A high-precision FMCW laser ranging method based on ESPRIT algorithm

Abstract

This invention discloses a high-precision FMCW laser ranging method based on the ESPRIT algorithm, belonging to the field of laser ranging technology. First, the laser beam is split into two beams by an optical beam splitter. One beam serves as the local oscillator beam, and the other as the signal beam. The signal beam hits the target object and returns, carrying the distance information of the target. The local oscillator beam and the signal beam are coupled in an optical coupler to obtain a difference frequency signal, which is then acquired by a photodetector and a digital acquisition card. A Hankel matrix is ​​constructed from the difference frequency signal. The Hankel matrix is ​​decomposed using singular value decomposition (SVD) to extract the signal subspace. Based on the decomposition of the signal subspace, an invertible matrix rotation operator is obtained and optimized to obtain the signal frequency, thereby calculating the distance to the target object. This invention is not only simple to implement and easy to operate, but also highly practical and suitable for widespread use.

Description

Technical Field

[0001] This invention belongs to the field of laser ranging technology, specifically relating to a high-precision FMCW laser ranging method based on the ESPRIT algorithm. Background Technology

[0002] Frequency Modulated Continuous Wave (FMCW) laser ranging technology is characterized by its non-contact nature, high precision, automation, and stability. It measures distance by establishing a linear relationship between frequency and time, and measuring changes in the signal frequency. FMCW laser ranging combines lidar with frequency-modulated continuous wave ranging, offering advantages such as simple ranging and velocity measurement principles, strong weak signal detection capabilities, and high-precision single-point measurement capabilities.

[0003] Currently, FMCW laser ranging mainly uses the FFT algorithm for extracting beat frequency signals, but the FFT algorithm itself has problems such as poor resolution and low algorithm accuracy. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a high-precision FMCW laser ranging method based on the ESPRIT algorithm to realize the distance measurement of target objects.

[0005] The technical problem addressed by this invention is solved as follows:

[0006] A high-precision FMCW laser ranging method based on the ESPRIT algorithm is implemented using a ranging system. The ranging system includes a tunable laser, a 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: A tunable laser source emits a laser beam, which is split into two beams by an optical beam splitter, denoted as the signal beam and the local oscillator beam, respectively. The signal beam passes through the first and second ports of a three-port circulator in sequence, then through a collimating lens to strike the target object. It then returns and passes through the collimating lens, the second port of the three-port circulator, and the third port to form a reflected signal beam. The reflected signal beam and the local oscillator beam generate a difference frequency signal in an 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 an invertible matrix rotation operator; the invertible matrix rotation operator is then subjected to eigenvalue decomposition to obtain the frequency estimate of the difference frequency signal and the distance to the target object.

[0011] Furthermore, in step 1, the complex optical field E of the local oscillator light... r Represented as:

[0012]

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

[0014] Complex optical field E of reflected signal light s Represented as:

[0015]

[0016] Among them, A s τ represents the 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 the difference frequency signal I(τ, t), which is expressed as:

[0018]

[0019] The superscript * indicates taking the conjugate;

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

[0021]

[0022] Among them, I s and I r These represent the light field intensities of the signal light and the local oscillator light, respectively, where || denotes the modulus.

[0023] In formula (3) If we ignore the term, then equation (4) can be expressed as:

[0024]

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

[0026]

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

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

[0029]

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

[0031] Singular value decomposition of Hankel:

[0032] H = USV (8)

[0033] Where 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 singular values ​​of the Hankel matrix arranged in descending order; extract the singular values ​​of the Hankel matrix that exceed a set threshold, and count the number of singular values ​​k.

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

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

[0036]

[0037] Where 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 elements of the first row; construct an (M-1)×2k matrix ψ based on matrices V1 and V2. TLS As a rotation operator for invertible matrices:

[0038] ψ TLS =V1 -1 V2 (10)

[0039] For matrix ψ TLS Eigenvalue decomposition yields eigenvalues ​​σ i Frequency estimation value of the difference frequency signal Represented as:

[0040]

[0041] Where i = 1, 2, ..., k, The measured beat frequency signal frequency corresponding to the collimating lens. Let f be the beat frequency signal frequency corresponding to the i-th spatial target object, arg represent the phase angle extraction operation, and f s The sampling period of the digital data acquisition card;

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

[0043]

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

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

[0046] The beneficial effects of this invention are:

[0047] (1) The method described in this invention innovatively uses the ESPRIT algorithm to process the FMCW difference frequency signal, thereby obtaining the relative distance of the detected object.

[0048] (2) The method described in this invention uses the ESPRIT algorithm to calculate the absolute distance to the object being detected, which has high accuracy, detection resolution and detection speed.

[0049] (3) The method described in this invention is for the ESPRIT algorithm, and gives the relevant formula for using the ESPRIT algorithm to realize absolute distance measurement in FMCW laser ranging, thus establishing the theoretical basis of this invention.

[0050] (4) The method described in this invention is not only simple to implement and easy to operate, but also highly practical and suitable for widespread use. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the method described in this invention;

[0052] Figure 2 This is a diagram of the optical path structure of the method described in this invention;

[0053] Figure 3 This is a graph showing the eigenvalue distribution of the Hankel matrix after singular value decomposition in the method described in the embodiment.

[0054] Figure 4The frequency point plot is obtained by calculating the eigenvalues ​​of the reversible rotation operator in the method described in the embodiment. Detailed Implementation

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

[0056] This embodiment provides a high-precision FMCW laser ranging method based on the ESPRIT algorithm, such as... Figure 1 As shown, the ESPRIT algorithm is used to process the difference frequency signal to achieve target distance measurement, which has 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 widespread use.

[0057] The method described in this embodiment employs, as follows: Figure 2 The structure shown is used to achieve this, specifically including 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 source is split into two beams by the optical beam splitter, denoted as the signal beam and the local oscillator beam, respectively. The signal beam passes sequentially through ports 1 and 2 of the three-port circulator, then through the collimating lens to strike the target under test. Returning, it couples with the local oscillator beam through the collimating lens, port 3 of the three-port circulator, and the local oscillator beam in the optical coupler to generate a difference frequency signal. This difference frequency signal is transmitted to the PC via the data acquisition card.

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

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

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

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

[0062]

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

[0064] In step 1, the optical coupler receives the frequency-modulated optical signal E reflected back from the object's surface after time τ. s It can be represented as:

[0065]

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

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

[0068]

[0069] The superscript * indicates taking the conjugate;

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

[0071]

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

[0073]

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

[0075] In step 2, the signal of equation (5) is detected by a photodetector, obtained by a digital acquisition card, and then discretized:

[0076]

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

[0078] Step 3: Construct the 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 from 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] Singular value decomposition of Hankel yields the left and right eigenvectors:

[0083]

[0084] Where U is an L×L square matrix, and V is the left eigenvector of the Hankel matrix; V is an M×M square matrix, and S is the right eigenvector of the Hankel matrix; S is an L×M matrix whose diagonal elements are the singular values ​​λ1 to λ2 of the Hankel matrix. L Sort in descending order; extract k singular values ​​of matrix S that exceed the set threshold of 0.1.

[0085] The V matrix is ​​divided into a signal subspace V based on the k singular values. s ∈C 2k×M and noise subspace V N ∈C (M-2k)×M .

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

[0087] For V s Decomposed into two intersecting subspaces:

[0088]

[0089] Where V1 and V2 are the signal subspaces V s The result is obtained by removing the last and first rows. A (M-1)×2k matrix ψ is constructed from V1 and V2. TLS As a rotation operator for invertible matrices:

[0090] ψ TLS =V1 -1 V2 (10)

[0091] Eigenvalue decomposition of equation (10) yields the eigenvalue σ. i (i = 1, 2, ..., k), then the frequency estimate of the difference frequency signal It can be represented as:

[0092]

[0093] Where the subscript i = 1 represents the first target object, which is the collimating lens number; 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. The measured beat frequency signal frequency corresponding to the collimating lens. Let f be the beat frequency signal frequency corresponding to the i-th spatial target object, arg represent the phase angle extraction operation, and f s This refers to the sampling cycle of the data acquisition card.

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

[0095]

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

[0097] In this embodiment, the tunable laser has a wavelength λ = 1550 nm, a modulation bandwidth B = 1.508 GHz, and a modulation frequency F. m =57KHz, the target detection distance from the collimating lens is 25cm. The eigenvalue distribution diagram after singular value decomposition of the Hankel matrix in this embodiment is as follows: Figure 3 As shown, the frequency point plot obtained by finding the eigenvalues ​​of the reversible rotation operator is as follows. Figure 4 As shown. 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. The error between this and the actual distance of 25 cm is approximately 0.5%.

[0098] This invention innovatively uses the ESPRIT algorithm to process the difference frequency signal in FMCW laser ranging, thereby achieving distance measurement of the detected target with high accuracy and high ranging efficiency. It also innovatively presents the relevant formulas for using the ESPRIT algorithm in FMCW laser ranging, namely equations (1)-(12), establishing the theoretical foundation of this invention and demonstrating significant substantive features and progress. This invention is not only simple to implement and easy to operate, but also highly practical and suitable for widespread use.

[0099] The above embodiments are merely one of the preferred embodiments of the present invention and should not be used to limit the scope of protection of the present invention. Any modifications or refinements made to the main design concept and spirit of the present invention that are not of substantial significance, but solve the same technical problem as the present invention, should be included within the scope of protection of the present invention.

Claims

1. A high-precision FMCW laser ranging method based on the ESPRIT algorithm, characterized in that, It is 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; Step 1: A tunable laser source emits a laser beam, which is split into two beams by an optical beam splitter, denoted as the signal beam and the local oscillator beam, respectively. The signal beam passes through the first and second ports of a three-port circulator in sequence, then through a collimating lens to strike the target object. It then returns and passes through the collimating lens, the second port of the three-port circulator, and the third port to form a reflected signal beam. The reflected signal beam and the local oscillator beam generate a difference frequency signal in an 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 an invertible matrix rotation operator; Eigenvalue decomposition is performed on the invertible matrix rotation operator to obtain the frequency estimate of the difference frequency signal and the distance to the target object.

2. The high-precision FMCW laser ranging method based on the ESPRIT algorithm according to claim 1, characterized in that, In step 1, the complex field E of the local oscillator light r Represented as: Among them, A r The signal amplitude of the local oscillator is given by j, where j is the imaginary part, t represents time, B is the modulation bandwidth of the tunable laser, and T is the signal amplitude of the local oscillator. m f0 is the modulation period, and f0 is the initial modulation frequency. This is the initial phase; Complex optical field E of reflected signal light s Represented as: Among them, A s τ represents the 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, characterized in that, In the optical coupler of step 1, the local oscillator light and the reflected signal light are coupled to obtain the difference frequency signal I(τ,t), which is expressed as: The superscript * indicates taking the conjugate; Substituting equations (1) and (2) into equation (3), equation (3) is expressed as: Among them, I s and I r These represent the light field intensities of the signal light and the local oscillator light, respectively, with || indicating the modulus. In formula (3) If we ignore the term, then equation (4) can be expressed as:

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

5. The high-precision FMCW laser ranging method based on the ESPRIT algorithm according to claim 4, characterized in that, In step 3, the discretized difference frequency data from equation (6) are used to construct an L×M Hankel matrix: In the above formula, M = N - L + 1, Indicates rounding down; Singular value decomposition of Hankel: H = USV (8) where U is an L×L square matrix and is the left eigenvector of the Hankel matrix; V is an M×M square matrix and 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 arranged in descending order; extract the singular values ​​of the Hankel matrix that exceed the set threshold and count the number of singular values ​​k. Divide matrix V into signal subspace V s ∈C 2k×M and 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, characterized in that, In step 4, matrix V s Decomposed into two intersecting subspaces: Where 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 elements of the first row; construct an (M-1)×2k matrix ψ based on matrices V1 and V2. TLS As a rotation operator for invertible matrices: ψ TLS =V1 -1 V2 (10) For matrix ψ TLS Eigenvalue decomposition yields eigenvalues ​​σ i Frequency estimation value of the difference frequency signal Represented as: Where i = 1, 2, ..., k, The measured beat frequency signal frequency corresponding to the collimating lens. Let f be the beat frequency signal frequency corresponding to the i-th spatial target object, arg represent the phase angle extraction operation, and f s The sampling period of the digital data acquisition card; The relative distance of the i-th target object with respect to the collimating lens: Where c is the speed of light and n0 represents the free space refractive index.

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

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