High-precision FMCW laser ranging method based on ESPRIT algorithm

Abstract

The invention discloses a high-precision FMCW laser ranging method based on an ESPRIT algorithm, and belongs to the technical field of laser ranging. Laser is divided into two beams through a light beam splitter, one beam serves as local oscillation light, the other beam serves as signal light, the signal light is emitted to a to-be-measured target object and returns, the signal light carries distance information of the to-be-measured target object, and the local oscillation light and the signal light obtain a difference frequency signal in an optical coupler; and the difference frequency signal is acquired through the photoelectric detector and the digital acquisition card in sequence. Constructing a Hankel matrix for the difference frequency signal, decomposing the Hankel Hankel matrix through a singular value decomposition method, and extracting a signal subspace; and decomposing according to the signal subspace to obtain a reversible matrix rotation operator, and optimizing the reversible matrix rotation operator to obtain a signal frequency so as to calculate the distance of the to-be-measured object. The method is simple in implementation mode, convenient to operate, high in practicability and suitable for application and popularization.

Description

Technical Field

[0001] The invention belongs to the technical field of laser ranging, and in particular relates to a high-precision FMCW laser ranging method based on an ESPRIT algorithm. Background Art

[0002] Frequency Modulated Continuous Wave (FMCW) laser ranging technology is non-contact, high-precision, automated, and stable. It measures distance by establishing a linear relationship between frequency and time and measuring changes in signal frequency. FMCW laser ranging combines laser radar with frequency modulated continuous wave ranging. It has the characteristics of simple ranging and speed measurement principles, strong weak signal detection capabilities, and high-precision single-point measurement capabilities.

[0003] At present, the main algorithm used for beat frequency signal extraction in FMCW laser ranging is FFT, but the FFT algorithm itself has problems such as poor resolution and low algorithm accuracy. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a high-precision FMCW laser ranging method based on the ESPRIT algorithm to achieve distance measurement for a target object.

[0005] The technical problem proposed by the present invention is solved in this way:

[0006] A high-precision FMCW laser ranging method based on ESPRIT algorithm is implemented based on a ranging system; the ranging system includes a tunable laser, an optical beam splitter, a three-port circulator, a collimating lens, an optical coupler, a balanced detector, a data acquisition card and a PC;

[0007] Step 1, the tunable laser light source emits laser light, which is divided into two beams through an optical beam splitter, respectively recorded as signal light and local oscillator light; the signal light passes through the first port and the second port of the three-port circulator in sequence, and then passes through the collimating lens to hit the target object to be measured, and returns through the collimating lens, the second port and the third port of the three-port circulator to form a reflected signal light; the reflected signal light and the local oscillator light generate a difference frequency signal in the optical coupler;

[0008] Step 2: The balanced detector detects the difference frequency signal and obtains the difference frequency data through the data acquisition card;

[0009] Step 3: The PC constructs a Hankel matrix based on the difference frequency data, performs singular value decomposition on the Hankel matrix and extracts the signal subspace;

[0010] Step 4: The PC decomposes the signal subspace and constructs a reversible matrix rotation operator; performs eigenvalue decomposition on the reversible matrix rotation operator to obtain the frequency estimation value of the difference frequency signal and the distance of the target object.

[0011] Furthermore, in step 1, the complex light field E of the local oscillator light r It is expressed as:

[0012]

[0013] Among them, A r is the signal amplitude of the local oscillator light, j is the symbol of the imaginary part, t represents time, B is the modulation bandwidth of the tunable laser, T m is the modulation period, f0 is the initial modulation frequency, is the initial phase.

[0014] Complex light field E of reflected signal light s It is expressed as:

[0015]

[0016] Among them, A s is the signal amplitude of the reflected signal light, and τ is the optical path time difference between the reflected signal light and the local oscillator light.

[0017] Furthermore, in the optical coupler of step 1, the local oscillator light and the reflected signal light are coupled to obtain a difference frequency signal I(τ, t), which is expressed as:

[0018]

[0019] Among them, the superscript * indicates conjugation;

[0020] Substituting equation (1) and equation (2) into equation (3), equation (3) is expressed as:

[0021]

[0022] Among them, I s and I r are the intensity of the signal light and the local oscillator light field respectively, | | represents the modulus;

[0023] In formula (3) If the term is ignored, then formula (4) can be expressed as:

[0024]

[0025] Furthermore, in step 2, the difference frequency signal is detected by a balanced detector, and the discrete difference frequency data is obtained through a digital acquisition card:

[0026]

[0027] Where I(n) represents the detected light intensity at the nth sampling point, 0≤n≤N-1, t s is the sampling period of the acquisition card, and N is the sampling window length.

[0028] Furthermore, in step 3, the discretized difference frequency data of equation (6) is used to construct an L×M Hankel matrix:

[0029]

[0030] In the above formula, M = N-L + 1, Indicates rounding down;

[0031] Perform singular value decomposition on Hankel:

[0032] H=USV (8)

[0033] Among them, U is an L×L square matrix, which is the left eigenvector of the Hankel matrix; V is an M×M square matrix, which is the right eigenvector of the Hankel matrix; S is an L×M matrix, whose diagonal elements are the Hankel matrix singular values ​​in descending order; extract the Hankel matrix singular values ​​that exceed the set threshold, and count the number of singular values ​​k;

[0034] Divide the matrix V into signal subspace V s ∈C 2k×M and the noise subspace V N ∈C (M-2k)×M .

[0035] Furthermore, in step 4, the matrix V s Decompose into two intersecting subspaces:

[0036]

[0037] Among them, V1 is the signal subspace V s The matrix obtained by removing the last row of elements, V2 is the signal subspace V s The matrix obtained by removing the first row of elements; construct a (M-1)×2k-order matrix ψ based on matrices V1 and V2 TLS Matrix rotation operators as reversible matrices:

[0038] ψ TLS =V1 -1 V2 (10)

[0039] For the matrix ψ TLS Perform eigenvalue decomposition to obtain the eigenvalue σ i , the frequency estimate of the difference frequency signal It is expressed as:

[0040]

[0041] Where i = 1, 2, ..., k, is the measured beat signal frequency corresponding to the collimating lens, is the beat signal frequency corresponding to the i-th space target object, arg represents the phase angle operation, f s is the sampling period of the digital acquisition card;

[0042] The relative distance of the i-th (i≠1) target object relative to the collimating lens:

[0043]

[0044] Where c is the speed of light and n0 is the refractive index of free space.

[0045] Furthermore, the wavelength of the tunable laser is λ=1550nm, the modulation bandwidth is B=1.508GHz, and the modulation frequency is F m =57KHz.

[0046] The beneficial effects of the present invention are:

[0047] (1) The method of the present invention innovatively uses the ESPRIT algorithm to process the FMCW difference frequency signal to obtain the relative distance of the detected object.

[0048] (2) The method described in the present invention uses the ESPRIT algorithm to realize the absolute distance measurement of the detected object, and has high accuracy, detection resolution and detection speed.

[0049] (3) The method described in the present invention is aimed at the ESPRIT algorithm, and provides relevant formulas for using the ESPRIT algorithm in FMCW laser ranging to achieve absolute distance measurement, thereby establishing the theoretical basis of the present invention.

[0050] (4) The method of the present invention is not only simple to implement and easy to operate, but also highly practical and suitable for popularization and use. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a schematic diagram of the process of the method of the present invention;

[0052] Figure 2 The optical path structure diagram of the method of the present invention;

[0053] Figure 3 It is a distribution diagram of eigenvalues ​​after singular value decomposition of the Hankel matrix in the method described in the embodiment;

[0054] Figure 4A frequency point diagram is obtained by calculating the characteristic value of the reversible rotation operator in the method described in the embodiment. DETAILED DESCRIPTION

[0055] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0056] This embodiment provides a high-precision FMCW laser ranging method based on the ESPRIT algorithm. Figure 1 As shown, the ESPRIT algorithm is used to process the difference frequency signal, so as to achieve the measurement of the target distance with high accuracy and very high ranging efficiency; the FMCW laser ranging method based on the ESPRIT algorithm described in this embodiment is not only simple to implement and easy to operate, but also has strong practicality and is suitable for popularization and use.

[0057] The method described in this embodiment adopts Figure 2 The structure shown in the figure is realized, and the structure specifically includes a tunable laser, an optical beam splitter, a three-port circulator, a collimating lens, an optical coupler, a balanced detector, a data acquisition card and a PC. The laser emitted by the tunable laser light source is divided into two beams of light by the optical beam splitter, which are respectively recorded as signal light and local oscillator light; the signal light passes through ports 1 and 2 of the three-port circulator in turn, and then passes through the collimating lens to hit the target to be measured, and then returns through the collimating lens, port 3 of the three-port circulator and the local oscillator light to couple in the optical coupler to generate a difference frequency signal, and the difference frequency signal is transmitted to the PC through the data acquisition card.

[0058] The specific process of the method described in this embodiment is:

[0059] Step 1: The optical beam splitter splits the linear tuning laser emitted by the tunable laser into two beams, one of which is the signal light and the other is the local oscillator light;

[0060] The signal light passes through ports 1 and 2 of the three-port circulator and the collimating lens to hit the target object to be measured, and returns along the original path through the collimating lens and port 3 of the three-port circulator, and couples with the local oscillator light in the optical coupler to generate a difference frequency signal.

[0061] The complex light field E of the local oscillator emitted by the light source in step 1 r It can be expressed as:

[0062]

[0063] Among them, A r is the optical signal amplitude, j is the imaginary part sign, t represents time, B is the modulation bandwidth of the tunable laser, T m is the modulation period, f0 is the initial modulation frequency, is the initial phase.

[0064] The signal light frequency modulation signal complex light field E received by the optical coupler after time τ and reflected from the surface of the object is s It can be expressed as:

[0065]

[0066] Among them, A s is the optical signal amplitude;

[0067] In step 1, the optical coupler couples the local oscillator light and the signal light to obtain a difference frequency signal I(τ, t), which is expressed as:

[0068]

[0069] The superscript * indicates conjugation;

[0070] Substituting (1) and (2) into (3), equation (3) can be expressed as:

[0071]

[0072] Among them, I s and I r are the intensity of the signal light and the local oscillator light field, respectively, and | | represents the modulus. In the ranging system, due to the extremely high propagation speed of light, the time difference τ caused by the optical path difference between the corresponding reference light signal and the measurement light signal is very small. In formula (4), the phase can be ignored, so equation (4) can be approximated as follows:

[0073]

[0074] Step 2: The difference frequency signal is measured by a balanced detector, and the difference frequency data is obtained through a data acquisition card.

[0075] In step 2, the signal of formula (5) is detected by the photoelectric detector, obtained by the digital acquisition card and discretized:

[0076]

[0077] Where I(n) represents the detected light intensity at sampling point n, t s is the sampling period of the acquisition card, and N is the sampling window length.

[0078] Step 3: construct a Hankel matrix based on the difference frequency data, perform singular value decomposition on the Hankel matrix and extract the signal subspace;

[0079] In step 3, the sampled signal of equation (6) is used to construct an L×M Hankel matrix, which is as follows:

[0080]

[0081] In the above formula, M = N-L + 1, Indicates rounding down;

[0082] Perform singular value decomposition on Hankel to obtain the left and right eigenvectors:

[0083]

[0084] Among them, U is an LxL square matrix, which is the left eigenvector of the Hankel matrix; V is an M×M square matrix, which is the right eigenvector of the Hankel matrix; S is an L×M matrix, whose diagonal elements are the singular values ​​of the Hankel matrix λ1~λ L Arrange in descending order; extract the singular values ​​of the matrix S that exceed the set threshold of 0.1, a total of k.

[0085] Divide the V matrix into signal subspace V according to k singular values s ∈C 2k×M and the noise subspace V N ∈C (M-2k)×M .

[0086] Step 4: Decompose the signal subspace, obtain the reversible matrix and matrix rotation operator, and optimize them to obtain the signal frequency and then the object distance.

[0087] V s Decompose into two intersecting subspaces:

[0088]

[0089] Among them, V1 and V2 are the signal subspace V s Remove the last row and the first row to get. Construct a (M-1)×2k-order matrix ψ from V1 and V2 TLS Matrix rotation operators as reversible matrices:

[0090] ψ TLS =V1 -1 V2 (10)

[0091] Perform eigenvalue decomposition on equation (10) to obtain the eigenvalue σ i (i=1,2...,k), then the frequency estimation value of the difference frequency signal is It can be expressed as:

[0092]

[0093] Wherein, the subscript i=1 represents the first target object, which is the number of the collimating lens; there are multiple target objects in the collimating lens-target object link, and the subscript i (i≠1) represents the number of each target object. is the measured beat signal frequency corresponding to the collimating lens, is the beat signal frequency corresponding to the i-th space target object, arg represents the phase angle operation, f s It is the sampling period of the acquisition card.

[0094] Therefore, according to formula (11), the relative distance of the i-th (i≠1) target object relative to the collimating lens can be measured:

[0095]

[0096] Where c is the speed of light and n0 is the refractive index of free space.

[0097] In this embodiment, the wavelength of the tunable laser is λ=1550nm, the modulation bandwidth is B=1.508GHz, and the modulation frequency is F m =57KHz, the distance between the detection target and the collimating lens is 25cm. In this embodiment, the eigenvalue distribution diagram after the singular value decomposition of the Hankel matrix is ​​as follows Figure 3 As shown, the frequency point diagram is obtained by calculating the characteristic value of the reversible rotation operator as shown in Figure 4 The measured frequency difference between the target and the collimating lens is Δf=575891.79 Hz, and the relative distance between the target and the collimating lens is Δd=0.2512441509 m, which is about 0.5% of the actual distance of 25 cm.

[0098] The present invention innovatively uses the ESPRIT algorithm to process the difference frequency signal in FMCW laser ranging, thereby realizing the measurement of the distance of the detection target with high accuracy and high ranging efficiency. The relevant formulas for using the ESPRIT algorithm to achieve ranging in FMCW laser ranging are innovatively given, namely, formula (1)-formula (12), which establish the theoretical basis of the present invention, have outstanding substantive characteristics and significant progress. The present invention is not only simple to implement and easy to operate, but also has strong practicality and is suitable for popularization and use.

[0099] The above embodiment is only one of the preferred implementation modes of the present invention and should not be used to limit the protection scope of the present invention. Any changes or modifications that are made to the main design concept and spirit of the present invention and have no substantive significance, and the technical problems they solve are still consistent with the present invention, should be included in the protection scope of the present invention.

Claims

1. A high-precision FMCW laser ranging method based on the ESPRIT algorithm, characterized in that: The distance measurement system is based on the realization of the system; the distance measurement system includes a tunable laser, an optical beam splitter, a three-port circulator, a collimating lens, an optical coupler, a balanced detector, a data acquisition card and a PC; Step 1, the tunable laser light source emits laser light, which is divided into two beams through an optical beam splitter, respectively recorded as signal light and local oscillator light; the signal light passes through the first port and the second port of the three-port circulator in sequence, and then passes through the collimating lens to hit the target object to be measured, and returns through the collimating lens, the second port and the third port of the three-port circulator to form a reflected signal light; the reflected signal light and the local oscillator light generate a difference frequency signal in the optical coupler; Step 2: The balanced detector detects the difference frequency signal and obtains the difference frequency data through the data acquisition card; Step 3: The PC constructs a Hankel matrix based on the difference frequency data, performs singular value decomposition on the Hankel matrix and extracts the signal subspace; Step 4: The PC decomposes the signal subspace and constructs a reversible matrix rotation operator; Perform eigenvalue decomposition on the reversible matrix rotation operator to obtain the frequency estimation value of the difference frequency signal and the distance of the target object.

2. The high-precision FMCW laser ranging method based on the ESPRIT algorithm according to claim 1 is characterized in that: In step 1, the complex light field E of the local oscillator light r It is expressed as: Among them, A r is the signal amplitude of the local oscillator light, j is the symbol of the imaginary part, t represents time, B is the modulation bandwidth of the tunable laser, T m is the modulation period, f0 is the initial modulation frequency, is the initial phase. Complex light field E of reflected signal light s It is expressed as: Among them, A s is the signal amplitude of the reflected signal light, and τ is the optical path time difference between the reflected signal light and the local oscillator light.

3. The high-precision FMCW laser ranging method based on the ESPRIT algorithm according to claim 2 is characterized in that: In the optical coupler of step 1, the local oscillator light and the reflected signal light are coupled to obtain a difference frequency signal I(τ, t), which is expressed as: The superscript * indicates conjugation; Substituting equation (1) and equation (2) into equation (3), equation (3) is expressed as: Among them, I s and I r are the intensity of the signal light and the local oscillator light field, respectively, and | | represents the modulus; In formula (3) If the term is ignored, then formula (4) can be expressed as:

4. The high-precision FMCW laser ranging method based on the ESPRIT algorithm according to claim 3 is characterized in that: In step 2, the difference frequency signal is detected by a balanced detector, and the discretized difference frequency data is obtained through a digital acquisition card: Where I(n) represents the detected light intensity at the nth sampling point, 0≤n≤N-1, t s is the sampling period of the acquisition card, and N is the sampling window length.

5. The high-precision FMCW laser ranging method based on the ESPRIT algorithm according to claim 4 is characterized in that: In step 3, the discretized difference frequency data of equation (6) is used to construct an L×M Hanke matrix: In the above formula, M = N-L + 1, Indicates rounding down; Perform singular value decomposition on Hankel: H=USV (8) Among them, U is an L×L square matrix, which is the left eigenvector of the Hankel matrix; V is an M×M square matrix, which is the right eigenvector of the Hankel matrix; S is an L×M matrix, whose diagonal elements are the Hankel matrix singular values ​​in descending order; extract the Hankel matrix singular values ​​that exceed the set threshold, and count the number of singular values ​​k; Divide the matrix V into signal subspace V s ∈C 2k×M and the noise subspace V N ∈C (M-2k)×M .

6. The high-precision FMCW laser ranging method based on the ESPRIT algorithm according to claim 5 is characterized in that: In step 4, the matrix V s Decompose into two intersecting subspaces: Among them, V1 is the signal subspace V s The matrix obtained by removing the last row of elements, V2 is the signal subspace V s The matrix obtained by removing the first row of elements; construct a (M-1)×2k-order matrix ψ based on matrices V1 and V2 TLS Matrix rotation operators as reversible matrices: ψ TLS =V1 -1 V2 (10) For the matrix ψ TLS Perform eigenvalue decomposition to obtain the eigenvalue σ i , the frequency estimate of the difference frequency signal It is expressed as: Where i = 1, 2, ..., k, is the measured beat signal frequency corresponding to the collimating lens, is the beat signal frequency corresponding to the i-th space target object, arg represents the phase angle operation, f s is the sampling period of the digital acquisition card; The relative distance of the i-th (i≠1) target object relative to the collimating lens: Where c is the speed of light and n0 is the refractive index of free space.

7. The high-precision FMCW laser ranging method based on the ESPRIT algorithm according to claim 1, characterized in that: The wavelength of the tunable laser is λ = 1550nm, the modulation bandwidth is B = 1.508GHz, and the modulation frequency is F m =57KHz.

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