A low elevation angle estimation method for high mountain mode of meter-wave MIMO radar based on dual carrier frequency

Abstract

The present invention belongs to the field of radar technology, and specifically relates to a method for estimating low elevation angles in high-altitude mode for a meter-wave MIMO radar based on dual carrier frequencies. The method comprises the following steps: Step 1: Assuming the MIMO radar is a co-located transmitter-receiver system, matched filtering is performed on the MIMO radar's transmitted signal, and the data is vectorized. Finally, the phase difference caused by the path difference between the MIMO radar's direct and reflected waves, as well as the radar received data, is obtained; Step 2: A maximum likelihood estimation criterion is established for calculating spatial spectrum values; Step 3: Based on the received data from Step 1, the spatial spectrum values ​​are calculated using the maximum likelihood estimation criterion from Step 2, and the peak values ​​of the spatial spectrum values ​​are read. The maximum value is used as the estimated value of the low elevation angle of the meter-wave MIMO radar in high-altitude mode. The present invention transplants dual carrier frequencies from conventional arrays to MIMO array radars, while improving the original dual carrier frequency algorithm, reducing the computational complexity by half. Simulation experiments demonstrate the effectiveness of the algorithm.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and in particular relates to a low elevation angle estimation method for a meter-wave MIMO radar high mountain mode based on dual carrier frequencies. Background Art

[0002] Meter-wave radar generally refers to radar operating in the meter-wave frequency band, typically VHF-band radar, which plays a vital role in air defense early warning. However, meter-wave radar is limited by its low frequency band, wide beamwidth, ground-skimming beam, and strong ground-reflected echo amplitude. Consequently, it encounters problems such as coherent multipath and low signal-to-noise ratio when detecting low-altitude targets. Ultimately, this results in poor elevation angle measurement accuracy, failing to meet guidance accuracy requirements. Therefore, low-elevation-angle target height measurement with meter-wave radar has long been a major issue in array radar signal processing.

[0003] Applying the MIMO system to meter-wave radars has attracted widespread attention in the study of DOA estimation for low-elevation-angle targets in meter-wave MIMO radars. Considering specular reflections from smooth surfaces on flat terrain, unlike conventional array radars, where one target corresponds to two reception paths, a MIMO radar corresponds to four transmission paths: transmitting a direct wave and receiving a direct wave; transmitting a direct wave and receiving a reflected wave; transmitting a reflected wave and receiving a direct wave; and transmitting a reflected wave and receiving a reflected wave. MIMO radar low-elevation-angle measurement can be divided into two categories: distributed MIMO radar and coherent MIMO radar. Currently, the main approaches for low-elevation-angle measurement in centralized MIMO radars include dimensionality reduction maximum likelihood estimation algorithms, generalized MUSIC, sparse representation, and lobe splitting. These research achievements have made significant contributions to MIMO radar. Other studies have explored low-elevation-angle measurement in undulating terrain, but these have not considered high-altitude terrain, a crucial aspect. This paper investigates low-elevation-angle target estimation in MIMO radars using high-altitude terrain. Summary of the Invention

[0004] To address the above problems, the present invention transplants dual-carrier frequency from conventional array to MIMO array radar, and improves the original dual-carrier frequency algorithm to reduce its computational complexity to half. The effectiveness of the algorithm of the present invention is demonstrated through simulation experiments.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A low elevation angle estimation method for high mountain mode of meter-wave MIMO radar based on dual carrier frequency, comprising:

[0007] Step 1: Assuming the MIMO radar is a co-located transmitter and receiver system, perform matched filtering on the MIMO radar's transmitted signal and perform vectorization on the data. Finally, the phase difference caused by the path difference between the MIMO radar's direct wave and reflected wave, as well as the radar received data, are obtained.

[0008] Step 2: Establish the maximum likelihood estimation criterion for calculating the spatial spectrum value;

[0009] Step 3: Based on the received data in step 1, the spatial spectrum value is calculated using the maximum likelihood estimation criterion in step 2, and the peak value of the spatial spectrum value is read. The maximum value is used as the estimated value of the low elevation angle of the meter-wave MIMO radar in the high mountain mode.

[0010] Preferably, the step 1 comprises:

[0011] Assume that the MIMO radar is a co-located transmitter-receiver system with M array elements and a vertical uniform linear array. The transmit signals are set to be orthogonal to each other. The low-elevation reflection area is a smooth flat reflective surface. The transmit signal is a horizontally polarized signal, and the steering vector of the transmit signal is the same as the steering vector of the receive signal. The transmit signal is matched filtered and the data is vectorized to obtain the following equation (1):

[0012]

[0013] Among them, θ d is the direct wave angle, θ s is the reflected wave angle, ρ h is the reflection coefficient of the horizontal polarization signal, β(τ) is the unknown complex reflection coefficient between different transmitted signals, and a t is the steering vector of the transmitted signal, a r is the steering vector of the received signal, e is a natural number, δ is the distance difference between the direct wave and the reflected wave, n is the noise signal, represents a complex set;

[0014] a in formula (1) t (θ) is the transmission signal array steering vector:

[0015] a t (θ)=[1,exp(-j2πdsin(θ) / λ),…,exp(-j2π(M-1)dsin(θ) / λ)] T (2)

[0016] Where d is the array element spacing, λ is the incident wavelength, θ is the unity of the direct wave angle and the reflected wave angle, and δ is:

[0017]

[0018] Among them, ha is the antenna height, h t is the target height, and R is the distance from the point where the target is vertically projected onto the ground to the radar.

[0019] Preferably, the step 2 is specifically as follows:

[0020] Step 2.1: Express the maximum likelihood estimation criterion of the spatial spectrum value and θ:

[0021]

[0022] Among them, f(θ) is the spatial spectrum value, is the maximum likelihood estimate of θ, A(θ) is the steering vector matrix, is the estimated value of the covariance matrix of the array output signal, P A(θ) is the projection matrix of the column vector space projected onto the steering vector matrix A(θ), P A(θ) The values ​​are:

[0023] P A(θ) =A(θ)[A H (θ)A(θ)] -1 A H (θ) (4)

[0024] Where, is the conjugate transpose of the steering vector matrix A(θ);

[0025] Step 2.2: Recombine the signal source and steering vector in the MIMO radar received data in equation (1) into the following equation:

[0026]

[0027] Then the received data in formula (1) can be written as follows:

[0028] z(τ)=a(θ)β(τ)+n(τ) (6)

[0029] in,

[0030] Therefore, for MIMO radar, θ=[θ d θ s ] are the direct wave and reflected wave of the target signal received by the MIMO radar.

[0031] A(θ)=a(θ),

[0032]

[0033] Among them, E is the mathematical expectation;

[0034] Step 2.3: The maximum likelihood estimation solution in equation (3) involves a two-dimensional nonlinear search. The mathematical relationship between the direct wave and the reflected wave is used to reduce the search dimension. The relationship is:

[0035] θ s = -arcsin(sinθ d +2h a / R) (7).

[0036] Preferably, the specific steps of step 3 are:

[0037] Step 3.1: When h a When ≤10m, the peak value of the spatial spectrum value f(θ) in formula (3) is the target low elevation angle estimation value;

[0038] Step 3.2: When the radar is in the high mountain mode, the maximum likelihood estimation criterion based on dual carrier frequency is used to calculate the low elevation angle estimate in the high mountain mode.

[0039] Preferably, the step 3.2 is specifically as follows:

[0040] Step 3.2.1: The MIMO radar transmits carrier frequency f1, and uses the corresponding received data to calculate a multi-peak spatial spectrum value using formula (3). At this time, the angle search range is 0-90°, and the multi-peak angle is extracted. As shown in the following formula:

[0041]

[0042] Step 3.2.2: The MIMO radar transmits carrier frequency f2, uses the corresponding received data, and converts the multi-peak angle of step 3.2.1 into Substitute into formula (3) again to calculate the spatial spectrum value f(n) corresponding to N angle points, and take the angle corresponding to the maximum spatial spectrum value As an estimate of the low elevation angle of the meter-wave MIMO radar in high mountain mode, the calculation is shown in the following formula:

[0043]

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present invention introduces a dual-carrier frequency height measurement method into meter-wave MIMO radar and proposes an improved method that can well estimate the angle of low-elevation-angle targets of meter-wave MIMO radar. Compared with the prior art, the dual-carrier frequency method of the present invention searches one less time than the original method; at the same time, the computational complexity of the dual-carrier frequency method is half of the original method. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0047] In the attached figure:

[0048] Figure 1 is a flow chart of the method of the present invention;

[0049] Figure 2 This is a schematic diagram of the angle estimation algorithm of the present invention;

[0050] Figure 3 The multi-peak spatial spectrum and e jδ Value periodic changes;

[0051] Figure 4 It is a dual-carrier spatial spectrum and the spatial spectrum of the present invention. DETAILED DESCRIPTION

[0052] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0053] Example:

[0054] Refer to the attached Figure 1-4 As shown, a low elevation angle estimation method for high mountain mode of meter-wave MIMO radar based on dual carrier frequency includes:

[0055] Step 1: Assuming that the MIMO radar is a co-located transmitter-receiver system, the MIMO radar's transmit signal is used to perform matched filtering and vectorize the data, and finally obtain the phase difference caused by the path difference between the direct wave and the reflected wave of the MIMO radar and the radar received data; Step 1 includes: assuming that the MIMO radar is a co-located transmitter-receiver system, its array has M elements, and the transmit array is a vertical uniform linear array. The MIMO radar is different from the traditional phased array radar in that the transmit signals are set to be orthogonal to each other. Assuming that the low-elevation-angle reflection area of ​​the MIMO radar system is a smooth and flat reflective surface, the transmit signal is a horizontally polarized signal, and the transmit and receive share the same antenna, that is, the transmit steering vector and the receive steering vector are the same; using the transmit signal to perform matched filtering on the above formula and vectorize the data (matched filtering is to multiply the receive data with the transmit signal, and vectorization is to arrange the matrix data into vector form by column), it can be obtained:

[0056]

[0057] Among them, θ d is the direct wave angle, θ s is the reflected wave angle, ρ his the reflection coefficient of the horizontal polarization signal, β(τ) is the unknown complex reflection coefficient between different transmitted signals, and a t is the steering vector of the transmitted signal, a r is the steering vector of the received signal, e is a natural number, δ is the distance difference between the direct wave and the reflected wave, n is the noise signal, represents a complex set;

[0058] a in formula (1) t (θ) is the transmission signal array steering vector:

[0059] a t (θ)=[1,exp(-j2πdsin(θ) / λ),…,exp(-j2π(M-1)dsin(θ) / λ)] T (2)

[0060] Where d is the array element spacing, λ is the incident wavelength, θ is the unity of the direct wave angle and the reflected wave angle, and δ is:

[0061]

[0062] Among them, h a is the antenna height, h t is the target height, and R is the distance from the target's vertical projection to the ground to the radar. The path difference is less than one range resolution unit, so the direct wave and the reflected wave cannot be distinguished in terms of distance. Assuming that the original noise is a zero-mean Gaussian random process, it can be obtained that after matched filtering and vectorization operations, the noise is still white noise. Different from the traditional signal mode, h a In flat terrain mode, half is a few meters, but in mountain mode, it may be hundreds of meters.

[0063] Step 2: Maximum likelihood estimation is one of the most commonly used and effective parameter estimation methods in array signal processing. Its parameter selection criteria indicate that this algorithm is not affected by inter-signal correlation. The specific derivation is based on existing techniques and will not be detailed here. Therefore, based on Step 1, the spatial spectrum value and maximum likelihood estimation are expressed as follows:

[0064] Step 2.1: Express the maximum likelihood estimation criterion of the spatial spectrum value and θ:

[0065]

[0066] Among them, f(θ) is the spatial spectrum value, is the maximum likelihood estimate of θ, A(θ) is the steering vector matrix, is the estimated value of the covariance matrix of the array output signal, P A(θ) is the projection matrix of the column vector space projected onto the steering vector matrix A(θ), PA(θ) The values ​​are:

[0067] P A(θ) =A(θ)[A H (θ)A(θ)] -1 A H (θ) (4)

[0068] Where, is the conjugate transpose of the steering vector matrix A(θ);

[0069] Step 2.2: Recombine the signal source and steering vector in the MIMO radar received data in equation (1) into the following equation:

[0070]

[0071] Then the received data in formula (1) can be written as follows:

[0072] z(τ)=a(θ)β(τ)+n(τ) (6)

[0073] in,

[0074] Therefore, for MIMO radar, θ=[θ d θ s ] are the direct wave and reflected wave of the target signal received by the MIMO radar.

[0075] A(θ)=a(θ),

[0076]

[0077] Among them, E is the mathematical expectation;

[0078] Step 2.3: The maximum likelihood estimation solution in equation (3) involves a two-dimensional nonlinear search. The mathematical relationship between the direct wave and the reflected wave is used to reduce the search dimension. The relationship is:

[0079] θ s = -arcsin(sinθ d +2h a / R) (7).

[0080] Step 3: Based on step 2, a dual-carrier frequency method is used to obtain the estimated value of the low elevation angle of the meter-wave MIMO radar in high mountain mode. The specific steps are:

[0081] Step 3.1: When h a When ≤10m, the peak value of the spatial spectrum value f(θ) in formula (3) is the target low elevation angle estimation value;

[0082] Step 3.2: Let ξ = e jδ, when the radar is in high mountain mode, when h a >10m, then A relatively large value directly causes ξ to exhibit periodic variations. In this case, the impact of ξ on angle estimation cannot be ignored, and the resulting spatial spectrum of the maximum likelihood steering vector algorithm will also exhibit periodic variations. Therefore, in addition to the spectral peak at the target, the steering vector synthesis algorithm will also periodically produce other false peaks. Without other prior information, it is impossible to distinguish the true target. Therefore, a dual-carrier frequency method is used to address the periodic ambiguity of the spatial spectrum value f(θ) in this mode. Specifically:

[0083] Step 3.2.1: The MIMO radar transmits carrier frequency f1, and uses the corresponding received data to calculate a multi-peak spatial spectrum value using formula (3). At this time, the angle search range is 0-90°, and the multi-peak angle is extracted. As shown in the following formula:

[0084]

[0085] Step 3.2.2: The MIMO radar transmits carrier frequency f2, uses the corresponding received data, and converts the multi-peak angle of step 3.2.1 into Substitute into formula (3) again to calculate the spatial spectrum value f(n) corresponding to N angle points, and take the angle corresponding to the maximum spatial spectrum value As an estimate of the low elevation angle of the meter-wave MIMO radar in high mountain mode, the calculation is shown in the following formula:

[0086]

[0087] in, Figure 2 Schematic diagram corresponding to steps 3.2.1 and 3.2.2.

[0088] Experimental simulation:

[0089] Consider the transmission array number M of the meter-wave MIMO array radar, which is 20, and the array element spacing is half a wavelength. The incident frequency 1 is 50 MHz, the incident wavelength λ is 6 meters, the incident frequency 2 is 60 MHz, the incident wavelength λ is 5 meters, the target direct wave angle is 3 degrees, and the reflection angle is calculated according to formula (7). The signal-to-noise ratio SNR is 10 dB, and the number of snapshots is 10. Among them, the antenna height h of the high mountain mode is a = 200 meters, target height h t = 5000 meters, set the freshwater scene, and then set the dielectric constant ε in the reflection coefficient r =75 and surface material conductivity σ e = 0.2. To ensure that the angle measurement is not ambiguous, the array element spacing is set to 2.5 meters. First, e jδThe periodic variation of the value, as well as the periodic spatial spectrum, such as Figure 3 As shown in this figure, the conclusion that multiple false peaks appear in the spatial spectrum is verified, and the change period of a and e are obtained. jδ The change cycles are not consistent. Figure 4 The spatial spectrum of the dual carrier frequency and the spatial spectrum of the proposed method are given. From the figure, we can clearly see the advantage of the proposed algorithm in terms of computational complexity, which is half of the existing algorithms.

[0090] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A low elevation angle estimation method for high mountain mode of meter-wave MIMO radar based on dual carrier frequency, characterized by: include: Step 1: Assuming the MIMO radar is a co-located transmitter and receiver system, perform matched filtering on the MIMO radar's transmitted signal and perform vectorization on the data. Finally, the phase difference caused by the path difference between the MIMO radar's direct wave and reflected wave, as well as the radar received data, are obtained. Step 2: Establish the maximum likelihood estimation criterion for calculating the spatial spectrum value; Step 2.1: Express the maximum likelihood estimation criterion for the spatial spectrum value and θ: Among them, f(θ) is the spatial spectrum value, is the maximum likelihood estimate of θ, A(θ) is the steering vector matrix, is the estimated value of the covariance matrix of the array output signal, P A(θ) is the projection matrix of the column vector space projected onto the steering vector matrix A(θ), P A(θ) The values ​​are: P A(θ) =A(θ)[A H (θ)A(θ)] -1 A H (i) (4) Among them, A H (θ) is the conjugate transpose of the steering vector matrix A(θ); Step 3: Based on the received data in step 1, the spatial spectrum value is calculated using the maximum likelihood estimation criterion in step 2, and the peak value of the spatial spectrum value is read. The maximum value among them is used as the estimated value of the low elevation angle of the meter-wave MIMO radar in the high mountain mode. The specific steps of step 3 are: Step 3.1: When h a When ≤10m, the peak value of the spatial spectrum value f(θ) in formula (3) is the target low elevation angle estimation value; where h a is the antenna height; Step 3.2: When the radar is in high mountain mode, the dual-carrier-frequency-based maximum likelihood estimation criterion is used to calculate the low elevation angle estimate in high mountain mode. Step 3.2 is as follows: Step 3.2.1: The MIMO radar transmits carrier frequency f1, and uses the corresponding received data to calculate a multi-peak spatial spectrum value using formula (3). At this time, the angle search range is 0-90°, and the multi-peak angle is extracted. n=1,...,N, as shown in the following formula: Step 3.2.2: The MIMO radar transmits carrier frequency f2, uses the corresponding received data, and converts the multi-peak angle of step 3.2.1 into Substitute n=1,...,N into formula (3) again to calculate the spatial spectrum value f(n) corresponding to N angle points, and take the angle corresponding to the maximum spatial spectrum value As an estimate of the low elevation angle of the meter-wave MIMO radar in high mountain mode, the calculation is shown in the following formula: in, Output the estimated covariance matrix of the signal to the array.

2. A method for estimating low elevation angles in a high-mountain mode of a meter-wave MIMO radar based on dual carrier frequency according to claim 1, characterized in that: The step 1 comprises: Assume that the MIMO radar is a co-located transmitter-receiver system with M array elements and a vertical uniform linear array. The transmit signals are set to be orthogonal to each other. The low-elevation-angle reflection area is a smooth flat reflective surface. The transmit signal is a horizontally polarized signal, and the steering vector of the transmit signal is the same as the steering vector of the receive signal. The transmit signal is matched filtered and vectorized to obtain the following equation (1): Among them, θ d is the direct wave angle, θ s is the reflected wave angle, ρ h is the reflection coefficient of the horizontal polarization signal, β(τ) is the unknown complex reflection coefficient between different transmitted signals, and a t is the steering vector of the transmitted signal, a r is the steering vector of the received signal, e is a natural number, δ is the distance difference between the direct wave and the reflected wave, n is the noise signal, represents a complex set; a in formula (1) t (θ) is the transmission signal array steering vector: a t (θ)=[1,exp(-j2πdsin(θ) / λ),…,exp(-j2π(M-1)dsin(θ) / λ)] T (2) Where d is the array element spacing, λ is the incident wavelength, θ is the unity of the direct wave angle and the reflected wave angle, and δ is: Among them, h t is the target height, and R is the distance from the point where the target is vertically projected onto the ground to the radar.

3. A method for estimating low elevation angles in a high-mountain mode of a meter-wave MIMO radar based on dual carrier frequency according to claim 2, characterized in that: The step 2 further comprises: Step 2.2: Recombine the target signal and the steering vector received by the MIMO radar in equation (1) into the following equation: Then the received signal data in formula (1) can be written as follows: z(τ)=a(θ)β(τ)+n(τ) (6) in, Therefore, for MIMO radar, θ=[θ d θ s ] are the direct wave and reflected wave of the target signal received by the MIMO radar, A(θ)=a(θ), Among them, E is the mathematical expectation; Step 2.3: The maximum likelihood estimation solution in equation (3) involves a two-dimensional nonlinear search. The mathematical relationship between the direct wave and the reflected wave is used to reduce the search dimension. The relationship is: <h2 style=";text-align:left;direction:ltr">θ<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> =-arcsin(sinθ<h2 style=";text-align:left;direction:ltr"> d <h2 style=";text-align:left;direction:ltr"> +2h<h2 style=";text-align:left;direction:ltr"> a <h2 style=";text-align:left;direction:ltr"> / R) (7)。

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