Single-base MIMO radar multi-target DOA estimation method

Abstract

The invention discloses a single-base MIMO radar multi-target DOA estimation method, and belongs to the field of signal processing. According to the method, a Shannon information theory method is combined, and a joint conditional probability density function of a received signal of the MIMO radar, a target direction angle and a target reflection coefficient is deduced by utilizing the property of noise in the received signal; according to a Bayesian formula, firstly, a posterior probability density function of a single-base MIMO radar multi-target reflection coefficient based on a uniform linear array is derived, and a posterior probability density function of a multi-target direction angle when a signal is received is further obtained by combining a derivation result. The azimuth angles of a plurality of targets can be obtained at the same time by performing spectral peak search on the posterior probability density function of the target direction angle. The invention provides a DOA (direction of arrival) detection method based on a posterior probability density function and aiming at the condition that a plurality of targets are densely distributed. According to the method, the posterior probability density function used for uniform linear array monostatic MIMO radar multi-target DOA estimation is deduced based on the information theory, all available information is organically combined through the Bayesian theory, and therefore more comprehensive angle estimation is provided.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing, and in particular to a method for estimating the azimuth angle of multiple targets in a monostatic MIMO radar. Background Technology

[0002] The application background of target orientation angle estimation is widely covered in many key fields. The application of this technology is mainly concentrated in radar systems, sonar systems, communication systems, aerospace, unmanned systems and earth observation.

[0003] Existing orientation estimation methods mostly employ algorithms such as MUSIC, RD-MUSIC, ESPRIT, and PM, which can accurately estimate the target orientation under ideal conditions. However, in low signal-to-noise ratio scenarios, these algorithms are quite sensitive to noise and easily affected by it. Summary of the Invention

[0004] This invention provides a method for estimating the direction angle (DOA) of multiple targets in a monostatic MIMO radar, offering a more accurate approach for DOA estimation in a uniform linear array monostatic MIMO radar under low signal-to-noise ratio (SNR).

[0005] This invention provides a method for estimating the azimuth angle of multiple targets in a monostatic MIMO radar based on a uniform linear array, comprising the following steps:

[0006] Step 1) Construct a monostatic MIMO radar detection system model based on a uniform linear array. Utilize the properties of noise in the received signal to construct the joint conditional probability density function of the received signal, target direction angle, and reflection coefficient of the radar detection system model.

[0007] Step 2), combined with Bayes' theorem, derive the posterior probability density function of the reflection coefficient of the target to be detected and the posterior probability density function of the direction angle of the multi-target in the monostatic MIMO radar detection system model;

[0008] Step 3) Perform a one-dimensional maximum scan of the posterior probability density function of the target orientation angle in the area to be detected to obtain the estimated orientation angle of sparsely distinguishable targets and the distribution area of ​​densely indistinguishable targets.

[0009] Step 4) For densely distributed target areas, perform multidimensional resolution on the posterior probability density function of the target orientation angle to obtain the estimated orientation angle of the densely distributed targets.

[0010] Optionally, in one embodiment of the present invention, in step 1), the MIMO radar transmitting array and receiving array respectively have Individual and Uniformly distributed array elements, and These are the element spacings of the transmitting array and the receiving array, respectively. , Wavelength;

[0011] Suppose there are Q targets to be detected in a certain space, and the radar transmits a sequence of orthogonal narrowband signals of equal power, with the average transmit power of each signal being... The sequence length is K; Let the m-th transmitted signal sequence of length K be represented by... Let Y represent the radar transmitted signal matrix, then the radar received signal Y is represented as:

[0012]

[0013] in, , Represents the complex Gaussian reflectance coefficient of the q-th target; matrix With a mean of 0 and a variance of It consists of additive complex Gaussian white noise random variables; This is the receiving direction matrix of the radar. Let be the radar's transmission direction matrix, and let the target direction vector be expanded as follows: , The departure (arrival) direction angle of the signal corresponding to the q-th target;

[0014] Stretching the received signal matrix yields the received signal vector form, which is represented as follows:

[0015]

[0016] in, Represents the Khatri-Rao product. The reflection coefficient vector, It is an additive complex Gaussian white noise vector;

[0017] Due to noise Given an additive complex white Gaussian noise sample, at the target direction angle and reflection coefficient Under known conditions, receive signal The multidimensional conditional probability density function is expressed as:

[0018]

[0019] Optionally, in one embodiment of the present invention, in step 2), the joint posterior probability density function of the multi-target reflection coefficients in the uniform linear array monostatic MIMO radar detection system model is derived using Bayes' theorem, including:

[0020]

[0021] in, Represents the vector of complex Gaussian reflection coefficients The probability follows a mean of 0 and a variance of . The Q-dimensional complex Gaussian distribution.

[0022] Optionally, in one embodiment of the present invention, in step 2), a model of a uniform linear array monostatic MIMO radar detection system is derived based on Bayes' theorem for a given received signal. In the case of multi-target orientation angle estimation, the posterior probability density function includes:

[0023] Assuming each target direction angle All within the observation interval If the interior follows a uniform distribution, then the target azimuth vector probability density function Given a constant, and according to Bayes' theorem, the MIMO radar detection system model under a given received signal is obtained. Target direction angle vector under certain conditions The posterior probability density function is:

[0024]

[0025] in, Represents the target detection range; matrix sum matrix Each satisfies

[0026]

[0027]

[0028] Optionally, in one embodiment of the present invention, in step 3),

[0029] Given a detection range, for a given received signal Target direction angle under certain conditions posterior probability density function A one-dimensional spectral peak search is performed, and the direction angle estimates of some sparse targets and the distribution areas of some dense, indistinguishable targets are obtained based on the search results.

[0030] Optionally, in one embodiment of the present invention, in step 4),

[0031] After obtaining the distribution area of ​​dense, indistinguishable targets, a multidimensional maximum search is performed on the posterior probability density function of the target orientation angle within this range. The angle corresponding to the maximum value is the estimated orientation angle of the dense targets.

[0032] Beneficial effects:

[0033] This invention presents a method for estimating the azimuth angle of multiple targets in a monostatic MIMO radar detection system. The proposed method only requires the posterior probability density function of the estimation parameters to estimate the azimuth angles of multiple targets in the system model, providing a multi-target azimuth angle estimation method independent of specific algorithms. Simultaneously, the posterior probability density function considers all available information, including observation data, prior information, and the relationships between estimation parameters. This information is organically combined using Bayesian theory, resulting in a more comprehensive and integrated estimate. By incorporating noise models and prior information, more accurate estimation results can be provided, especially under low signal-to-noise ratio conditions. Utilizing the posterior probability density function for multi-target azimuth angle estimation provides more comprehensive, accurate, and robust estimation results. Compared with traditional DOA estimation algorithms, this method considers multiple aspects of information, provides information on the uncertainties in parameter estimation, and can better handle complex estimation problems.

[0034] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0035] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0036] Figure 1 A flowchart illustrating a method for estimating the azimuth angle of a monostatic MIMO radar according to an embodiment of the present invention;

[0037] Figure 2 This is a model diagram of a monostatic MIMO radar detection system according to an embodiment of the present invention;

[0038] Figure 3 Images of scanning results in different dimensions of the posterior probability density function of the target orientation angle in an embodiment of the invention.

[0039] Figure 4 The spectrum peaks of the posterior probability density function of the target orientation angle under different SNR conditions are shown in the embodiment of the invention.

[0040] Figure 5 A top view of the spectral peak diagram of the posterior probability density function of the target orientation angle under different SNR conditions in an embodiment of the invention;

[0041] Figure 6 A scatter plot comparing the method of the present invention and the MUSIC algorithm for multi-objective DOA estimation. Detailed Implementation

[0042] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0043] The following describes a method for estimating the direction of attack (DOA) of a monostatic MIMO radar according to embodiments of the present invention, with reference to the accompanying drawings. As mentioned in the background section, existing multi-target DOA estimation algorithms are typically sensitive to noise and easily affected by it under low signal-to-noise ratio (SNR) conditions. Based on this problem, the present invention proposes a method for estimating the DOA of a monostatic MIMO radar using the unified framework and applicability to various signal and noise types inherent in information theory. Simulation comparisons verify that the proposed method provides more accurate estimates than other DOA estimation algorithms under low SNR conditions.

[0044] Specifically, Figure 1 This is a flowchart of a method for estimating the azimuth angle of a monostatic MIMO radar according to an embodiment of the present invention.

[0045] like Figure 1 As shown, the method for estimating the multi-target bearing angle of a monostatic MIMO radar includes the following steps:

[0046] Step 1) Construct a monostatic MIMO radar detection system model. Utilize the noise properties in the received signal to construct the joint conditional probability density function of the received signal, target direction angle, and reflection coefficient in the radar detection system model.

[0047] Specifically, the received signal vector in the monostatic MIMO radar detection system model is constructed using the prior probability density function of the noise. In the known and Conditional probability density function under the condition ;

[0048] like Figure 2 As shown, the transceiver array of the monostatic MIMO radar is a uniform linear array, with the transmitting and receiving arrays having [missing information]. Individual and Uniformly distributed array elements, and These are the element spacings of the transmitting array and the receiving array, respectively. , Wavelength;

[0049] Suppose there are Q targets to be detected in a certain space, and the radar transmits a sequence of orthogonal narrowband signals with equal power. The average transmit power of a single signal is... The sequence length is K; Let the m-th transmitted signal sequence of length K be represented by... This represents the radar transmitted signal matrix, where the signal reflected by the q-th target is expressed in terms of azimuth angle. When incident on the receiving array, the received signal matrix Y of the monostatic MIMO radar described above is expressed as:

[0050]

[0051] in, , This represents the complex Gaussian reflectance coefficient of the q-th target; The mean of the radar is 0, and the variance is... Additive complex white Gaussian noise, This is the receiving direction matrix of the radar. Let be the radar's transmission direction matrix, and let the target direction vector be expanded as follows: , The departure (arrival) direction angle of the signal corresponding to the q-th target;

[0052] Where the direction matrix and They are respectively represented as

[0053]

[0054]

[0055] in:

[0056] The radar transmission direction vector corresponding to the q-th target

[0057] The radar receiving direction vector corresponding to the q-th target

[0058] For ease of study, the received signal matrix is ​​stretched to obtain a vector form, denoted as:

[0059]

[0060] in, Represents the Khatri-Rao product. The reflection coefficient vector;

[0061] Due to noise Given an additive complex white Gaussian noise sample, at the target direction angle and reflection coefficient Under known conditions, receive signal The multidimensional conditional probability density function is expressed as:

[0062]

[0063] Step 2) Using Bayes' theorem, the joint posterior probability density function of the received signal, target reflection coefficient, and azimuth angle in the monostatic MIMO radar detection system model is derived, as well as the posterior probability density function of the multi-target azimuth angle vector under a given received signal.

[0064] First, prior assumptions are made regarding the complex Gaussian reflection coefficient and the target's orientation angle. The reflection coefficient is assumed to be... All have a mean of 0 and a variance of . For a complex Gaussian random variable, the reflection coefficient vector The prior probability density function is expressed as:

[0065]

[0066] in,

[0067] Assuming the target's direction angle In the observation interval If the interior follows a uniform distribution, then the target direction vector The prior probability density function:

[0068]

[0069] Based on Bayes' theorem, the model of the MIMO radar detection system is obtained under the assumption of the received signal. and target direction angle Target reflection coefficient under known conditions The posterior probability density function is:

[0070]

[0071] Since the reflection coefficient is independent of the target orientation angle, therefore... .

[0072] Simultaneously, based on Bayes' theorem, the model of the MIMO radar detection system under a given received signal is obtained. Target direction angle under certain conditions The posterior probability density function is:

[0073]

[0074] in, Represents the target detection range; matrix sum matrix Each satisfies

[0075]

[0076]

[0077] Step 3) Perform a one-dimensional maximum search on the posterior probability density function of the target orientation angle to obtain the estimated values ​​of the orientation angles of the partially sparsely distributed targets and the orientation angle distribution areas of the densely distributed targets.

[0078] Step 4) In the dense target distribution area, perform a multidimensional maximum search on the posterior probability density function of the target orientation angle to obtain the orientation angle estimate of the densely distributed targets, and then obtain the orientation angle estimate of all targets in the space to be detected.

[0079] Figure 3 The images show a one-dimensional scan and a two-dimensional scan of a densely distributed target area, representing the posterior probability density function of the target orientation angle in an embodiment of the invention, with an SNR of 0 dB. The simulation conditions are: total number of targets... The number of elements in the transmitting uniform linear array and the receiving uniform linear array is , The actual location of the target is .from Figure 3 As can be seen, densely distributed targets can be successfully detected by performing multi-dimensional scanning of the posterior probability density function of the target orientation angle. This indicates that increasing the scanning dimension of the posterior probability density function of the target orientation angle can improve the detection accuracy of MIMO radar and enhance the target detection precision.

[0080] Figure 4 This is a two-dimensional spectral peak diagram of the posterior probability density function of the target orientation angle under different SNR conditions in an embodiment of the invention. The simulation conditions are: number of targets... The number of elements in the transmitting uniform linear array and the receiving uniform linear array is , The actual location of the target is .from Figure 4 As can be seen, the spectral peaks of the posterior probability density function of the target orientation angle exhibit peaks of varying intensities and distributions at signal-to-noise ratios (SNRs) of -10 dB, -5 dB, 0 dB, and 5 dB. Under high SNR conditions, the peaks are sharper and more intense, reflecting the accuracy and confidence of the estimation. As the SNR decreases, the peaks gradually become blurred and their intensity weakens, indicating that the estimation results are significantly affected by noise under low SNR conditions. However, the information-theoretic method can still accurately estimate the precise location of the target source, and a clear peak is observed, reflecting the applicability of the information-theoretic method for multi-target azimuth estimation.

[0081] Figure 5 This is a top view of the spectral peak diagram of the posterior probability density function of the multi-target orientation angle under different SNR conditions, according to an embodiment of the invention. Simulation conditions are: number of targets... The number of elements in the transmitting uniform linear array and the receiving uniform linear array is , The actual location of the target is . Figure 5 To more comprehensively evaluate the estimation performance, a top-view analysis of the spectral peak plot was conducted. True values ​​were added to the top view of the spectral peak plot for direct comparison with the estimated peak values. These true values ​​represent the actual azimuth angles of the two targets. By comparing the true values ​​with the estimated peak values, the consistency between the estimation results and the actual situation can be more clearly understood, demonstrating the accuracy of this method for estimating the azimuth angles of multiple targets in a uniform linear array monostatic MIMO radar.

[0082] Figure 6 This is a scatter plot comparing the method of the invention embodiment with the MUSIC algorithm for multi-objective DOA estimation. The simulation conditions are: number of objectives. The number of elements in the transmitting uniform linear array and the receiving uniform linear array is , The actual location of the target is Simulation times As can be observed from the figure, the Shannon information theory method, by utilizing the statistical properties of noise for modeling, performs excellently in low signal-to-noise ratio (SNR) environments. In the scatter plot, regardless of the SNR, the estimated value of this method has high accuracy and a small error compared to the true value. In contrast, the MUSIC algorithm can accurately estimate the target orientation angle under high SNR conditions, but performs poorly under low SNR conditions, with a larger error compared to the true value. This indicates that, under the same experimental conditions, the estimation of this invention has higher accuracy and is more adaptable to complex environments. Comparing the two methods, this invention overcomes the performance disadvantage of existing algorithms under low SNR conditions and has better estimation performance.

[0083] The proposed method for estimating the multi-target orientation angle (DOA) of a monostatic MIMO radar according to embodiments of the present invention employs an information-theoretic approach based on a probabilistic framework, enabling more flexible handling of uncertainties. By modeling the probability density function, a confidence measure of the estimate can be provided, particularly in low signal-to-noise ratio (SNR) environments, where it can better handle uncertainties and improve the robustness of the estimation. Furthermore, the information-theoretic method demonstrates advantages over other DOA estimation algorithms in terms of global optimization, probabilistic framework, multi-dimensional information synthesis, adaptability, and performance under low SNR conditions. Simulation comparisons verify the rationality and accuracy of the proposed method.

[0084] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0085] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0086] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

Claims

1. A method for estimating the DOA of multiple targets in a monostatic MIMO radar, characterized in that, Includes the following steps: Step 1): Based on the model of a monostatic MIMO radar detection system using a uniform linear array, construct the joint conditional probability density function of the received signal, target direction angle, and reflection coefficient in the detection system model by utilizing the noise properties of the received signal. Step 2), based on Bayes' theorem, derive the posterior probability density function of the reflection coefficient of the target to be detected and the posterior probability density function of the multi-target orientation angle of the detection system model; Step 3) Perform a one-dimensional maximum search on the posterior probability density function of the direction angle of the target to be detected to obtain the dense distribution area of ​​the direction angle of the target to be detected. Step 4) For the densely distributed area, perform a multidimensional maximum search on the posterior probability density function of the target orientation angle to obtain the orientation angle estimates of multiple dense targets.

2. The method according to claim 1, characterized in that, In step 1), the MIMO radar transmitting array and receiving array respectively have One and Uniformly distributed array elements, and These are the element spacings of the transmitting array and the receiving array, respectively. , Wavelength; Suppose there are Q targets to be detected in a certain space, and the radar transmits a sequence of orthogonal narrowband signals of equal power, with the average transmit power of each signal being... The sequence length is K; Let the m-th transmitted signal sequence of length K be represented by... Let the radar transmitted signal matrix represent the radar received signal matrix. Represented as: ； in, , This represents the complex Gaussian reflectance coefficient of the q-th target; The mean of the radar received signal is 0, and the variance is... Additive complex Gaussian white noise; This is the receiving direction matrix of the radar. Let be the radar's transmission direction matrix, and let the target direction vector be expanded as follows: , The departure angle of the signal corresponding to the q-th target; Stretching the received signal matrix yields the received signal vector form, which is represented as follows: ； in, Represents the Khatri-Rao product. The reflection coefficient vector; Due to noise Given an additive complex white Gaussian noise sample, the angular vector in the target direction... and reflection coefficient vector Under known conditions, the received signal vector The multidimensional conditional probability density function is expressed as: ； in, This indicates the conjugate transpose operation.

3. The method according to claim 2, characterized in that, In step 2), the posterior probability density function of the multi-target reflection coefficient vector of the detection system model is derived using Bayes' theorem, including: ； in, Represents the vector of complex Gaussian reflection coefficients The probability follows a mean of 0 and a variance of . The Q-dimensional complex Gaussian distribution.

4. The method according to claim 3, characterized in that, In step 2), the posterior probability density function of the multi-target orientation angle of the detection system model is derived using Bayes' theorem, including: Setting the first The direction angle corresponding to each target exist If the target azimuth vector follows a uniform distribution within the observation interval, then... probability Given a constant, and according to Bayes' theorem, the detection system model under a given received signal is obtained. Target direction angle vector under certain conditions The posterior probability density function is: ； Among them, matrix sum matrix They respectively satisfy: ； 。 5. The method according to claim 4, characterized in that, In step 3), given the target search range, the known received signal is... The posterior probability density function of the target orientation angle under the given condition A one-dimensional maximum search is performed to obtain the estimated direction angles of distinguishable targets and the distribution area of ​​densely inseparable targets.

6. The method according to claim 5, characterized in that, In step 4), based on the one-dimensional maximum search result, a logarithmic function is applied to the densely distributed, inseparable target regions. Perform a multidimensional maximum value search to obtain the estimated direction angle of each target. The angle corresponding to the maximum value is the estimated direction angle of the target.

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