A speed measurement method of Doppler microwave radar sensor using wavelet transform

By installing Doppler microwave radar sensors on the roadside and using wavelet transformation technology to process microwave signals, the existing vehicle speed detection methods are solved, and efficient and accurate vehicle speed detection is achieved.

CN114839625BActive Publication Date: 2025-04-01XIDIAN UNIV
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Patent Information

Application Number
CN202210405549.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-04-18
Publication Date
2025-04-01
Estimated Expiration
2042-04-18

AI Technical Summary

Technical Problem

The existing vehicle speed detection methods have high cost, difficulty in deployment and maintenance, and low detection accuracy, and are difficult to widely use in smart transportation.

Method used

Wavelet transformation technology is used to process the time-frequency domain of the microwave signal of the Doppler microwave radar sensor. By installing a single Doppler microwave radar sensor on the roadside, the microwave signal is sent in real time and the reflected signal is received, and the wavelet transformation is performed to calculate the vehicle speed.

Benefits of technology

The cost of vehicle speed detection is reduced, the efficiency and accuracy of detection is improved, and deployment and maintenance are relatively easy.

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Abstract

The present invention discloses a Doppler radar sensor speed measurement method using wavelet transform, which mainly solves the problems of difficult deployment, high cost and low accuracy of existing vehicle speed detection methods. The scheme is: a single Doppler microwave radar sensor is arranged on the roadside to calculate the Doppler microwave time domain output signal; wavelet transform is performed on the time domain output signal to convert the time domain output signal into a time-frequency domain image; binarization processing, open operation and soft threshold processing are sequentially performed on the time-frequency domain image to denoise; peak search is performed on the denoised image or the peak frequency f is obtained through the deployment parameters of the Doppler microwave radar sensor dm Or the frequency appearance time t of the time-frequency graph and the driving distance L1 and L2 of the left and right wheels of the vehicle through the detection range of the Doppler microwave radar sensor, and the speed of the moving vehicle is estimated based on these parameters. The present invention reduces the cost of vehicle speed detection, reduces the amount of calculation, improves the time resolution and frequency resolution, and can be applied to smart roads.
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Description

Technical Field

[0001] The invention belongs to the field of intelligent traffic technology, and further relates to a Doppler microwave radar sensor speed measurement method, which can be used for speed detection of motor vehicles to realize highway intelligence. Background Art

[0002] Traffic is a key factor affecting urban development. With the surge in the number of cars, modern cars have brought convenience to people, but also brought increasingly severe problems such as traffic jams and traffic accidents, which seriously affect the social and economic development of cities. The intelligentization of highways is the key to solving the above traffic problems and supporting the sustainable development of cities. As an important part of building a coordinated and integrated perception body of people, cars, roads, and networks, smart highways will be combined with intelligent driving technology to strongly support the application of autonomous driving and promote the construction of intelligent transportation. As an important part of smart highways, vehicle speed detection is widely used in the fields of intelligent assisted driving, intelligent monitoring, and intelligent traffic safety.

[0003] In the application scenario of smart highways, driving a motor vehicle exceeding the prescribed speed is one of the most serious road traffic violations and one of the important causes of road traffic accidents. Therefore, real-time monitoring of the speed of vehicles on the road and ensuring that the speed of motor vehicles is within a safe range are of great significance for preventing, reducing and controlling traffic violations and accidents caused by speeding. The motor vehicle speed measurement system is one of the most important devices for detecting whether a vehicle is speeding during driving. The speed measurement methods currently on the market mainly include speed measurement based on loop coils, speed measurement based on camera image processing, and radar speed measurement, among which;

[0004] The speed measurement method based on loop coil uses an inductor loop as a resonant circuit and places the loop coil in the road. When a vehicle passes by, the current in the loop coil changes, and the type and speed of the vehicle are determined by the strength of the current change. However, this solution requires the road to be closed during deployment and maintenance, and the loop coil sensor is large and needs to be deployed underground, which is extremely expensive.

[0005] Most speed measurement solutions based on video image processing use cameras, infrared signals, and light signals to collect images of passing vehicles, perform coordinate transformation on the images, and measure the vehicle speed based on the relationship between the distance moved by the pixels in the image and the elapsed time. The disadvantages of this solution are that, first of all, image processing is highly dependent on highly robust image calculation algorithms, and the detection success rate is extremely low in bad weather.

[0006] The speed measurement scheme based on radar is more inclined to judge the vehicle speed according to the difference of the received radar signal. There are three main schemes. One is that the current research proposes to use a pair of transmitter-receiver antennas to perform multi-path and multi-path identification detection at the same time. According to the characteristics of channel changes, the position, speed and type of the vehicle can be determined; the second is a scheme that uses the phase information of the target echo to cancel the clutter and measure the target speed; the third is to convert the received microwave signal to the frequency domain or time-frequency domain according to the difference of the spectrum diagram, and then calculate the vehicle speed. For the detection method based on microwave radar, the scheme of using a pair of transmitters for identification detection will have channel conflicts under high-density traffic conditions, resulting in erroneous detection results; the scheme using clutter cancellation is easily affected by the environment and has extremely high accuracy requirements; in the frequency domain monitoring schemes proposed in the current research, the time domain signal is converted to the frequency domain by short-time Fourier transform STFT, and then the vehicle speed is calculated, but the time resolution and frequency resolution of the STFT method are low, and the detection efficiency is not high.

[0007] The above methods result in that the current detection scheme cannot be widely used in smart transportation, and the accuracy of detection needs to be improved. Summary of the invention

[0008] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and to propose a speed measurement method using a Doppler microwave radar sensor using wavelet transform to reduce the speed measurement cost and improve the vehicle speed detection efficiency and accuracy.

[0009] The technical idea of ​​realizing the present invention is: by installing a single Doppler microwave radar sensor on the roadside, the installed Doppler microwave radar sensor sends microwave signals in real time, receives microwave signals reflected by vehicles, processes the received signals, performs wavelet transformation, and then measures the vehicle speed.

[0010] According to the above ideas, the technical solution of the present invention includes the following:

[0011] Technical solution 1:

[0012] 1. A Doppler microwave radar sensor speed measurement method using wavelet transform, characterized by comprising the following:

[0013] (1) Place the Doppler microwave radar sensor on the roadside;

[0014] (2) When a vehicle passes by, the Doppler microwave radar sensor receives the microwave signal reflected by the vehicle and obtains the Doppler frequency f according to the Doppler effect. d (t), according to the relationship between frequency and time domain signals, the Doppler microwave time domain signal X(t) is calculated;

[0015] (3) Performing time-frequency conversion on the output time-domain signal when the vehicle passes by, and transforming the Doppler microwave time-domain signal into a time-frequency domain image;

[0016] (4) De-noising the image transformed into the time-frequency domain:

[0017] (4a) Binarizing the image transformed into the video domain to remove environmental noise;

[0018] (4b) performing an opening operation on the binarized image to remove isolated high-frequency noise;

[0019] (4c) performing soft threshold processing on the image after the opening operation to remove low-frequency noise;

[0020] (5) Search the denoised image from top to bottom for its highest frequency. This highest frequency point is the peak frequency f of the Doppler microwave time-frequency domain signal. dm ;

[0021] (6) According to the peak frequency f dm Calculate the vehicle's speed v:

[0022]

[0023] Where c is the wave velocity of the Doppler microwave radar sensor, α is the deployment angle of the Doppler microwave radar sensor, θ is the horizontal beam angle of the Doppler microwave radar sensor, and f t is the transmitting frequency of the Doppler microwave radar sensor.

[0024] Technical solution 2:

[0025] 2. A Doppler microwave radar sensor speed measurement method using wavelet transform, characterized by comprising the following:

[0026] 1) Place the Doppler microwave radar sensor on the roadside unit;

[0027] 2) When a vehicle passes by, the Doppler microwave radar sensor receives the microwave signal reflected by the vehicle and calculates the Doppler frequency f according to the Doppler effect. d (t), according to the relationship between frequency and time domain signals, the Doppler microwave time domain signal X(t) is calculated;

[0028] 3) Perform time-frequency conversion on the output time domain signal when the vehicle passes by, and transform the Doppler microwave time domain signal into a time-frequency domain image;

[0029] 4) De-noising the image transformed to the time-frequency domain:

[0030] 4a) Binarizing the image transformed into the video domain to remove environmental noise;

[0031] 4b) performing an opening operation on the binarized image to remove isolated high-frequency noise;

[0032] 4c) performing soft threshold processing on the image after the opening operation to remove low-frequency noise;

[0033] 5) For the denoised time-frequency domain image, record the minimum time t1 of the highest frequency, the minimum time t2 of the lowest frequency, the maximum time t3 of the highest frequency, and the maximum time t4 of the lowest frequency;

[0034] 6) According to the deployment angle of the Doppler microwave radar sensor and the road width, calculate the driving distances L1 and L2 of the left and right wheels of the vehicle passing through the detection range of the Doppler microwave radar sensor;

[0035] 7) Calculate the vehicle's left wheel speed v1 and right wheel speed v2 based on the parameters obtained in 5) and 6):

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] 1. Low cost

[0038] In the existing speed measurement solutions using loop coils, a loop coil costs approximately 600 yuan on the market, and in the existing speed measurement solutions using video images, an infrared camera costs an average of 150 yuan.

[0039] The present invention adopts a Doppler microwave radar sensor to detect the vehicle speed. The price of the sensor is only 40 yuan, which reduces the speed measurement cost compared with the existing technology.

[0040] 2. Easy to deploy and maintain

[0041] The loop coil speed measurement solution and the camera image speed measurement solution used in the existing technology both need to be installed, deployed and maintained on the road, which seriously affects normal traffic during the deployment and maintenance period;

[0042] The deployment of the Doppler microwave radar sensor in the present invention only requires the Doppler microwave radar sensor to be deployed on the road side without construction in the road, and is easy to deploy and maintain.

[0043] 3. High speed detection accuracy

[0044] The existing frequency domain recognition schemes all use short-time Fourier transform (STFT), which results in low time resolution and frequency resolution, and poor speed measurement effect;

[0045] The present invention uses wavelet transform to process microwave signals in the time and frequency domain. Compared with the traditional short-time Fourier transform method, the wavelet transform is compressed at high frequency and the time window becomes narrower, thereby producing higher time resolution and frequency resolution, and then collecting complete vehicle passing frequency information; thus improving the accuracy of vehicle speed detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying any creative work.

[0047] Figure 1 This is a flow chart for implementing technical solution 1 of the present invention;

[0048] Figure 2 This is a flow chart for implementing technical solution 2 of the present invention;

[0049] Figure 3 It is a schematic diagram of the driving state of the vehicle in the present invention;

[0050] Figure 4 A vehicle driving model diagram in the present invention;

[0051] Figure 5 This is a time-frequency diagram for extracting the peak frequency and the time-frequency correspondence in the present invention. DETAILED DESCRIPTION

[0052] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0053] Embodiment 1

[0054] Reference Figure 1 , the implementation steps of this embodiment are as follows:

[0055] Step 1: Arrange a single Doppler microwave radar sensor on the roadside and calculate the Doppler microwave time domain signal X(t).

[0056] 1.1) Place the Doppler microwave radar sensor on either side of the road where the vehicle is traveling, and emit microwave signals in real time to form a detection range that can cover the entire width of the road, such as Figure 3 shown.

[0057] 1.2) When a vehicle passes by, the Doppler microwave radar sensor receives the microwave signal reflected by the vehicle and calculates the Doppler frequency f d (t):

[0058] Reference Figure 4When the vehicle moves at a constant speed v parallel to the roadside, the distance between the center of the vehicle head and the Doppler microwave radar sensor placed on the roadside is L, the vertical distance from the center of the vehicle head to the roadside is D, and the angle between the center of the vehicle head and the Doppler microwave radar sensor is α(t). When the vehicle just enters the detection range of the Doppler microwave radar sensor, the angle between the vehicle head and the Doppler microwave radar sensor is α(t1). According to the Doppler effect, the Doppler frequency f is obtained. d (t):

[0059]

[0060]

[0061] Where f0 represents the microwave frequency, c represents the wave speed,

[0062] 1.3) According to the Doppler frequency f d (t) to obtain the output time domain signal X(t), which is the reflected microwave signal of the receiving vehicle:

[0063] X(t)=A(t)sin(2πf d (t)t)

[0064] Where A(t) represents the signal peak.

[0065] Step 2: Perform time-frequency domain image conversion on the output time domain signal X(t) when the vehicle passes by.

[0066] The output time domain signal X(t) when the vehicle passes by is subjected to wavelet transform to obtain the Doppler microwave time domain signal transformed into a time-frequency domain image WT(a,τ) consisting of multiple sampling points with time as the horizontal axis and frequency as the vertical axis. The formula is as follows:

[0067]

[0068] Where a represents the scale parameter, τ represents the offset, ψ(t) is the wavelet basis function, and * is the dot multiplication operation.

[0069] Step 3: De-noise the image transformed into the time-frequency domain.

[0070] 3.1) Binarize the image transformed to the time-frequency domain to obtain the binary value η of the image after the binarization process H (w,λ), and for η H The image is fitted at the point where the (w,λ) value is 1, and the binary image F is obtained:

[0071] η H (w,λ)=1{|w|>λ}

[0072] η H(w,λ)=0{|w|<λ}

[0073]

[0074] Where w represents the frequency of the time-frequency domain image after wavelet transform, k represents the total number of samples, and η Hi (w,λ) represents the binary value corresponding to the i-th sampling point; λ represents the threshold frequency, whose value is the maximum value of the frequency collected when no vehicle passes by; when the frequency w collected when a vehicle passes by is greater than the threshold λ, η H (w,λ) is defined as 1. When the frequency w collected when the vehicle passes is less than the threshold λ, it is judged as environmental noise. H (w,λ) is defined as 0;

[0075] 3.2) Perform an opening operation on the binary image F:

[0076] After binarization, the environmental noise in the time-frequency domain image is eliminated, but there are still high-frequency noise and low-frequency noise in the time-frequency domain image. The time-frequency domain image is opened to remove the high-frequency noise.

[0077] The opening operation is to first perform an erosion operation on the binary image F, and then perform an expansion operation on it, wherein:

[0078] The corrosion operation formula is:

[0079] The expansion operation formula is:

[0080] In the formula, F represents the preprocessed image, b represents the structural element of morphological filtering, and D b represents the range of the structural element, the size of the structural element is the horizontal length of the detection range of the Doppler microwave radar sensor, (u,v) is the pixel coordinate of the preprocessed image, (u′,v′) is the pixel coordinate of the structural element, Θ represents the image corrosion operation, Represents the image dilation operation;

[0081] 3.3) Soft threshold processing:

[0082] After the opening operation, although the isolated high-frequency noise points in the time-frequency domain image are eliminated, low-frequency noise still exists in the time-frequency domain image, and it is necessary to use soft threshold denoising to remove the time-frequency domain image.

[0083] This example uses the soft threshold convex logarithmic probability function y as the denoising function to perform denoising on the time-frequency domain image after the opening operation, and obtains the processed image F':

[0084]

[0085]

[0086] Where a represents the soft threshold coefficient, f represents the signal frequency, and f max Represents the highest frequency of the signal;

[0087] This soft threshold function can be used to filter out low-frequency noise near zero frequency, and it also has a good denoising effect on low-frequency noise above 300 Hz.

[0088] Step 4: Calculate the vehicle speed v based on the denoised image.

[0089] The highest frequency of the denoised time-frequency domain image is searched from top to bottom. The highest frequency point found is the peak frequency f of the Doppler microwave time-frequency domain signal. dm ;

[0090] According to the peak frequency f dm Calculate the vehicle's speed v:

[0091]

[0092] Where c is the wave velocity of the Doppler microwave radar sensor, α is the deployment angle of the Doppler microwave radar sensor, θ is the horizontal beam angle of the Doppler microwave radar sensor, and f t is the transmitting frequency of the Doppler microwave radar sensor.

[0093] Embodiment 2

[0094] Reference Figure 2 , the implementation steps of this example are as follows:

[0095] Step A: a single Doppler microwave radar sensor is arranged on the road side to calculate the Doppler microwave time domain output signal X(t).

[0096] The specific implementation of this step is the same as step 1 in Example 1;

[0097] Step B: convert the output time domain signal X(t) when the vehicle passes by into a time-frequency domain image.

[0098] The specific implementation of this step is the same as step 2 in Example 1;

[0099] Step C: denoising the image transformed into the time-frequency domain.

[0100] The specific implementation of this step is the same as step 3 in Example 1;

[0101] Step D, calculating the vehicle speed v according to the denoised time-frequency domain image and the deployment parameters of the Doppler microwave radar sensor.

[0102] D1) Reference Figure 5 , search the denoised time-frequency domain image, and record the minimum time t1 of the highest frequency, the minimum time t2 of the lowest frequency, the maximum time t3 of the highest frequency, and the maximum time t4 of the lowest frequency;

[0103] D2) Reference Figure 4 , the vehicle is traveling horizontally with the shoulder, the sensor is deployed on the shoulder, and the driving distance L1 and L2 of the left and right wheels of the vehicle passing through the detection range of the Doppler microwave radar sensor are calculated:

[0104]

[0105] Where d is the road width, k is the vehicle width, θ is the deployment angle between the Doppler microwave radar sensor and the roadside, and β is the monitoring angle of the Doppler microwave radar sensor.

[0106] D3) Calculate the left wheel speed v1 and the right wheel speed v2 according to the parameters t1, t2, t3, t4 obtained in D1) and the parameters L1, L2 obtained in D2):

[0107]

[0108] D4) Calculate the vehicle speed v according to the left wheel speed v1 and the right wheel speed v2:

[0109]

[0110] The above descriptions are only two specific examples of the present invention and do not constitute any limitation to the present invention. Obviously, for professionals in this field, after understanding the content and principles of the present invention, it is possible to make various modifications and changes in form and details without departing from the principles and structures of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A Doppler microwave radar sensor speed measurement method using wavelet transform, characterized in that: These include: (1) Place the Doppler microwave radar sensor on the roadside; (2) When a vehicle passes by, the Doppler microwave radar sensor receives the microwave signal reflected by the vehicle and obtains the Doppler frequency f according to the Doppler effect. d (t), according to the relationship between frequency and time domain signals, the Doppler microwave time domain signal X(t) is calculated; (3) The output time domain signal when the vehicle passes by is converted into the time-frequency domain, and the Doppler microwave time domain signal is converted into a time-frequency domain image; specifically, the output time domain signal when the vehicle passes by is converted into a time-frequency domain image by wavelet transform, and the formula is as follows: Where a represents the scale parameter, τ represents the offset, ψ(t) is the wavelet basis function, and * is the dot multiplication operation; (4) De-noising the image transformed into the time-frequency domain: (4a) Binarizing the image transformed into the time-frequency domain to remove environmental noise; (4b) performing an opening operation on the binarized image to remove isolated high-frequency noise; (4c) performing soft threshold processing on the image after the opening operation to remove low-frequency noise; Specifically, the convex logarithmic probability function y on the soft threshold is selected as the denoising function to perform denoising processing, and the processed image F' is obtained: Among them, F represents the image after binarization, a' represents the soft threshold coefficient, f represents the signal frequency, and f max Represents the highest frequency of the signal; (5) Search the denoised image from top to bottom for its highest frequency. This highest frequency point is the peak frequency f of the Doppler microwave time-frequency domain signal. dm ; (6) According to the peak frequency f dm Calculate the vehicle's speed v: Where c is the wave velocity of the Doppler microwave radar sensor, α is the deployment angle of the Doppler microwave radar sensor, θ is the horizontal beam angle of the Doppler microwave radar sensor, and f t is the transmitting frequency of the Doppler microwave radar sensor.

2. The method according to claim 1, characterized in that The Doppler microwave radar sensor in (1) is placed on the roadside and is set at an angle of 30°-60° to the horizontal roadside.

3. The method according to claim 1, characterized in that The Doppler frequency f is obtained from (2) d (t), which is implemented as follows: 2a) Define the angle α(t) between the center of the vehicle head and the Doppler microwave radar sensor: Wherein, v represents the vehicle's speed, L represents the distance from the center of the vehicle head to the Doppler microwave radar sensor, D represents the vertical distance from the vehicle to the roadside, and α(t1) represents the angle between the center of the vehicle head and the Doppler microwave radar sensor when the vehicle enters the receiving range of the Doppler microwave radar sensor; 2b) According to the Doppler effect, the Doppler frequency f of the vehicle passing by is obtained d (t): Where f0 is the microwave frequency and c is the microwave wave speed.

4. The method according to claim 1, characterized in that: The Doppler microwave time domain signal X(t) is calculated by (2) as follows: X(t)=A(t)sin(2πf d (t)t) where f d (t) represents the Doppler frequency and A(t) represents the signal peak.

5. The method according to claim 1, characterized in that In (4a), the image transformed into the time-frequency domain is binarized, which is implemented as follows: 4a1) setting the Doppler frequency collected by the Doppler microwave radar sensor when no vehicle passes as the discrimination threshold λ; 4a2) Compare the signal frequency w collected by the Doppler microwave radar sensor when a car passes by with the threshold λ: If |w|>λ, then η H (w,λ)=1, If |w|<λ, then η H (w,λ)=0; where η H (w,λ) represents the binary value of the collected signal frequency after binarization processing; 4a3) for η H The image is fitted at the point where (w,λ) is 1, and the image F is obtained: Where k represents the total number of samples, η Hi (w,λ) represents the binary value corresponding to the i-th sampling point.

6. The method according to claim 1, characterized in that In (4b), the opening operation is performed on the binary image, which is implemented as follows: 4b1) Perform corrosion operation on the binary image, the formula is as follows: Among them, F represents the image after binarization, b represents the structural element of morphological filtering, and D b represents the range of the structural element, the size of the structural element is the horizontal length of the detection range of the Doppler microwave radar sensor, (u,v) is the pixel coordinate of the preprocessed image, (u′,v′) is the pixel coordinate of the structural element, Θ represents the image erosion operation; 4b2) Perform dilation operation on the image after corrosion operation, the formula is as follows: in, Represents an image dilation operation.

7. A Doppler microwave radar sensor speed measurement method using wavelet transform, characterized in that: These include: 1) Place the Doppler microwave radar sensor on the roadside unit; 2) When a vehicle passes by, the Doppler microwave radar sensor receives the microwave signal reflected by the vehicle and calculates the Doppler frequency f according to the Doppler effect. d (t), according to the relationship between frequency and time domain signals, the Doppler microwave time domain signal X(t) is calculated; 3) Perform time-frequency domain conversion on the output time domain signal when the vehicle passes by, and transform the Doppler microwave time domain signal into a time-frequency domain image; specifically, perform wavelet transform on the output time domain signal when the vehicle passes by, and convert it into a time-frequency domain image, the formula is as follows: Where a represents the scale parameter, τ represents the offset, ψ(t) is the wavelet basis function, and * is the dot multiplication operation; 4) De-noising the image transformed to the time-frequency domain: 4a) Binarizing the image transformed into the time-frequency domain to remove environmental noise; 4b) performing an opening operation on the binarized image to remove isolated high-frequency noise; 4c) performing soft threshold processing on the image after the opening operation to remove low-frequency noise; Specifically, the convex logarithmic probability function y on the soft threshold is selected as the denoising function to perform denoising processing, and the processed image F' is obtained: Among them, F represents the image after binarization, a' represents the soft threshold coefficient, f represents the signal frequency, and f max Represents the highest frequency of the signal; 5) For the denoised time-frequency domain image, record the minimum time t1 of the highest frequency, the minimum time t2 of the lowest frequency, the maximum time t3 of the highest frequency, and the maximum time t4 of the lowest frequency; 6) According to the deployment angle of the Doppler microwave radar sensor and the road width, calculate the driving distances L1 and L2 of the left and right wheels of the vehicle passing through the detection range of the Doppler microwave radar sensor; 7) Calculate the vehicle's left wheel speed v1 and right wheel speed v2 based on the parameters obtained in 5) and 6): 8) Calculate the vehicle speed v according to the left wheel speed v1 and the right wheel speed v2 in 7):

8. The method according to claim 7, characterized in that In the above 6), the travel distances L1 and L2 of the left and right wheels of the vehicle through the detection range of the Doppler microwave radar sensor are calculated using the following formula: Where d is the road width, k is the vehicle width, θ is the deployment angle between the Doppler microwave radar sensor and the roadside, and β is the monitoring angle of the Doppler microwave radar sensor.

Citation Information

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