Speed and distance measuring method of zigzag linear frequency modulation continuous wave radar

Abstract

The invention discloses a speed and distance measuring method for a zigzag linear frequency modulation continuous wave radar, and the method specifically comprises the steps: enabling the radar to periodically transmit a zigzag linear frequency modulation continuous wave transmitting signal, and employing the instantaneous frequency difference value of the transmitting signal and an echo signal at the same time, calculating the radial speed and distance between the target and the radar according to the instantaneous frequency of the transmitting signal and the instantaneous frequency of the echo signal of the transmitting signal and the time difference when the instantaneous frequency of the transmitting signal is equal to the instantaneous frequency of the echo signal of the transmitting signal, and calculating the instantaneous frequency difference by adopting discrete Fourier transform of a difference signal of the transmitting signal and the echo signal of the transmitting signal in a specified time window; and calculating the time difference value by adopting a cross-correlation function of a transmitting signal and an echo signal thereof. Compared with an existing speed measurement and distance measurement method, the speed measurement and distance measurement method has higher speed measurement and distance measurement precision.

Description

Technical Field

[0001] The invention relates to the technical field of continuous wave radar speed and distance measurement, and in particular to a speed and distance measurement method of a sawtooth linear frequency modulation continuous wave radar. Background Art

[0002] According to the radar signal form, there are mainly pulse radar, continuous wave radar, pulse compression radar and frequency agile radar, among which continuous wave radar mainly includes non-modulated single frequency, non-modulated multi-frequency continuous wave radar and frequency modulated continuous wave (FMCW) radar. The most widely used frequency modulated continuous wave radar is linear frequency modulated continuous wave (LFMCW) radar. Commonly used linear frequency modulated continuous wave radars mainly include sawtooth linear frequency modulated continuous wave radar and triangle linear frequency modulated continuous wave radar.

[0003] For sawtooth linear frequency modulation continuous wave radar, the existing speed measurement method uses the Doppler frequency shift of the echo signal to calculate the radial velocity between the target and the radar. However, the Doppler frequency shift is closely related to the frequency of the transmitted signal. The higher the frequency of the transmitted signal, the greater the Doppler frequency shift. The sawtooth linear frequency modulation continuous wave transmission signal is a bandpass signal with rich frequency components. It is difficult to accurately calculate the Doppler frequency shift corresponding to each frequency component in engineering, resulting in low speed measurement accuracy of the existing speed measurement method.

[0004] For sawtooth linear frequency modulation continuous wave radar, the existing ranging method uses the delay of the echo signal to calculate the distance between the target and the radar. This requires calculating the moment when the instantaneous frequency of the echo signal jumps. However, calculating the instantaneous frequency requires a time window, which makes it difficult to accurately calculate the moment when the instantaneous frequency of the echo signal jumps in engineering, resulting in low ranging accuracy of the existing ranging method. Summary of the invention

[0005] The invention provides a speed and distance measuring method of a sawtooth linear frequency modulation continuous wave radar. Compared with the existing speed and distance measuring method, the speed and distance measuring method of the invention has higher speed and distance measuring accuracy.

[0006] A speed and distance measurement method for a sawtooth linear frequency modulation continuous wave radar, which specifically comprises: the radar periodically transmits a sawtooth linear frequency modulation continuous wave transmission signal, and uses the instantaneous frequency difference between the transmission signal and its echo signal at the same time, and the time difference when the instantaneous frequency of the transmission signal and the instantaneous frequency of the echo signal are equal to each other to calculate the radial speed and distance between the target and the radar, and uses the discrete Fourier transform of the difference signal between the transmission signal and its echo signal in a specified time window to calculate the instantaneous frequency difference, and uses the cross-correlation function of the transmission signal and its echo signal to calculate the time difference. The calculation formula of the radial speed between the target and the radar is as follows:

[0007]

[0008] The calculation formula of the distance between the target and the radar is as follows:

[0009]

[0010] Where v represents the radial velocity between the target and the radar, R represents the distance between the target and the radar, and c represents the speed of light. represents the frequency slope of the transmitted signal, f1 represents the lowest instantaneous frequency of the transmitted signal, f2 represents the highest instantaneous frequency of the transmitted signal, T represents the duration of the transmitted signal within one cycle, τ represents the time independent variable of the instantaneous frequency of the transmitted signal and its echo signal changing with time, Δf(τ) represents the instantaneous frequency difference between the transmitted signal and its echo signal at time τ, that is, Δf(τ)=f s (τ)-f r (τ), f s (τ) represents the instantaneous frequency of the transmitted signal at time τ, f r (τ) represents the instantaneous frequency of the echo signal at time τ, Δτ represents the time difference when the instantaneous frequency of the transmitted signal is equal to the instantaneous frequency of its echo signal, As known values, Δf(τ) and Δτ are calculated using the following method.

[0011] The Δf(τ) value can be calculated by using the discrete Fourier transform (DFT) of the difference signal between the transmitted signal and its echo signal in a specified time window centered on τ. The specific method is as follows:

[0012] Let t represent the time independent variable of the transmitted signal and its echo signal, s(t) represent the replica signal of the transmitted signal within a transmission cycle, and r(t) represent the echo signal of the transmitted signal within the same transmission cycle after being amplified by the receiver. Adjust the receiver amplification factor so that r(t) and s(t) have the same amplitude; d(t) represents the difference signal between s(t) and r(t) in a specified time window centered on τ, that is, where τ c represents half of the duration of the time window, and d(n) represents the digital signal obtained by sampling d(t) at equal intervals, then in represents the sampling time interval of s(t) and r(t), f s represents the sampling frequency of s(t) and r(t), f s The value of must meet the following conditions:

[0013]

[0014] Where B = f H -fL , f H Take the larger value of the highest cutoff frequency of s(t) and the highest cutoff frequency of r(t), f L Take the smaller value of the lowest cutoff frequency of s(t) and the lowest cutoff frequency of r(t), L represents The integer part of The decimal part of

[0015] Let D[k] represent the discrete Fourier transform (DFT) of d(n). The calculation formula of D[k] is as follows:

[0016]

[0017] Where N represents the number of sampling points of s(t) and r(t), and k represents the independent variable of D[k]. Represents the rotation factor of DFT. The value of N must meet the following conditions:

[0018]

[0019] The d(t) spectrum can be obtained from the calculation result D[k] of formula (8); LC Denote the lowest cutoff frequency of the d(t) spectrum, denoted by f HC Represents the highest cutoff frequency of the d(t) spectrum; since d(t) is also a linear frequency modulation signal, the calculation formula of Δf(τ) is as follows:

[0020]

[0021] The Δf(τ) value can also be calculated by using the discrete Fourier transform (DFT) of the difference signal between the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to its echo signal within a specified time window centered on τ. The specific method is as follows:

[0022] Let t represent the time independent variable of the transmitted signal and its echo signal, let s(t) represent the replica signal of the transmitted signal within a transmission cycle, let r(t) represent the echo signal of the transmitted signal within the same transmission cycle after being amplified by the receiver, and adjust the receiver amplification factor so that r(t) and s(t) have the same amplitude; represents the baseband signal obtained by down-converting s(t), then use represents the baseband signal obtained by down-conversion of r(t), then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; express and The difference signal within the specified time window centered on τ is where τc Represents half the duration of a specified time window centered on τ, with Express The digital signal obtained by equal-interval sampling is in represent The sampling time interval, The value of must meet the following conditions:

[0023]

[0024] where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency;

[0025] use express Discrete Fourier Transform (DFT), The calculation formula is as follows:

[0026]

[0027] Where N represents The number of sampling points, k represents The independent variable, Represents the rotation factor of DFT. The value of N must meet the following conditions:

[0028]

[0029] From the calculation results of formula (9) Available spectrum; use express The lowest cutoff frequency of the spectrum, express The highest cutoff frequency of the spectrum; due to It is also a linear frequency modulation signal, so the calculation formula of Δf(τ) is as follows:

[0030]

[0031] The Δτ value can be calculated by using the cross-correlation function between the transmitted signal and its echo signal. The specific method is as follows:

[0032] Let t represent the time independent variable of the transmitted signal and its echo signal, let s(t) represent the replica signal of the transmitted signal within a transmission cycle, let r(t) represent the echo signal of the transmitted signal within the same transmission cycle after being amplified by the receiver, adjust the receiver amplification factor so that r(t) has a certain amplitude, preferably r(t) and s(t) have the same amplitude; let s(n) represent the digital signal obtained by sampling s(t) at equal intervals, then Let r(n) represent the digital signal obtained by sampling r(t) at equal intervals. in represents the sampling time interval of s(t) and r(t), f s represents the sampling frequency of s(t) and r(t), f s The value of must meet the following conditions:

[0033]

[0034] Where B = f H -f L , f H Take the larger value of the highest cutoff frequency of s(t) and the highest cutoff frequency of r(t), f L Take the smaller value of the lowest cutoff frequency of s(t) and the lowest cutoff frequency of r(t), L represents The integer part of The decimal part of

[0035] Let x(m) represent the cross-correlation function of s(n) and r(n), m represents the independent variable of x(m), and x(m) is calculated based on the inverse discrete Fourier transform (IDFT). The specific algorithm is as follows:

[0036]

[0037] Where N represents the number of sampling points of s(t) and r(t), and k represents S[k] and R g [k] is the independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions:

[0038]

[0039] S[k] represents the discrete Fourier transform (DFT) of s(n). The calculation formula of S[k] is as follows:

[0040]

[0041] R g [k] represents r * (n) discrete Fourier transform (DFT), r *(n) represents the conjugate signal of r(n), the superscript “*” represents the conjugate operation, R g The calculation formula for [k] is as follows:

[0042]

[0043] in Represents the rotation factor of DFT;

[0044] The cross-correlation function x(m) calculated according to formula (10) is a function with a maximum peak value. M represents the m value corresponding to the maximum peak value of x(m). The calculation formula of Δτ is as follows:

[0045] Δτ=MT s .

[0046] The Δτ value can also be calculated by using the cross-correlation function between the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to its echo signal. The specific method is as follows:

[0047] Let t represent the time independent variable of the transmission signal and its echo signal, let s(t) represent the replica signal of the transmission signal in one transmission cycle, let r(t) represent the echo signal of the transmission signal in the same transmission cycle after being amplified by the receiver, adjust the receiver amplification factor so that r(t) has a certain amplitude, preferably r(t) and s(t) have the same amplitude; represents the baseband signal obtained by down-converting s(t), then use represents the baseband signal obtained by down-conversion of r(t), then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; Express The digital signal obtained by equal-interval sampling is use Express The digital signal obtained by equal-interval sampling is in represent The sampling time interval, The value of must meet the following conditions:

[0048]

[0049] where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency;

[0050] use express and The cross-correlation function, m represents The independent variable, The calculation is based on the inverse discrete Fourier transform (IDFT), and the specific algorithm is as follows:

[0051]

[0052] Where N represents The number of sampling points, k represents The independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions:

[0053]

[0054] represent The discrete Fourier transform (DFT) of The calculation formula is as follows:

[0055]

[0056] represent The discrete Fourier transform (DFT) of represent The conjugate signal of , the superscript “*” represents the conjugate operation, The calculation formula is as follows:

[0057]

[0058] in Represents the rotation factor of DFT;

[0059] The cross-correlation function calculated according to formula (11) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then the calculation formula of Δτ is as follows:

[0060]

[0061] The beneficial effects of the speed and distance measuring method of the present invention are as follows:

[0062] 1. From the analysis of the background technology, it can be seen that the existing speed and distance measurement methods have the problem of low speed and distance measurement accuracy. The present invention uses Δf(τ) and Δτ values ​​to calculate the radial speed and distance between the target and the radar. The calculation formula of the radial speed and distance between the target and the radar is given without any approximate processing in the derivation process, thereby theoretically ensuring the speed and distance measurement accuracy of the present invention.

[0063] 2. The present invention uses the discrete Fourier transform (DFT) of the difference signal between the transmitted signal and its echo signal in a specified time window to calculate the Δf(τ) value. Since the difference signal is also a linear frequency modulation signal, the Af(τ) value can be accurately calculated. The present invention uses the cross-correlation function between the transmitted signal and its echo signal to calculate the Δτ value. Since the cross-correlation function calculation makes full use of the transmitted signal and its echo signal in the entire cycle, the cross-correlation function can accurately calculate the Δτ value. Since the Δf(τ) and Δτ values ​​can be accurately calculated, the speed and distance measurement method of the present invention has higher speed and distance measurement accuracy compared with the existing speed and distance measurement methods.

[0064] 3. In the calculation formulas of Δf(τ) and Δτ of the present invention, all discrete Fourier transforms (DFT) can be calculated using fast Fourier transforms (FFT), and all inverse discrete Fourier transforms (IDFT) can be calculated using inverse fast Fourier transforms (IFFT). Therefore, the speed and distance measurement method of the present invention has the advantage of low calculation amount.

[0065] 4. The present invention can use the transmitted signal and its echo signal to calculate the Δf(τ) and Δτ values. In addition, the present invention can also use the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to the echo signal to calculate the Δf(τ) and Δτ values. Sampling the baseband signal reduces the performance requirements for the analog-to-digital converter (ADC) and is easier to implement in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0067] Figure 1 Schematic diagram of the instantaneous frequency of the transmitted signal and its echo signal changing with time

[0068] In the figure: 1 represents the curve of the instantaneous frequency of the transmitted signal changing with time; 2 represents the curve of the instantaneous frequency of the echo signal changing with time. DETAILED DESCRIPTION

[0069] The technical solution of the present invention is described clearly and completely below in conjunction with the accompanying drawings in the present invention. The following description is only a partial embodiment of the present invention, not all embodiments. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative work belong to the protection scope of the present invention.

[0070] A method for measuring speed and distance using a sawtooth linear frequency modulation continuous wave radar, referring to Figure 1 The radar periodically transmits a sawtooth linear frequency modulation continuous wave transmission signal, and uses the instantaneous frequency difference between the transmission signal and its echo signal at the same time, and the time difference when the instantaneous frequency of the transmission signal is equal to the instantaneous frequency of its echo signal to calculate the radial velocity and distance between the target and the radar, and uses the discrete Fourier transform of the difference signal between the transmission signal and its echo signal in a specified time window to calculate the instantaneous frequency difference, and uses the cross-correlation function of the transmission signal and its echo signal to calculate the time difference. The specific method is as follows:

[0071] Let t represent the time independent variable of the transmitted signal and its echo signal, let τ represent the time independent variable of the instantaneous frequency of the transmitted signal and its echo signal changing with time, let s(t) represent the replica signal of the transmitted signal within a transmission cycle, and s(t) is represented by the following formula:

[0072]

[0073] in represents the frequency slope of s(t), f1 represents the lowest instantaneous frequency of the transmitted signal, f2 represents the highest instantaneous frequency of the transmitted signal, T represents the duration of the transmitted signal in one cycle, j represents an imaginary unit, 0≤t, τ≤T represents 0≤t≤T and 0≤τ≤T (hereinafter similar expressions have the same meaning);

[0074] Use f s (τ) represents the instantaneous frequency of s(t) at time τ. From formula (1), we can see that f s (τ) is expressed by the following formula:

[0075]

[0076] R represents the distance between the target and the radar, v represents the radial velocity between the target and the radar, c represents the speed of light, and r(t) represents the echo signal of the transmitted signal in the same transmission cycle after being amplified by the receiver. Without loss of generality, the echo signal r(t) and s(t) after being amplified by the receiver have the same amplitude. Considering that r(t) is mainly composed of the delayed signal of s(t), r(t) is expressed by the following formula:

[0077]

[0078] Use f r (τ) represents the instantaneous frequency of r(t) at time τ. From formula (3), we can see that f r (τ) is expressed by the following formula:

[0079]

[0080] Δf(τ) represents the instantaneous frequency difference between the transmitted signal and its echo signal at time τ, that is, Δf(τ) = f s (τ)-f r (τ); Subtracting equation (4) from equation (2) yields the following relationship:

[0081]

[0082] Δτ represents the time difference when the instantaneous frequency of the transmitted signal is equal to the instantaneous frequency of its echo signal, and f r (τ+Δτ) represents the instantaneous frequency of r(t) at the moment τ+Δτ; when f r (τ+Δτ)=f s (τ), according to equation (2) and equation (4), we get the following relationship:

[0083]

[0084] Subtracting equation (6) from equation (5) yields the following calculation formula for the radial velocity v between the target and the radar:

[0085]

[0086] Substituting formula (7) into formula (5), the calculation formula for the distance R between the target and the radar is as follows:

[0087]

[0088] Where c, K, f s (τ) is a known value, and Δf(τ) and Δτ are calculated using the following method.

[0089] The Δf(τ) value can be calculated by using the discrete Fourier transform (DFT) of the difference signal between the transmitted signal and its echo signal in a specified time window centered on τ. The specific method is as follows:

[0090] Adjust the receiver gain so that r(t) and s(t) have the same amplitude; use d(t) to represent the difference signal between s(t) and r(t) in a specified time window centered on τ, that is, where τ c represents half of the duration of the time window, and d(n) represents the digital signal obtained by sampling d(t) at equal intervals, then in represents the sampling time interval of s(t) and r(t), f s represents the sampling frequency of s(t) and r(t), f s The value of must meet the following conditions:

[0091]

[0092] Where B = f H -f L , f H Take the larger value of the highest cutoff frequency of s(t) and the highest cutoff frequency of r(t), f L Take the smaller value of the lowest cutoff frequency of s(t) and the lowest cutoff frequency of r(t), L represents The integer part of The decimal part of

[0093] Let D[k] represent the discrete Fourier transform (DFT) of d(n). The calculation formula of D[k] is as follows:

[0094]

[0095] Where N represents the number of sampling points of s(t) and r(t), and k represents the independent variable of D[k]. Represents the rotation factor of DFT. The value of N must meet the following conditions:

[0096]

[0097] From the physical meaning of DFT, we know that D[k] represents the spectrum of d(n), and d(n) represents the digital signal obtained by sampling d(t) at equal intervals. Therefore, the spectrum of d(t) can be obtained from the calculation result D[k] of formula (8); LC Denote the lowest cutoff frequency of the d(t) spectrum, denoted by f HC Represents the highest cutoff frequency of the d(t) spectrum; since d(t) is also a linear frequency modulation signal, the calculation formula of Δf(τ) is as follows:

[0098]

[0099] The Δf(τ) value can also be calculated by using the discrete Fourier transform (DFT) of the difference signal between the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to its echo signal within a specified time window centered on τ. The specific method is as follows:

[0100] Adjust the receiver gain so that r(t) and s(t) have the same amplitude; use represents the baseband signal obtained by down-converting s(t), then use represents the baseband signal obtained by down-conversion of r(t), then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; express and The difference signal within a specified time window centered at τ,

[0101] Right now where τ c Represents half the duration of a specified time window centered on τ, with Express The digital signal obtained by sampling at equal intervals is

[0102] but in represent The sampling time interval, The value of must meet the following conditions:

[0103]

[0104] where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency;

[0105] use express Discrete Fourier Transform (DFT), The calculation formula is as follows:

[0106]

[0107] Where N represents The number of sampling points, k represents The independent variable, Represents the rotation factor of DFT. The value of N must meet the following conditions:

[0108]

[0109] From the physical meaning of DFT, we can know that represent spectrum, and Representatives The digital signal obtained by equal-interval sampling is: Available spectrum; use express The lowest cutoff frequency of the spectrum, express The highest cutoff frequency of the spectrum; due to It is also a linear frequency modulation signal, so the calculation formula of Δf(τ) is as follows:

[0110]

[0111] The Δτ value can be calculated by using the cross-correlation function between the transmitted signal and its echo signal. The specific method is as follows:

[0112] Adjust the receiver gain so that r(t) has a certain amplitude, preferably r(t) and s(t) have the same amplitude; s(n) represents the digital signal obtained by sampling s(t) at equal intervals, then Let r(n) represent the digital signal obtained by sampling r(t) at equal intervals. in represents the sampling time interval of s(t) and r(t), f s represents the sampling frequency of s(t) and r(t), f s The value of must meet the following conditions:

[0113]

[0114] Where B = f H -f L , f H Take the larger value of the highest cutoff frequency of s(t) and the highest cutoff frequency of r(t), f L Take the smaller value of the lowest cutoff frequency of s(t) and the lowest cutoff frequency of r(t), : represents The integer part of The decimal part of

[0115] Let x(m) represent the cross-correlation function of s(n) and r(n), m represents the independent variable of x(m), and x(m) is calculated based on the inverse discrete Fourier transform (IDFT). The specific algorithm is as follows:

[0116]

[0117] Where N represents the number of sampling points of s(t) and r(t), and k represents S[k] and R g [k] is the independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions:

[0118]

[0119] S[k] represents the discrete Fourier transform (DFT) of s(n). The calculation formula of S[k] is as follows:

[0120]

[0121] R g [k] represents r * (n) discrete Fourier transform (DFT), r * (n) represents the conjugate signal of r(n), the superscript “*” represents the conjugate operation, R g The calculation formula for [k] is as follows:

[0122]

[0123] in Represents the rotation factor of DFT;

[0124] The cross-correlation function x(m) calculated according to formula (10) is a function with a maximum peak value. M represents the m value corresponding to the maximum peak value of x(m). The calculation formula of Δτ is as follows:

[0125] Δτ=MT s .

[0126] The Δτ value can also be calculated by using the cross-correlation function between the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to its echo signal. The specific method is as follows:

[0127] Adjust the receiver gain so that r(t) has a certain amplitude, preferably r(t) and s(t) have the same amplitude; use represents the baseband signal obtained by down-converting s(t), then use represents the baseband signal obtained by down-conversion of r(t), then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; Express The digital signal obtained by equal-interval sampling is use Express The digital signal obtained by equal-interval sampling is in represent The sampling time interval, The value of must meet the following conditions:

[0128]

[0129] where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency;

[0130] use express and The cross-correlation function, m represents The independent variable, The calculation is based on the inverse discrete Fourier transform (IDFT), and the specific algorithm is as follows:

[0131]

[0132] Where N represents The number of sampling points, k represents The independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions:

[0133]

[0134] represent The discrete Fourier transform (DFT) of The calculation formula is as follows:

[0135]

[0136] represent The discrete Fourier transform (DFT) of represent The conjugate signal of , the superscript “*” represents the conjugate operation, The calculation formula is as follows:

[0137]

[0138] in Represents the rotation factor of DFT;

[0139] The cross-correlation function calculated according to formula (11) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, the calculation formula of Δr is as follows:

[0140]

[0141] The above embodiments specifically illustrate the contents of the present invention, but the present invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the concept of the present invention, and these equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A speed measurement method using a sawtooth linear frequency modulation continuous wave radar, characterized in that: The radar periodically transmits a sawtooth linear frequency modulation continuous wave transmission signal, and uses the instantaneous frequency difference between the transmission signal and its echo signal at the same time, as well as the time difference when the instantaneous frequency of the transmission signal is equal to the instantaneous frequency of its echo signal to calculate the radial velocity between the target and the radar. The specific calculation formula is as follows: Where v represents the radial velocity between the target and the radar, c represents the speed of light, represents the frequency slope of the transmitted signal, f1 represents the lowest instantaneous frequency of the transmitted signal, f2 represents the highest instantaneous frequency of the transmitted signal, T represents the duration of the transmitted signal within one cycle, τ represents the time independent variable of the instantaneous frequency of the transmitted signal and its echo signal changing with time, Δf(τ) represents the instantaneous frequency difference between the transmitted signal and its echo signal at time τ, and Δτ represents the time difference when the instantaneous frequency of the transmitted signal is equal to the instantaneous frequency of its echo signal.

2. The speed measurement method of sawtooth linear frequency modulation continuous wave radar according to claim 1, characterized in that: The Δf(τ) value is calculated by using the discrete Fourier transform of the difference signal between the transmitted signal and its echo signal in a specified time window centered on τ. The specific method is as follows: Let s(t) represent the replica signal of the transmitted signal within a transmission cycle, and let r(t) represent the echo signal of the transmitted signal within the same transmission cycle after being amplified by the receiver. Adjust the receiver amplification factor so that r(t) and s(t) have the same amplitude; let d(t) represent the difference signal between s(t) and r(t) in a specified time window centered on τ, that is, where τ c represents half of the duration of the time window, and d(n) represents the digital signal obtained by sampling d(t) at equal intervals, then in represents the sampling time interval of s(t) and r(t), f s represents the sampling frequency of s(t) and r(t), f s The value of must meet the following conditions: Where B = f H -f L , f H Take the larger value of the highest cutoff frequency of s(t) and the highest cutoff frequency of r(t), f L Take the smaller value of the lowest cutoff frequency of s(t) and the lowest cutoff frequency of r(t), L represents The integer part of The decimal part of Let D[k] represent the discrete Fourier transform (DFT) of d(n). The calculation formula of D[k] is as follows: Where N represents the number of sampling points of s(t) and r(t), Represents the rotation factor of DFT. The value of N must meet the following conditions: From the calculation result D[k] of formula (8), we can get the d(t) spectrum, which can be expressed as f LC Denote the lowest cutoff frequency of the d(t) spectrum, denoted by f HC represents the highest cutoff frequency of the d(t) spectrum, then the calculation formula of Δf(τ) is as follows:

3. The speed measurement method of sawtooth linear frequency modulation continuous wave radar according to claim 1, characterized in that: The Δf(τ) value is calculated by using the discrete Fourier transform of the difference signal of the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to the echo signal within a specified time window centered on τ. The specific method is as follows: Let s(t) represent the replica signal of the transmitted signal in a transmission cycle, and let r(t) represent the echo signal of the transmitted signal in the same transmission cycle after being amplified by the receiver. Adjust the receiver amplification factor so that r(t) and s(t) have the same amplitude. represents the baseband signal obtained by down-converting s(t), then use represents the baseband signal obtained by down-conversion of r(t), then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; express and The difference signal within a specified time window centered at τ, Right now where τ c Represents half the duration of a specified time window centered on τ, with Express The digital signal obtained by sampling at equal intervals is but in represent The sampling time interval, The value of must meet the following conditions: where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency; use express Discrete Fourier Transform (DFT), The calculation formula is as follows: Where N represents The number of sampling points, Represents the rotation factor of DFT. The value of N must meet the following conditions: From the calculation results of formula (9) Available Spectrum, with express The lowest cutoff frequency of the spectrum, express The highest cutoff frequency of the spectrum, then the calculation formula of Δf(τ) is as follows:

4. The speed measurement method of the sawtooth linear frequency modulation continuous wave radar according to any one of claims 1 to 3, characterized in that: The cross-correlation function between the transmitted signal and its echo signal is used to calculate the Δτ value. The specific method is as follows: Let s(t) represent the replica signal of the transmitted signal in a transmission cycle, r(t) represent the echo signal of the transmitted signal in the same transmission cycle after being amplified by the receiver, and s(n) represent the digital signal obtained by sampling s(t) at equal intervals. Then Let r(n) represent the digital signal obtained by sampling r(t) at equal intervals. in represents the sampling time interval of s(t) and r(t), f s represents the sampling frequency of s(t) and r(t), f s The value of must meet the following conditions: Where B = f H -f L , f H Take the larger value of the highest cutoff frequency of s(t) and the highest cutoff frequency of r(t), f L Take the smaller value of the lowest cutoff frequency of s(t) and the lowest cutoff frequency of r(t), L represents The integer part of The decimal part of Let x(m) represent the cross-correlation function of s(n) and T(n), m represents the independent variable of x(m), and x(m) is calculated based on the inverse discrete Fourier transform (IDFT). The specific algorithm is as follows: Where N represents the number of sampling points of s(t) and r(t), and k represents S[k] and R g [k] is the independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions: S[k] represents the discrete Fourier transform (DFT) of s(n). The calculation formula of S[k] is as follows: R g [k] represents r * (n) discrete Fourier transform (DFT), r * (n) represents the conjugate signal of r(n), the superscript "*" represents the conjugate operation, R g The calculation formula for [k] is as follows: in Represents the rotation factor of DFT; The cross-correlation function x(m) calculated according to formula (10) is a function with a maximum peak value. M represents the m value corresponding to the maximum peak value of x(m). The calculation formula of Δτ is as follows: Δτ=MT s 。 5. The speed measurement method of the sawtooth linear frequency modulation continuous wave radar according to any one of claims 1 to 3, characterized in that: The Δτ value is calculated by using the cross-correlation function of the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to its echo signal. The specific method is as follows: Let s(t) represent the replica signal of the transmitted signal in a transmission cycle, r(t) represent the echo signal of the transmitted signal in the same transmission cycle after being amplified by the receiver, and represents the baseband signal obtained by down-converting s(t), then use represents the baseband signal obtained by down-conversion of r(t), then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; Express The digital signal obtained by equal-interval sampling is use Express The digital signal obtained by equal-interval sampling is in represent The sampling time interval, The value of must meet the following conditions: where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency; use express and The cross-correlation function, m represents The independent variable, The calculation is based on the inverse discrete Fourier transform (IDFT), and the specific algorithm is as follows: Where N represents The number of sampling points, k represents The independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions: represent The discrete Fourier transform (DFT) of The calculation formula is as follows: represent The discrete Fourier transform (DFT) of represent The conjugate signal of , the superscript "*" represents the conjugate operation, The calculation formula is as follows: in Represents the rotation factor of DFT; The cross-correlation function calculated according to formula (11) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then the calculation formula of Δτ is as follows:

6. A ranging method for a sawtooth linear frequency modulation continuous wave radar, characterized in that: The radar periodically transmits a sawtooth linear frequency modulation continuous wave transmission signal, and uses the instantaneous frequency difference between the transmission signal and its echo signal at the same time, as well as the time difference when the instantaneous frequency of the transmission signal is equal to the instantaneous frequency of its echo signal to calculate the distance between the target and the radar. The specific calculation formula is as follows: Where R represents the distance between the target and the radar, c represents the speed of light, represents the frequency slope of the transmitted signal, f1 represents the lowest instantaneous frequency of the transmitted signal, f2 represents the highest instantaneous frequency of the transmitted signal, T represents the duration of the transmitted signal within one cycle, τ represents the time independent variable of the instantaneous frequency of the transmitted signal and its echo signal changing with time, represents the instantaneous frequency of the transmitted signal at time τ, Δf(τ) represents the instantaneous frequency difference between the transmitted signal and its echo signal at time τ, and Δτ represents the time difference when the instantaneous frequency of the transmitted signal is equal to the instantaneous frequency of its echo signal.

7. The ranging method of sawtooth linear frequency modulation continuous wave radar according to claim 6, characterized in that: The Δf(τ) value is calculated by using the discrete Fourier transform of the difference signal between the transmitted signal and its echo signal in a specified time window centered on τ. The specific method is as follows: Let s(t) represent the replica signal of the transmitted signal within a transmission cycle, and let r(t) represent the echo signal of the transmitted signal within the same transmission cycle after being amplified by the receiver. Adjust the receiver amplification factor so that r(t) and s(t) have the same amplitude; let d(t) represent the difference signal between s(t) and r(t) in a specified time window centered on τ, that is, where τ c represents half of the duration of the time window, and d(n) represents the digital signal obtained by sampling d(t) at equal intervals, then in represents the sampling time interval of s(t) and r(t), f s represents the sampling frequency of s(t) and r(t), f s The value of must meet the following conditions: Where B = f H -f L , f H Take the larger value of the highest cutoff frequency of s(t) and the highest cutoff frequency of r(t), f L Take the smaller value of the lowest cutoff frequency of s(t) and the lowest cutoff frequency of r(t), L represents The integer part of The decimal part of Let D[k] represent the discrete Fourier transform (DFT) of d(n). The calculation formula of D[k] is as follows: Where N represents the number of sampling points of s(t) and r(t), Represents the rotation factor of DFT. The value of N must meet the following conditions: From the calculation result D[k] of formula (8), we can get the d(t) spectrum, which can be expressed as f LC Denote the lowest cutoff frequency of the d(t) spectrum, denoted by f HC represents the highest cutoff frequency of the d(t) spectrum, then the calculation formula of Δf(τ) is as follows:

8. The ranging method of sawtooth linear frequency modulation continuous wave radar according to claim 6, characterized in that: The Δf(τ) value is calculated by using the discrete Fourier transform of the difference signal of the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to the echo signal within a specified time window centered on τ. The specific method is as follows: Let s(t) represent the replica signal of the transmitted signal in a transmission cycle, and let r(t) represent the echo signal of the transmitted signal in the same transmission cycle after being amplified by the receiver. Adjust the receiver amplification factor so that r(t) and s(t) have the same amplitude. represents the baseband signal obtained by down-converting s(t), then use represents the baseband signal obtained by down-conversion of r(t), then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; express and The difference signal within the specified time window centered on τ is where τ c Represents half the duration of a specified time window centered on τ, with Express The digital signal obtained by sampling at equal intervals is but in represent The sampling time interval, The value of must meet the following conditions: where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency; use express Discrete Fourier Transform (DFT), The calculation formula is as follows: Where N represents The number of sampling points, Represents the rotation factor of DFT. The value of N must meet the following conditions: From the calculation results of formula (9) Available Spectrum, with express The lowest cutoff frequency of the spectrum, express The highest cutoff frequency of the spectrum, then the calculation formula of Δf(τ) is as follows:

9. The ranging method of the sawtooth linear frequency modulation continuous wave radar according to any one of claims 6 to 8, characterized in that: The cross-correlation function between the transmitted signal and its echo signal is used to calculate the Δτ value. The specific method is as follows: Let s(t) represent the replica signal of the transmitted signal in a transmission cycle, r(t) represent the echo signal of the transmitted signal in the same transmission cycle after being amplified by the receiver, and s(n) represent the digital signal obtained by sampling s(t) at equal intervals. Then Let r(n) represent the digital signal obtained by sampling r(t) at equal intervals. in represents the sampling time interval of s(t) and r(t), f s represents the sampling frequency of s(t) and r(t), f s The value of must meet the following conditions: Where B = f H -f L , f H Take the larger value of the highest cutoff frequency of s(t) and the highest cutoff frequency of r(t), f L Take the smaller value of the lowest cutoff frequency of s(t) and the lowest cutoff frequency of r(t), L represents The integer part of The decimal part of Let x(m) represent the cross-correlation function of s(n) and r(n), m represents the independent variable of x(m), and x(m) is calculated based on the inverse discrete Fourier transform (IDFT). The specific algorithm is as follows: Where N represents the number of sampling points of s(t) and r(t), and k represents S[k] and R g [k] is the independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions: S[k] represents the discrete Fourier transform (DFT) of s(n). The calculation formula of S[k] is as follows: R g [k] represents r * (n) discrete Fourier transform (DFT), r * (n) represents the conjugate signal of r(n), the superscript "*" represents the conjugate operation, R g The calculation formula for [k] is as follows: in Represents the rotation factor of DFT; The cross-correlation function x(m) calculated according to formula (10) is a function with a maximum peak value. M represents the m value corresponding to the maximum peak value of x(m). The calculation formula of Δτ is as follows: Δτ=MT s 。 10. The ranging method of sawtooth linear frequency modulation continuous wave radar according to any one of claims 6 to 8, characterized in that: The Δτ value is calculated by using the cross-correlation function of the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to its echo signal. The specific method is as follows: Let s(t) represent the replica signal of the transmitted signal in a transmission cycle, r(t) represent the echo signal of the transmitted signal in the same transmission cycle after being amplified by the receiver, and represents the baseband signal obtained by down-converting s(t), then use represents the baseband signal obtained by down-conversion of r(t), then Where f0 represents the frequency of the local sine wave oscillator for down-conversion, Express The digital signal obtained by equal-interval sampling is use Express The digital signal obtained by equal-interval sampling is in represent The sampling time interval, The value of must meet the following conditions: where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency; use express and The cross-correlation function, m represents The independent variable, The calculation is based on the inverse discrete Fourier transform (IDFT), and the specific algorithm is as follows: Where N represents The number of sampling points, k represents The independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions: represent The discrete Fourier transform (DFT) of The calculation formula is as follows: represent The discrete Fourier transform (DFT) of represent The conjugate signal of , the superscript "*" represents the conjugate operation, The calculation formula is as follows: in Represents the rotation factor of DFT; The cross-correlation function calculated according to formula (11) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then the calculation formula of Δτ is as follows:

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