improvement of 90%.

[0035] Scenario 2) Two Mode S signals are incident, with a signal-to-noise ratio of -16dB:

[0036] At a sampling rate of 33MHz, the RMSE of the DOA estimation of this method is reduced from 16 degrees to 10 degrees (with 5 array elements), an improvement of 37.5%; and from 6.5 degrees to 0.6 degrees (with 10 array elements), an improvement of 90.7%.

[0037] At a sampling rate of 44MHz, the RMSE of the DOA estimation of this method is reduced from 16.5 degrees to 7 degrees (with 5 array elements), an improvement of 57.5%; and from 5 degrees to 0.56 degrees (with 10 array elements), an improvement of 89%.

[0038] The present invention can be applied to:

[0039] 1) The TCAS system's direction finding significantly improves the angle estimation accuracy in low signal-to-noise ratio environments, enables more precise angle tracking of target aircraft, and effectively reduces the TCAS system's false alarm probability.

[0040] 2) ADS-B anti-spoofing jamming. Since this method has excellent estimation performance and high confidence in low signal-to-noise ratio environments, it can expand the operating range of ADS-B anti-spoofing jamming ground stations, reduce the density of ground station deployment, and reduce costs while ensuring airspace safety.

[0041] 3) Other scenarios where the direction of arrival of Mode S signals needs to be estimated. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0043] FIG1 is a flow chart of a method for estimating the direction of arrival of a low signal-to-noise ratio (S-mode) signal using correlation accumulation provided by the present invention;

[0044] Figure 2 shows the waveform structure of the baseband signal of the Mode S message;

[0045] FIG3 is a block diagram of a correlation accumulation direction-of-arrival estimator for low signal-to-noise ratio (S-mode) signals;

[0046] Figure 4 shows the autocorrelation and cross-correlation of two different S-mode signals at different time delays;

[0047] Figure 5 shows the expected autocorrelation and cross-correlation of two different Mode S signals at different time delays;

[0048] Figure 6 shows the root mean square error (RMS) of the DOA estimation results for a single S-mode signal with an incident angle of 30 degrees at a 33 MHz A / D sampling rate using weighted correlation accumulation, full correlation accumulation, and the classic MUSIC method at different numbers of array elements and different signal-to-noise ratios.

[0049] FIG7 shows the root mean square error (RMS) of the DOA estimation results for a single S-mode signal with an incident angle of 30 degrees at a 44 MHz A / D sampling rate using the weighted correlation accumulation method (an embodiment of the present invention), the full correlation accumulation method, and the classic MUSIC method at different numbers of array elements and different signal-to-noise ratios.

[0050] FIG8 shows the spatial spectra of the weighted correlation accumulation (embodiment of the present invention), the full correlation accumulation, and the classic MUSIC method in an experiment for two S-mode signals with incident angles of -30 degrees and 30 degrees, respectively, at an A / D sampling rate of 33 MHz.

[0051] FIG9 shows the root mean square error (RMS) of the DOA estimation results of the weighted correlation accumulation (an embodiment of the present invention), the full correlation accumulation, and the classic MUSIC method at different numbers of array elements and different signal-to-noise ratios for two S-mode signals with incident angles of -30 degrees and 30 degrees, respectively, at an A / D sampling rate of 33 MHz.

[0052] Figure 10 shows the root mean square error (RMS) of the DOA estimation results for two S-mode signals with incident angles of -30 degrees and 30 degrees, respectively, at a 44 MHz A / D sampling rate, using weighted correlation accumulation (an embodiment of the present invention), full correlation accumulation, and the classic MUSIC method at different numbers of array elements and different signal-to-noise ratios. DETAILED DESCRIPTION

[0053] The embodiments of the present disclosure are described in detail below with reference to the accompanying drawings.

[0054] The following describes the embodiments of the present disclosure through specific examples, and those skilled in the art can easily understand other advantages and effects of the present disclosure from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all of the embodiments. The present disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present disclosure.

[0055] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0056] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present disclosure. The illustrations only show components related to the present disclosure and are not drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component can be changed at will, and the component layout type may also be more complicated.

[0057] Additionally, in the following description, specific details are provided to provide a thorough understanding of the examples. However, one skilled in the art will appreciate that the aspects described can be practiced without these specific details.

[0058] In one embodiment of the present invention, a method for estimating direction of arrival of a low signal-to-noise ratio (S-mode) signal using covariance accumulation is proposed, comprising the following steps performed in sequence:

[0059] S1 obtains the S-mode discrete signal after multi-channel sampling from the receiver with array antenna as the S1 stage of array output data;

[0060] S2 multiplies the array output data of the S1 stage with the conjugate transpose of its own time delay to obtain the maximum likelihood estimate of the covariance matrix of the delayed array output data, which is recorded as the S2 stage;

[0061] S3 is the S3 stage where the weights are obtained based on the expectation of the correlation function of the S-mode signal and the sampling interval;

[0062] S4 multiplies the weight obtained in step S3 by the maximum likelihood estimate of the delayed data covariance matrix obtained in step S2, and then accumulates the weighted accumulated data covariance matrix to obtain the S4 stage;

[0063] S5: performing eigenvalue decomposition on the weighted accumulated data covariance matrix obtained in step S4 to obtain the noise subspace eigenvector S5;

[0064] S6 uses the noise subspace eigenvector obtained in step S5 and the constructed direction vector to calculate the spatial spectrum function, perform spectrum peak search, and then obtain the S6 stage of the wave arrival direction.

[0065] The structural diagram of the estimator used in this embodiment is shown in FIG3 .

[0066] In this embodiment, S1 is specifically:

[0067] After down-conversion and sampling, a receiver with an array antenna with M elements obtains M-channel discrete signals. After detecting the header of the S-mode downlink signal, for each channel, starting from the sampling point at the rising edge of the first pulse of the header, the following L-1 consecutive samples are taken, and finally M discrete signal sequences of length L are obtained, forming an M×L order matrix X(l) as the array output data.

[0068] In this embodiment, S2 is specifically as follows: delaying the array output data matrix X(l) obtained in S1 by τ sampling points to obtain X(l-τ), and then performing conjugate transposition on X(l-τ) to obtain X H (l-τ), and finally X(l) and X H Multiply (l-τ) and divide by L to get the covariance matrix R of the array output data at delay τ X Maximum likelihood estimate of (τ) τ is changed from -L+1 to L-1, and finally the maximum likelihood estimate of the covariance matrix of 2L-1 delayed array output data is obtained.

[0069] In this embodiment, in S3, the method of obtaining the weight according to the expectation of the correlation function of the S-mode signal and the sampling interval is to examine the autocorrelation and cross-correlation of the two S-mode signals and calculate the expectation of the correlation function. s When the absolute value of the product of is less than or equal to one-third of the symbol width (the symbol width is 1 μs), the autocorrelation value of the S-mode signal is greater than the cross-correlation value, and the covariance matrix of the array output data corresponding to these time delays τ is calculated. The weight value is 1, and the covariance matrix of the delayed array output data corresponding to the remaining delay τ is Assign a weight of 0 and set The weight is 0.

[0070] In this embodiment, in S4, the weights obtained in S3 are multiplied by the maximum likelihood estimate of the delayed data covariance matrix obtained in S2, and then accumulated to obtain the weighted accumulated data covariance matrix. Multiply the weight w at each τ obtained in S3 respectively τ Then multiply by the complex multiplier Then add up and get the weighted accumulated data covariance matrix

[0071] In this embodiment, in S5, the weighted accumulated data covariance matrix obtained in S4 is subjected to eigenvalue decomposition to obtain the noise subspace eigenvector. Perform eigenvalue decomposition to obtain M eigenvalues ​​and corresponding eigenvectors. Arrange the M eigenvalues ​​from large to small, sort the eigenvectors corresponding to each eigenvalue in the same order as the eigenvalues, extract the eigenvectors corresponding to the last MK smaller eigenvalues, and obtain the noise subspace eigenvector U N .

[0072] In this embodiment, in S6, the noise subspace eigenvector obtained in S5 and the constructed direction vector are used to calculate the spatial spectrum function, perform spectrum peak search, and then obtain the direction of arrival by setting the search start and end points and search step size of the direction of arrival, searching for a total of S times, selecting the reference point of the array antenna, and searching the angle θ. current When θ current The phase difference between the incoming wave incident on each element of the array and the reference point forms a steering vector a(θ current ), use U in S5 N and a(θ current ) calculate the value of the spectral function After the search is completed, plot P(θ current ) spectrum, find the θ corresponding to the first K (K is the number of signal sources) highest spectrum peaks current , which is the estimated direction of arrival.

[0073] Further explanation:

[0074] As shown in FIG1 and FIG2 , the correlation accumulation direction-of-arrival estimation method for low-SNR S-mode signals provided in this embodiment includes the following steps performed in sequence:

[0075] (1) Obtaining the multi-channel sampled S-mode discrete signal from the receiver with array antenna as the array output data in the S1 stage:

[0076] After down-conversion (the carrier frequency of the S-mode signal after down-conversion is ω) and sampling, the receiver with an array antenna with M elements will output M-channel discrete signals. After detecting the header of the S-mode downlink signal, for each channel, starting from the sampling point at the rising edge of the first pulse of the header, the following L-1 consecutive samples (L is the number of sampling points of the entire S-mode signal) are taken, and finally M discrete signal sequences of length L are obtained, forming an M×L order matrix X(l) as the array output data.

[0077] The mathematical model of array output data is explained below:

[0078] The S-mode downlink signal carrier frequency is 1090 MHz. A single S-mode signal consists of a header and a data block. Figure 2 shows the baseband signal structure. The header, which lasts 8 μs and contains four short pulses of 0.5 μs each, is used for modulation. The data block uses pulse position modulation and consists of 56 or 112 symbols of 1 μs each. Each symbol is split into two 0.5 μs slices: a pulse followed by a silent pulse represents a binary 1, while a silent pulse followed by a pulse represents a binary 0. The data block contains various responses or broadcast information.

[0079] A single symbol waveform can be represented by b(t,u,d), and its time domain expression is b(t,u,d)=d·rect(t-uT b )+(1-d)·rect(t-uT b -T b / twenty one)

[0080] Where u is the standard symbol width T of the current symbol relative to the first symbol delay b (T b =1μs), d is the binary value of the code element, which can be 0 or 1. And rect(·) is the width of T b / 2 rectangular pulse function, the expression is

[0081] Assuming that an S-mode baseband signal contains U code elements and the header is ignored, the envelope g(t) of the baseband waveform can be modeled as

[0082] The signal of formula (3) adopts frequency f s Sampling is performed with a sampling interval of T s =1 / f s, then \(g(t)\) can be discretized into

[0083] To achieve the direction finding of the S-mode signal source, an array antenna is used to receive spatial signals. Suppose there are \(K\) signals incident on an \(M\) (\(K < M\))-element array at a certain moment with angles \(\{\theta_1, \ldots, \theta\) K \(\}\), then the output data of the \(m\)th channel can be expressed as

[0084] where is the \(k\)th S-mode signal incident in space, and \(g\) k (l) is the envelope of the signal, \(\omega\) is the carrier frequency, and \(\psi\) k is the initial phase of the carrier. \(\varphi\) mk E]] is the phase difference generated by the \(k\)th signal between the \(m\)th array element and the selected reference point, and \(n\) m (l) = \(n\) m (lT s ) is the noise of the \(m\)th channel. Then, the array output data is represented by the matrix as \(X(l) = A(\theta)S(l)+N(l)\) (6)

[0085] where \(X(l)=[x_1(l)x_2(l)\ldots x\) <00000"43>(l)] T is the array output data, \(A(\theta)=[a(\theta_1)a(\theta_2)\ldots a(\theta\) K )] is the array manifold matrix, and the steering vector of the \(k\)th incident signal is

[0086] and \(S(l)=[s_1(l)s_2(l)\ldots s\) K (l)] T in Equation (6) is the incident signal matrix. According to the incident signal model, \(S(l)\) can be written as

[0087] where

[0088] is the complex amplitude vector. \(N(l)=[n_1(l)n_2(l)\ldots n\) M (l)] T in Equation (6) is the array channel noise matrix.

[0089] \(X(l)\) is the array output data obtained from the receiver, which contains \(L\) sets of snapshots after \(L\) samplings.

[0090] (2) Multiply the array output data obtained in step (1) by the conjugate transpose of the time delay of the array output data to obtain the S2 stage of the maximum likelihood estimation of the covariance matrix of the array output data with delay:

[0091] In this stage, the array output data matrix X(l) obtained in step (1) is first delayed by τ sampling points to obtain X(l-τ), and then X(l-τ) is conjugate transposed to obtain X H (l-τ), and finally X(l) and X H Multiply (l-τ) and divide by L to get the covariance matrix R of the array output data at delay τ X Maximum likelihood estimate of (τ) τ is changed from -L+1 to L-1, and finally the maximum likelihood estimate of the covariance matrix of 2L-1 delayed array output data is obtained.

[0092] The covariance matrix R of the delayed array output data is as follows X The mathematical model of (τ) is explained as follows:

[0093] Assuming that different incident signals are uncorrelated, different steering vectors a(θ k ) are linearly independent of each other, and the channel noise is a complex Gaussian random process and is uncorrelated with the signal, and the noise between different channels is uncorrelated, then the covariance matrix R of the array output data X R X =E[X(l)X H (l)]=A(θ)R G A H (θ)+σ 2 I M×M (10)

[0094] Among them, R G =E[G(l)G H (l)] is the covariance matrix of the signal, which is a non-singular diagonal matrix, and the diagonal elements are the powers of each incident signal; σ 2 is the channel noise power, I M×M is an M-order unit matrix. X For a Hermitian matrix, it can be decomposed into eigenvalues, and the eigenvectors corresponding to any two eigenvalues ​​are orthogonal.

[0095] The basis of eigenvalue decomposition in MUSIC is R X , which is the covariance matrix of the array output data X(l) at time delay τ = 0. Its diagonal elements are the variance of the data of a certain channel, which is the sum of the signal energy and the noise energy; the off-diagonal positions are the covariances of the data of different channels, which ideally do not contain noise energy. As shown in Figure 2, the S-mode baseband signal contains a fixed number of bit slices with a length of 0.5μs. Therefore, the product s(l)s of the incident signal s(l) and its own conjugate transpose at time delay τ = 0 is H(l) is the largest, which indicates that the autocorrelation is the strongest at this time. As τ gradually increases or decreases, s(l)s H (l-τ) gradually decreases, indicating that the autocorrelation gradually decreases. When τ≥0.5μs or τ≤-0.5μs, since the S-mode baseband signal chips are few or just no longer have high-level overlap, s(l)s H The value of (l-τ) will become very small, indicating that the autocorrelation is very low. Since the noise is independent at different times, the product of the noise n(l) and its own conjugate transpose when the delay τ≠0 is n(l)n H (l) is 0, that is, uncorrelated. Therefore, if we multiply X(l) by its own conjugate transpose at τ, X(l-τ), we can calculate the covariance matrix R of the array output data at the delay τ. X Maximum likelihood estimate of (τ) Then R X The noise energy on the diagonal (τ) can be eliminated, thus effectively improving the signal-to-noise ratio. The covariance matrix of the array output data at the delay τ is R X (τ) = E[X(l)X H (l-τ)] (11)

[0096] According to the assumptions, R X (τ) can be written as R X (τ)=A(θ)R S (τ)A H (θ)+R N (τ) (12)

[0097] where R S (τ)=E[S(l)S H (l-τ)] (13)

[0098] Substituting formula (8) into formula (13) we can get

[0099]

[0100] where R G (τ)=E[G(l)G H (l-τ)] (15)

[0101] is the covariance matrix of the complex envelope. G (τ), substituting formula (9) into formula (15) we have

[0102] in, have

[0103] g i(l) and g j (l)h j (l), where L is the number of snapshots, * To take conjugate.

[0104] According to the assumption that different incident signals are uncorrelated, R G The diagonal elements of (0) are the energies of the incident signals, while the off-diagonal elements are all 0. Therefore, is an ideal situation, and in an ideal situation, However, there is a certain correlation between the actual incident S-mode signals. For the actual signal, when τ≠0, and are not 0. Therefore, to approach the ideal situation, we hope that at the time delay τ, As large as possible, and As small as possible, and and The difference As big as possible.

[0105] Next, we examine the delayed noise covariance matrix, R in Eq. (12) N (τ) is R N (τ)=E[N(l)N H (l-τ)] (18)

[0106] Since the noise is independent and uncorrelated at different times, equation (18) can be written as

[0107] Among them I M×M is an M×M order unit matrix. It can be seen from formula (19) that according to the Gaussian white noise assumption, it only has a high autocorrelation characteristic at τ = 0.

[0108] Therefore, R at multiple τ can be X (τ) selectively added, because only R X (0) contains noise energy, and the accumulated covariance matrix of the delayed array output data can significantly improve the signal-to-noise ratio.

[0109] (3) The S3 stage where the weights are obtained based on the expected correlation function of the S-mode signal and the sampling interval:

[0110] In step (2), a total of 2L-1 maximum likelihood estimates of the covariance matrix of the delayed array output data are obtained. They cannot be accumulated because, on the one hand, the computational complexity will be seriously increased. On the other hand, according to step (2), not every R at the delay τ is equal to X(τ) will have a positive contribution to the result. It is necessary to analyze the R at different time delays τ based on the statistical characteristics of the autocorrelation and cross-correlation of the baseband signal and noise. X (τ) weighted value, retaining R that is beneficial to the estimation results X (τ), discard R that is not conducive to the estimation results X (τ).

[0111] Figure 4 reflects the two pulse position modulation signals g i (l) and g j (l), the number of two signal symbols U = 6, the signal duration is 6μs, each symbol is randomly selected from 0 and 1, the signal sampling rate is 33MHz, and the number of snapshots L = 198. As shown in Figure 4, it is obvious that at τ = 0, maximum, so R G (0) The signal energy is significantly concentrated on the diagonal line. i (l) and g j Each binary value of (l) is random, so and The expectation of the statistical mean is obtained. According to the signal model of formula (4), when |τT s |>T b Sometimes, there are When T b / 2≤|τT s |≤T b Sometimes, there are In |τT s |≤T b / 2 range, there are

[0112] From formula (20), we can see that only when |τT s |≤T b / 3, only then Figure 5 reflects the expectation of the correlation between the two signals in Figure 4. As shown in Figure 5, in |τT s |≤T b / 3, there is At other time delays, there are

[0113] From step (2), we can see that R X The selection principle of (τ) is to satisfy the time delay τ. As large as possible, and As small as possible, and and The difference As large as possible, so that the covariance matrix of the data at multiple delays can be accumulated closer to the ideal situation, so only the one that satisfies |τT can be taken.s |≤T b R corresponding to τ / 3 G (τ), and from formula (19), we can know that R N (τ) is only autocorrelated at τ = 0, so we no longer need to take R at τ = 0 X (τ), that is, let R X The weight of (0) is 0, which can eliminate R N (0), thus significantly improving the signal-to-noise ratio. Can be ordered

[0114] (4) Multiply the weights obtained in step (3) by the maximum likelihood estimate of the delayed data covariance matrix obtained in step (2), and then add them together to obtain the S4 stage of the weighted accumulated data covariance matrix:

[0115] All the τ obtained in step (2) Multiply the weight w at each τ obtained in step (3) by τ Then multiply by the complex multiplier Then add up and get the weighted accumulated data covariance matrix

[0116] The following combination The mathematical model of details the principle that weighted accumulation can improve the signal-to-noise ratio:

[0117] The weight vector obtained in step (3) is W = [w -L+1 …w0…w L-1 ], and in order to eliminate the complex multiplier in formula (14) The impact of R X The weighted accumulation of (τ) is

[0118] The above formula can be further written as

[0119] in

[0120] and

[0121] From the above formula, we can see that, ideally, the noise term is completely eliminated by accumulation. However, in reality, the noise cannot be completely eliminated, and a considerable amount of noise energy will definitely remain. The energy of the signal in is greatly enhanced by accumulation, so the signal-to-noise ratio is significantly improved. Moreover, while the signal-to-noise ratio is improved, it can be seen from step (3) that the selective weighted accumulation will make The assumption of conditions closer to the ideal condition is conducive to improving the performance of direction of arrival estimation.

[0122] (5) Perform eigenvalue decomposition on the weighted accumulated data covariance matrix obtained in step (4) to obtain the S5 stage of the noise subspace eigenvector:

[0123] right Perform eigenvalue decomposition:

[0124] Among them, Σ is an M×M diagonal matrix, and its M elements on the diagonal are The corresponding U is an M×M matrix composed of eigenvectors, and the mth column of U is the eigenvector corresponding to the mth eigenvalue in Σ. Arrange the M eigenvalues ​​from large to small and record them as λ1,…,λ K ,…,λ M , sort the eigenvectors corresponding to each eigenvalue in the same order as the eigenvalues, and sort λ K+1 to λ M The eigenvectors corresponding to these MK eigenvalues ​​are extracted, that is, the columns of U are reordered and the MK columns are extracted, which are recorded as U N , which is the noise subspace eigenvector.

[0125] (6) Using the noise subspace eigenvector obtained in step (5) and the constructed direction vector, the spatial spectrum function is calculated and the spectrum peak search is performed to obtain the S6 stage of the wave arrival direction:

[0126] According to the properties of the antenna array, the search start and end points of the wave arrival direction are set to θ start and θ end , set the search step to △ θ , from θ start Start, each step △ θ , a total of S searches, the angle of one of the searches is θ current Select the reference point of the array antenna. The reference point can be a certain array element or any point in space. Assume that the direction of arrival is θ current , calculate the current The phase difference between the incident wave incident on each element of the array and the incident wave incident on the reference point is recorded as φ1, φ2, ..., φ M , construct the steering vector a(θ current )for

[0127] Change U in step (5) N and a(θ current ) into formula (28), and the value of the spectral function P(θ current )

[0128] From θ start Scan to θ end , calculate a set of P(θ current ) array, with the horizontal axis as θ current , the vertical axis is P(θ current ), draw the spectrum, and find the θ corresponding to the first K highest peaks current , which is the estimated direction of arrival.

[0129] Simulation experiment

[0130] The effect of the covariance accumulation direction of arrival estimation method for low signal-to-noise ratio S-mode signals provided by the present invention can be further illustrated by the following simulation data experiments.

[0131] The calculation expression of the test statistic root mean square error RMSE in the simulation experiment is:

[0132] Where N c The S-mode signal carrier frequency in the experiment is 1090 MHz, which is mixed at 1030 MHz and then down-converted to an intermediate frequency of 60 MHz. Different sampling rates are used for intermediate frequency bandpass sampling, and the number of baseband symbols is 64.

[0133] The simulation experiments used a uniform linear array with a half-wavelength element spacing and a signal-to-noise ratio ranging from -20dB to -5dB. The experiments were repeated 100 times under each condition. The RMSE of the classic MUSIC method, the full correlation accumulation method, and the weighted correlation accumulation method (of the present invention) were compared at different sampling rates and signal-to-noise ratios.

[0134] First, we simulated a single incident signal at a 30-degree angle, focusing on the method's improvement in signal-to-noise ratio. Figures 6 and 7 show the RMSE of the three methods at different array element numbers and signal-to-noise ratios at 33MHz and 44MHz A / D sampling rates, respectively.

[0135] As shown in Figures 6 and 7, RMSE decreases as the signal-to-noise ratio increases. At the same sampling rate, the weighted correlation accumulation method always has the smallest RMSE, the full correlation accumulation method has a slightly higher RMSE than the weighted correlation accumulation method, and the MUSIC method has the largest RMSE. Furthermore, when the signal-to-noise ratio is close to -20 dB, the RMSE of the MUSIC method is very large, while the RMSE of the weighted correlation accumulation method is always controlled within 2 degrees, an improvement of 5 to 30 degrees compared to the RMSE of the MUSIC method. This shows that at low signal-to-noise ratios, the weighted correlation accumulation method greatly improves the signal-to-noise ratio, resulting in a high confidence level in the direction of arrival estimation angle and a greatly improved estimation accuracy compared to the MUSIC method.

[0136] Next, simulations were conducted with two signals incident at angles of -30 degrees and 30 degrees, respectively. This dual-signal incident scenario not only examined the method's improvement in signal-to-noise ratio, but also considered the impact of latency on multi-signal correlation. Figure 8 shows the spatial spectra of the three methods in a single experiment at a 33MHz A / D sampling rate. Figures 9 and 10 show the RMSE of the three methods at different array element numbers and signal-to-noise ratios at 33MHz and 44MHz A / D sampling rates, respectively.

[0137] As shown in Figure 8, compared to the MUSIC method, the weighted correlation accumulation method significantly sharpens the spectral peaks, improving the signal-to-noise ratio while maintaining the resolution of the two signals, and does not affect the orthogonality of the subspace after the multi-signal matrix decomposition. In contrast, the full correlation accumulation method, while improving the signal-to-noise ratio, deviates from the ideal assumption by not considering the influence of signal correlation, which in turn affects the orthogonality of the subspace after the cumulative covariance matrix decomposition. Ultimately, the spectral peaks are not only not sharpened, but are actually greatly widened. As shown in Figures 9 and 10, at the same sampling rate, the RMSE of the full correlation accumulation method remains very high, indicating that the full correlation accumulation method fails when multiple signal sources are incident. However, compared with the MUSIC method, the RMSE of the weighted correlation accumulation method is significantly improved. When the signal-to-noise ratio is close to -18 dB, the RMSE of the weighted correlation accumulation method is improved by more than 10 degrees compared with the MUSIC method. The RMSE of the weighted correlation accumulation method can be controlled within 3 degrees, and the estimated direction of arrival angle has a high confidence level, and the estimation accuracy is greatly improved compared with the MUSIC method.

[0138] Complexity Analysis

[0139] The computational complexity of the covariance accumulation direction of arrival estimation method for low signal-to-noise ratio S-mode signals provided by the present invention can be explained through the following analysis.

[0140] The complexity of the present invention includes three parts:

[0141] 1) The complexity of calculating the cumulative data covariance matrix

[0142] This method reconstructs the data covariance matrix by accumulating the data covariance matrices at multiple time delays. R X The computational complexity of (τ) is O(M 2 L), due to R X (τ) = R X (-τ) has symmetry, so we only need to calculate R X (τ), The computational complexity becomes

[0143] 2) Complexity of matrix eigenvalue decomposition

[0144] The computational complexity of eigendecomposition of a matrix is ​​generally O(M 3 ).

[0145] 3) Complexity of peak search

[0146] The complexity of the peak search needs to be determined according to the search range and search step size. If the number of searches is S, then S searches require a total of S(M(MK)M+M 2 +M) operations, so the computational complexity of the peak search is O(SM 3 ).

[0147] Since the number of snapshots L is generally much larger than the number of array elements M, and the number of searches S>>1, the overall computational complexity of this method is In comparison, the overall computational complexity of the classic MUSIC algorithm is O((L+SM)M 2 ). This method does not significantly increase the computational complexity.

[0148] The above description is merely a specific embodiment of the present disclosure, but the scope of protection of the present disclosure is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this disclosure should be included in the scope of protection of the present disclosure. Therefore, the scope of protection of the present disclosure should be based on the scope of protection of the claims.

Claims

1. A covariance accumulation direction of arrival estimation method for low signal-to-noise ratio S-mode signals, characterized in that: The method for estimating the direction of arrival of a low signal-to-noise ratio S-mode signal by covariance accumulation comprises the following steps performed in sequence: S1 obtains the S-mode discrete signal after multi-channel sampling from the receiver with array antenna as the S1 stage of array output data; S2 multiplies the array output data of the S1 stage by the conjugate transpose of its own time delay to obtain the maximum likelihood estimate of the covariance matrix of the delayed array output data, which is recorded as the S2 stage; S3 is the S3 stage where the weights are obtained based on the expectation of the correlation function of the S-mode signal and the sampling interval; S4: multiplying the weight obtained in step S3 by the maximum likelihood estimate of the delayed data covariance matrix obtained in step S2, and then accumulating the weighted accumulated data covariance matrix to obtain the S4 stage; S5: performing eigenvalue decomposition on the weighted accumulated data covariance matrix obtained in step S4 to obtain the S5 stage of the noise subspace eigenvector; S6 uses the noise subspace eigenvector obtained in step S5 and the constructed direction vector to calculate the spatial spectrum function, perform spectrum peak search, and then obtain the S6 stage of the wave arrival direction.

2. The method for estimating the direction of arrival of a low signal-to-noise ratio S-mode signal according to claim 1, characterized in that: The S1 is specifically: After down-conversion and sampling, a receiver with an array antenna having M elements obtains M-channel discrete signals. After detecting the header of the S-mode downlink signal, for each channel, starting from the sampling point at the rising edge of the first pulse of the header, the following L-1 consecutive samples are taken, and finally M discrete signal sequences of length L are obtained, forming an M×L-order matrix X(l) as the array output data.

3. The method for estimating the direction of arrival of a low signal-to-noise ratio S-mode signal according to claim 1, characterized in that: S2 specifically includes: delaying the array output data matrix X(l) obtained in S1 by τ sampling points to obtain X(l-τ), and then performing conjugate transposition on X(l-τ) to obtain X H (l-τ), and finally X(l) and X H (l-τ) is multiplied and then divided by L to obtain the covariance matrix R of the array output data at the delay τ X Maximum likelihood estimate of (τ) τ changes from -L+1 to L-1, and finally obtains the maximum likelihood estimate of the covariance matrix of 2L-1 delayed array output data.

4. The method for estimating the direction of arrival of a low signal-to-noise ratio S-mode signal according to claim 1, characterized in that: In S3, the method of obtaining weights according to the expectation of the correlation function of the S-mode signal and the sampling interval is to examine the autocorrelation and cross-correlation of the two S-mode signals, and calculate the expectation of the correlation function, and calculate the weights according to the time delay τ and the sampling interval T. s When the absolute value of the product is less than or equal to one-third of the code element width, the autocorrelation value of the S-mode signal is greater than the cross-correlation value. The covariance matrix of the array output data corresponding to these time delays τ is The weight value is 1, and the covariance matrix of the delayed array output data corresponding to the remaining delay τ is Assign a weight value of 0 and set The weight of is 0.

5. The method for estimating the direction of arrival of a low signal-to-noise ratio S-mode signal according to claim 1, characterized in that: In S4, the method of multiplying the weights obtained in S3 with the maximum likelihood estimate of the delayed data covariance matrix obtained in S2 and then accumulating to obtain the weighted accumulated data covariance matrix is ​​to add all the τ values ​​obtained in S2 to the weighted covariance matrix. Multiply each weight w at τ obtained in S3 by τ Then multiply by the complex multiplier After accumulation, the weighted accumulated data covariance matrix is ​​obtained 6. The method for estimating direction of arrival of a low signal-to-noise ratio S-mode signal by covariance accumulation according to claim 1, characterized in that: In S5, the weighted accumulated data covariance matrix obtained in S4 is subjected to eigenvalue decomposition to obtain the noise subspace eigenvector. Perform eigenvalue decomposition to obtain M eigenvalues ​​and corresponding eigenvectors, arrange the M eigenvalues ​​from large to small, sort the eigenvectors corresponding to each eigenvalue in the same order as the eigenvalues, extract the eigenvectors corresponding to the last MK smaller eigenvalues, and obtain the noise subspace eigenvector U N .

7. The method for estimating the direction of arrival of a low signal-to-noise ratio S-mode signal by covariance accumulation according to claim 1, characterized in that: In S6, the method of calculating the spatial spectrum function using the noise subspace eigenvector obtained in S5 and the constructed direction vector to search for the spectrum peak and then obtain the direction of arrival is to set the search start and end points and the search step length of the direction of arrival, search a total of S times, select the reference point of the array antenna, and search the angle θ. current When θ current The phase difference between the incoming wave incident on each element of the array and the reference point forms a steering vector a(θ current ), use U in S5 N and a(θ current ) calculates the value of the spectral function After the search is completed, P(θ current ) spectrum, find the θ corresponding to the first K highest peaks current , which is the estimated direction of arrival.

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