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

Abstract

The invention discloses a speed and distance measuring method for a triangular linear frequency modulation continuous wave radar, and the method specifically comprises the steps: enabling the radar to periodically transmit equilateral triangular linear frequency modulation continuous wave transmitting signals, and employing a time difference value when the instantaneous frequency of a transmitting signal of a frequency rising segment is equal to the instantaneous frequency of an echo signal of the transmitting signal; 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 in the frequency drop section 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 accurately calculating the time difference by adopting a cross-correlation function of the transmitting signal and the echo signal of the transmitting signal; the speed measurement and distance measurement method has the advantages of high speed measurement and distance measurement precision, strong anti-interference and anti-noise capability and low calculation amount.

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 triangle 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. Linear frequency modulated continuous wave radar mainly includes sawtooth linear frequency modulated continuous wave radar and triangle linear frequency modulated continuous wave radar.

[0003] The triangular linear frequency modulation continuous wave transmission signal includes the transmission signal of the frequency rising section and the transmission signal of the frequency falling section. The existing speed and distance measurement method needs to calculate the instantaneous frequency difference between the transmission signal of the frequency rising section and its echo signal at the same time, and the instantaneous frequency difference between the transmission signal of the frequency falling section and its echo signal at the same time. At present, algorithms such as short-time Fourier transform (STFT) and wavelet transform (WT) are used in engineering to calculate the instantaneous frequency of the transmission signal and its echo signal. According to the Heisenberg uncertainty principle, algorithms such as STFT and WT cannot accurately calculate the instantaneous frequency of the transmission signal and its echo signal, resulting in low speed and distance measurement accuracy of the existing speed and distance measurement methods. Summary of the invention

[0004] The present invention provides a speed and distance measurement method of a triangular linear frequency modulation continuous wave radar, which uses the time difference when the instantaneous frequency is equal to calculate the radial speed and distance between the target and the radar, and uses the cross-correlation function of the transmitted signal and its echo signal to accurately calculate the time difference. The method can effectively improve the speed and distance measurement accuracy.

[0005] A speed and distance measurement method for a triangular linear frequency modulation continuous wave radar, wherein the radar periodically and continuously transmits an equilateral triangle linear frequency modulation continuous wave transmission signal, wherein the equilateral triangle linear frequency modulation continuous wave transmission signal comprises a transmission signal of a frequency rising section and a transmission signal of a frequency falling section, and the duration of the transmission signal of the frequency rising section is controlled to be equal to the duration of the transmission signal of the frequency falling section, the lowest instantaneous frequency of the transmission signal of the frequency rising section is equal to the lowest instantaneous frequency of the transmission signal of the frequency falling section, and the highest instantaneous frequency of the transmission signal of the frequency rising section is equal to the highest instantaneous frequency of the transmission signal of the frequency falling section; the radial speed and distance between the target and the radar are calculated by using the time difference when the instantaneous frequency of the transmission signal of the frequency rising section is equal to the instantaneous frequency of its echo signal, and the time difference when the instantaneous frequency of the transmission signal of the frequency falling section is equal to the instantaneous frequency of its echo signal, and the radial speed and distance between the target and the radar are calculated by using the radial speed calculation formula between the target and the radar as follows:

[0006]

[0007] The calculation formula of the distance between the target and the radar is as follows:

[0008]

[0009] Where v represents the radial velocity between the target and the radar, R represents the distance between the target and the radar, c represents the speed of light, f1 represents the lowest instantaneous frequency of the transmitted signal in the frequency increase segment and the lowest instantaneous frequency of the transmitted signal in the frequency decrease segment, f2 represents the highest instantaneous frequency of the transmitted signal in the frequency increase segment and the highest instantaneous frequency of the transmitted signal in the frequency decrease segment, represents the frequency slope of the transmitted signal in the frequency rising section, T represents the duration of the transmitted signal in the frequency rising section and the duration of the transmitted signal in the frequency falling section, Δt u Represents the time difference when the instantaneous frequency of the transmitted signal in the frequency rising section is equal to the instantaneous frequency of its echo signal, Δt d The time difference when the instantaneous frequency of the transmitted signal representing the frequency drop segment is equal to the instantaneous frequency of its echo signal.

[0010] The cross-correlation function between the transmitted signal in the frequency rising section and its echo signal can be used to calculate Δt u The specific method is as follows:

[0011] Use s u (t) represents the replica signal of the transmitted signal in the frequency rising section within a transmission cycle, and r u (t) represents the echo signal of the frequency rising segment of the transmission signal in the same transmission cycle after being amplified by the receiver. The receiver amplification factor is adjusted so that r u (t) has a certain amplitude, preferably ru (t) and s u (t) has the same amplitude, for s u (t) The digital signal obtained by sampling at equal intervals is s u (n) means, then R u (t) The digital signal obtained by equal-interval sampling is represented by r u (n) means, then Where t represents s u (t), r u (t) is the independent variable, n represents s u (n), r u (n) is the independent variable, Representatives u (t), r u (t) is the sampling time interval, f s Representatives u (t), r u The sampling frequency of (t), f s The value of must meet the following conditions:

[0012]

[0013] Where B = f H -f L , f H Take u (t) The highest cutoff frequency and r u The larger value of the highest cutoff frequency of (t), f L Take u (t) the lowest cutoff frequency and r u (t) and the minimum cutoff frequency, L represents the smaller value. The integer part of The decimal part of

[0014] Use x u (m) means s u (n) and r u (n), m represents x u The independent variable of (m), x u (m) is calculated based on the inverse discrete Fourier transform (IDFT), and the specific algorithm is as follows:

[0015]

[0016] Where N represents s u (t), r u (t) is the number of sampling points, k represents S u [k], The independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions:

[0017]

[0018] S u [k] stands for s u (n) discrete Fourier transform (DFT), S u The calculation formula for [k] is as follows:

[0019]

[0020] represent The discrete Fourier transform (DFT) of Represents r u The conjugate signal of (n), the superscript “*” represents the conjugate operation, The calculation formula is as follows:

[0021]

[0022] in Represents the rotation factor of DFT;

[0023] The cross-correlation function x calculated according to formula (13) is u (m) is a function with the largest peak value, and M represents x u (m) The m value corresponding to the maximum peak value, then Δt u The calculation formula is as follows:

[0024] Δt u =MT s .

[0025] The cross-correlation function between the baseband signal corresponding to the transmitted signal in the frequency rising section and the baseband signal corresponding to its echo signal can also be used to calculate Δt u The specific method is as follows:

[0026] Use s u (t) represents the replica signal of the transmitted signal in the frequency rising section within a transmission cycle, and r u (t) represents the echo signal of the frequency rising segment of the transmission signal in the same transmission cycle after being amplified by the receiver. The receiver amplification factor is adjusted so that r u (t) has a certain amplitude, preferably r u (t) and s u (t) have the same amplitude, Indicates u (t) The baseband signal obtained by down-conversion, then use Represents r u (t) The baseband signal obtained by down-conversion, then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; The digital signal obtained by equal-interval sampling is used Indicates that right The digital signal obtained by equal-interval sampling is used Indicates that Where t represents s u (t) r u (t) The independent variable, n represents The independent variable, represent The sampling time interval, The value of must meet the following conditions:

[0027]

[0028] where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency;

[0029] 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:

[0030]

[0031] 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:

[0032]

[0033] represent The discrete Fourier transform (DFT) of The calculation formula is as follows:

[0034]

[0035] represent The discrete Fourier transform (DFT) of represent The conjugate signal of , the superscript “*” represents the conjugate operation, The calculation formula is as follows:

[0036]

[0037] in Represents the rotation factor of DFT;

[0038] The cross-correlation function calculated according to formula (14) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then Δt u The calculation formula is as follows:

[0039]

[0040] The cross-correlation function between the transmitted signal in the frequency drop section and its echo signal can be used to calculate Δt d The specific method is as follows:

[0041] Use s d (t) represents the replica signal of the transmitted signal in the frequency reduction segment within a transmission cycle, and r d (t) represents the echo signal of the transmitted signal in the frequency drop section within the same transmission cycle after being amplified by the receiver. The receiver amplification factor is adjusted so that r d (t) has a certain amplitude, preferably r d (t) and s d (t) has the same amplitude, for s d (t) The digital signal obtained by sampling at equal intervals is s d (n) means, then R d (t) The digital signal obtained by equal-interval sampling is represented by r d (n) means, then Where t represents s d (t), r d (t) is the independent variable, n represents s d (n), r d (n) is the independent variable, Representatives d (t), r d (t) is the sampling time interval, f s Representatives d (t), r d The sampling frequency of (t), f s The value of must meet the following conditions:

[0042]

[0043] Where B = f H -f L , f H Take d (t) The highest cutoff frequency and r d The larger value of the highest cutoff frequency of (t), f L Take d (t) the lowest cutoff frequency and r d (t) and the minimum cutoff frequency, L represents the smaller value. The integer part of The decimal part of

[0044] Use x d (m) means s d (n) and r d (n), m represents x d The independent variable of (m), x d (m) is calculated based on the inverse discrete Fourier transform (IDFT), and the specific algorithm is as follows:

[0045]

[0046] Where N represents s d (t), r d (t) is the number of sampling points, k represents S d [k], The independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions:

[0047]

[0048] S d [k] stands for s d (n) discrete Fourier transform (DFT), S d The calculation formula for [k] is as follows:

[0049]

[0050] represent The discrete Fourier transform of Represents r d The conjugate signal of (n), the superscript “*” represents the conjugate operation, The calculation formula is as follows:

[0051]

[0052] in Represents the rotation factor of DFT;

[0053] The cross-correlation function x calculated according to formula (15) is d (m) is a function with the largest peak value, and I represents x d (m) The m value corresponding to the maximum peak value, then Δt d The calculation formula is as follows:

[0054] Δt d =IT s .

[0055] The cross-correlation function between the baseband signal corresponding to the transmitted signal in the frequency drop section and the baseband signal corresponding to its echo signal can also be used to calculate Δt d The specific method is as follows:

[0056] Use s d (t) represents the replica signal of the transmitted signal in the frequency reduction segment within a transmission cycle, and r d (t) represents the echo signal of the transmitted signal in the frequency drop section within the same transmission cycle after being amplified by the receiver. The receiver amplification factor is adjusted so that r d (t) has a certain amplitude, preferably r d (t) and s d (t) have the same amplitude, Indicates d (t) The baseband signal obtained by down-conversion, then use Represents r d (t) The baseband signal obtained by down-conversion, then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; The digital signal obtained by equal-interval sampling is used Indicates that right The digital signal obtained by equal-interval sampling is used Indicates that Where t represents s d (t) r d (t) The independent variable, n represents The independent variable, represent The sampling time interval, The value of must meet the following conditions:

[0057]

[0058] where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency;

[0059] 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:

[0060]

[0061] 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:

[0062]

[0063] represent The discrete Fourier transform (DFT) of The calculation formula is as follows:

[0064]

[0065] represent The discrete Fourier transform (DFT) of represent The conjugate signal of , the superscript “*” represents the conjugate operation, The calculation formula is as follows:

[0066]

[0067] in Represents the rotation factor of DFT;

[0068] The cross-correlation function calculated according to formula (16) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then Δt d The calculation formula is as follows:

[0069]

[0070] The beneficial effects of the speed and distance measuring method of the present invention are as follows:

[0071] 1. In the speed and distance measuring method of the present invention, all discrete Fourier transforms (DFT) can be calculated by fast Fourier transform (FFT), and all inverse discrete Fourier transforms (IDFT) can be calculated by inverse fast Fourier transform (IFFT). Therefore, the speed and distance measuring method of the present invention has the advantage of low calculation amount.

[0072] 2. The existing speed and distance measurement method uses the instantaneous frequency difference between the transmission signal and its echo signal to calculate the radial speed and distance between the target and the radar. Since the instantaneous frequency of the transmission signal and its echo signal changes rapidly with time (the characteristic of the linear frequency modulation continuous wave signal), the instantaneous frequency of the transmission signal and its echo signal can only be calculated by sampling the transmission signal and its echo signal in a very short time. According to the Heisenberg uncertainty principle, it is impossible to accurately calculate the instantaneous frequency of the transmission signal and its echo signal using the signal in a very short time, resulting in low speed and distance measurement accuracy of the existing speed and distance measurement method; the speed and distance measurement method of the present invention uses the time difference when the instantaneous frequency is equal to calculate the radial speed and distance between the target and the radar, and uses the cross-correlation function of the transmission signal and its echo signal to calculate the time difference. Since the cross-correlation function calculation effectively utilizes the transmission signal and its echo signal in the entire period, the cross-correlation function can accurately calculate the time difference, thereby effectively improving the speed and distance measurement accuracy of the speed and distance measurement method of the present invention.

[0073] 3. The existing speed and distance measurement method only uses the signal in a very short time to calculate the instantaneous frequency of the transmission signal and its echo signal, and does not make full use of the transmission signal and its echo signal in the entire cycle. Therefore, the existing speed and distance measurement method has poor anti-interference and anti-noise performance. If the signal in a longer time is used to calculate the instantaneous frequency of the transmission signal and its echo signal, although the anti-interference and anti-noise performance can be improved, the instantaneous frequency at a specified moment cannot be determined because the instantaneous frequency changes rapidly with time; the speed and distance measurement method of the present invention makes full use of the transmission signal and its echo signal in the entire cycle to calculate the cross-correlation function. Since the cross-correlation function algorithm is a numerical integration algorithm, the cross-correlation function algorithm can greatly suppress interference and noise, thereby effectively improving the anti-interference and anti-noise performance of the speed and distance measurement method of the present invention.

[0074] 4. The present invention can use the cross-correlation function of the transmitted signal and its echo signal to calculate the time difference. In addition, the present invention can also use the baseband signal corresponding to the transmitted signal and the baseband signal corresponding to its echo signal to calculate the time difference. 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

[0075] 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.

[0076] Figure 1 Schematic diagram of the instantaneous frequency of the transmitted signal and its echo signal changing with time

[0077] In the figure: broken line 1 represents the instantaneous frequency of the transmission signal changing with time; broken line 2 represents the instantaneous frequency of the echo signal changing with time. DETAILED DESCRIPTION

[0078] 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.

[0079] A method for measuring speed and distance using a triangular linear frequency modulation continuous wave radar, referring to Figure 1 The radar periodically and continuously transmits an equilateral triangle linear frequency modulation continuous wave transmission signal, wherein the equilateral triangle linear frequency modulation continuous wave transmission signal includes a transmission signal of a frequency increase section and a transmission signal of a frequency decrease section, and controls the duration of the transmission signal of the frequency increase section to be equal to the duration of the transmission signal of the frequency decrease section, the lowest instantaneous frequency of the transmission signal of the frequency increase section to be equal to the lowest instantaneous frequency of the transmission signal of the frequency decrease section, and the highest instantaneous frequency of the transmission signal of the frequency increase section to be equal to the highest instantaneous frequency of the transmission signal of the frequency decrease section; the radial velocity and distance between the target and the radar are calculated by using the time difference when the instantaneous frequency of the transmission signal of the frequency increase section is equal to the instantaneous frequency of its echo signal, and the time difference when the instantaneous frequency of the transmission signal of the frequency decrease section is equal to the instantaneous frequency of its echo signal, and the specific method is as follows:

[0080] 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 r represent the duration of the transmitted signal in the frequency rising section and the duration of the transmitted signal in the frequency falling section, and let s represent the duration of the transmitted signal in the frequency rising section and the duration of the transmitted signal in the frequency falling section. u (t) represents the replica signal of the transmitted signal in the frequency rising section within a transmission cycle, s u (t) is expressed by the following formula:

[0081]

[0082] Where f1 represents s u The lowest instantaneous frequency of (t), Representatives u (t) frequency slope, f2 represents s u (t) is the highest instantaneous frequency, j represents an imaginary unit, 0≤t, τ≤T represents 0≤t≤T and 0≤τ≤T (hereinafter similar expressions have the same meaning);

[0083] Use f us (τ) represents s u (t) is the instantaneous frequency at the time τ. From formula (1), we know that f us (τ) is expressed by the following formula:

[0084]

[0085] Use s d (t) represents the replica signal of the transmitted signal in the frequency reduction segment within the same transmission cycle. d The maximum instantaneous frequency of (t) and s u The highest instantaneous frequency of (t) is equal to s d The minimum instantaneous frequency of (t) and s u (t) The lowest instantaneous frequency is equal, s d The duration of (t) is related to s u (t) are equal in duration, then s d The frequency slope of (t) is -K, s d (t) is expressed by the following formula:

[0086]

[0087] Use f ds (τ) represents s d (t) is the instantaneous frequency at the time τ. From formula (3), we know that f ds (τ) is expressed by the following formula:

[0088]

[0089] 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 represents the speed of light. u (t) represents the echo signal of the transmitted signal in the frequency rising segment within the same transmission cycle after being amplified by the receiver; without loss of generality, the echo signal after being amplified by the receiver is r u (t) and s u (t) have the same magnitude, considering r u (t) Mainly composed of s u (t) is composed of the delayed signal, r u(t) is expressed by the following formula:

[0090]

[0091] Use f ur (τ) represents r u (t) is the instantaneous frequency at the time τ. From equation (5), we know that f ur (τ) is expressed by the following formula:

[0092]

[0093] Use r d (t) represents the echo signal of the transmitted signal in the frequency drop segment within the same transmission cycle after being amplified by the receiver; without loss of generality, the echo signal after being amplified by the receiver is r d (t) and s d (t) have the same magnitude, considering r d (t) Mainly composed of s d (t) is composed of the delayed signal, r d (t) is expressed by the following formula:

[0094]

[0095] Use f dr (τ) represents r d (t) is the instantaneous frequency at the time τ. From equation (7), we know that f dr (τ) is expressed by the following formula:

[0096]

[0097] With Δt u The time difference between the instantaneous frequency of the transmitted signal in the frequency rising section and the instantaneous frequency of its echo signal is equal, and is represented by f ur (τ+Δt u ) represents r u (t) at its τ+Δt u The instantaneous frequency at the moment, when f ur (τ+Δt u ) and f us When (τ) are equal, according to equation (2) and equation (6), the following relationship is obtained:

[0098]

[0099] Formula (9) is simplified to obtain the following relationship:

[0100]

[0101] With Δt dThe time difference between the instantaneous frequency of the transmitted signal in the frequency drop section and the instantaneous frequency of its echo signal is equal, and is represented by f dr (τ+Δt d ) represents r d (t) at its τ+Δt d The instantaneous frequency at the moment, when f dr (τ+Δt d ) and f ds When (τ) are equal, according to equation (4) and equation (8), the following relationship is obtained:

[0102]

[0103] Formula (11) is simplified to obtain the following relationship:

[0104]

[0105] Subtracting equation (12) from equation (10) yields the following calculation formula for the radial velocity v between the target and the radar:

[0106]

[0107] Where f1, f2, K, c are known values, Δt u , Δt d The following method is used for calculation.

[0108] Since the radial velocity V between the target and the radar is much smaller than the speed of light c, Where “≈” represents “approximately equal to”. Subtracting equation (11) from equation (9) yields the following calculation formula for the distance R between the target and the radar:

[0109]

[0110] Where c is a known value, Δt u , Δt d The following method is used for calculation.

[0111] The cross-correlation function between the transmitted signal in the frequency rising section and its echo signal can be used to calculate Δt u The specific method is as follows:

[0112] Adjust the receiver gain so that r u (t) has a certain amplitude, preferably r u (t) and s u (t) has the same amplitude, for s u (t) The digital signal obtained by sampling at equal intervals is s u (n) means, then R u (t) The digital signal obtained by equal-interval sampling is represented by ru (n) means, then Where t represents s u (t), r u (t) is the time variable, n represents s u (n), r u (n) is the independent variable, Representatives u (t), r u (t) is the sampling time interval, f s Representatives u (t), r u The sampling frequency of (t), f s The value of must meet the following conditions:

[0113]

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

[0115] Use x u (m) means s u (n) and r u (n), m represents x u The independent variable of (m), x u (m) is calculated based on the inverse discrete Fourier transform (IDFT), and the specific algorithm is as follows:

[0116]

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

[0118]

[0119] S u [k] stands for s u(n) discrete Fourier transform (DFT), S u The calculation formula for [k] is as follows:

[0120]

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

[0122]

[0123] in Represents the rotation factor of DFT;

[0124] The cross-correlation function x calculated according to formula (13) is u (m) is a function with the largest peak value, and M represents x u (m) The m value corresponding to the maximum peak value, then Δt u The calculation formula is as follows:

[0125] Δt u =MT s .

[0126] The cross-correlation function between the baseband signal corresponding to the transmitted signal in the frequency rising section and the baseband signal corresponding to its echo signal can also be used to calculate Δt u The specific method is as follows:

[0127] Adjust the receiver gain so that r u (t) has a certain amplitude, preferably r u (t) and s u (t) have the same amplitude, Indicates u (t) The baseband signal obtained by down-conversion, then use Represents r u (t) The baseband signal obtained by down-conversion, then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; The digital signal obtained by equal-interval sampling is used Indicates that right The digital signal obtained by equal-interval sampling is used Indicates that Where t represents s u (t) r u(t) The time variable, n represents The independent variable, 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 (14) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then Δt u The calculation formula is as follows:

[0140]

[0141] The cross-correlation function between the transmitted signal in the frequency drop section and its echo signal can be used to calculate Δt d The specific method is as follows:

[0142] Adjust the receiver gain so that r d (t) has a certain amplitude, preferably r d (t) and s d (t) has the same amplitude, for s d (t) The digital signal obtained by sampling at equal intervals is s d (n) means, then R d (t) The digital signal obtained by equal-interval sampling is represented by r d (n) means, then Where t represents s d (t), r d (t) is the time variable, n represents s d (n), r d (n) is the independent variable, Representatives d (t), r d (t) is the sampling time interval, f s Representatives d (t), r d The sampling frequency of (t), f s The value of must meet the following conditions:

[0143]

[0144] Where B = f H -f L , f H Take d (t) The highest cutoff frequency and r d The larger value of the highest cutoff frequency of (t), f L Take d (t) the lowest cutoff frequency and r d (t) and the minimum cutoff frequency, L represents the smaller value. The integer part of The decimal part of

[0145] Use x d (m) means s d (n) and r d(n), m represents x d The independent variable of (m), x d (m) is calculated based on the inverse discrete Fourier transform (IDFT), and the specific algorithm is as follows:

[0146]

[0147] Where N represents s d (t), r d (t) is the number of sampling points, k represents S d [k], The independent variable, Represents the IDFT rotation factor. The value of N must meet the following conditions:

[0148]

[0149] S d [k] stands for s d (n) discrete Fourier transform (DFT), S d The calculation formula for [k] is as follows:

[0150]

[0151] represent The discrete Fourier transform of Represents r d The conjugate signal of (n), the superscript “*” represents the conjugate operation, The calculation formula is as follows:

[0152]

[0153] in Represents the rotation factor of DFT;

[0154] The cross-correlation function x calculated according to formula (15) is d (m) is a function with the largest peak value, and I represents x d (m) The m value corresponding to the maximum peak value, then Δt d The calculation formula is as follows:

[0155] Δt d =IT s .

[0156] The cross-correlation function between the baseband signal corresponding to the transmitted signal in the frequency drop section and the baseband signal corresponding to its echo signal can also be used to calculate Δt d The specific method is as follows:

[0157] Adjust the receiver gain so that r d(t) has a certain amplitude, preferably r d (t) and s d (t) have the same amplitude, Indicates d (t) The baseband signal obtained by down-conversion, then use Represents r d (t) The baseband signal obtained by down-conversion, then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; The digital signal obtained by equal-interval sampling is used Indicates that right The digital signal obtained by equal-interval sampling is used Indicates that Where t represents s d (t) r d (t) The time variable, n represents The independent variable, represent The sampling time interval, The value of must meet the following conditions:

[0158]

[0159] where f m Pick The maximum cutoff frequency and The larger value of the highest cutoff frequency;

[0160] 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:

[0161]

[0162] 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:

[0163]

[0164] represent The discrete Fourier transform (DFT) of The calculation formula is as follows:

[0165]

[0166] represent The discrete Fourier transform (DFT) of represent The conjugate signal of , the superscript “*” represents the conjugate operation, The calculation formula is as follows:

[0167]

[0168] in Represents the rotation factor of DFT;

[0169] The cross-correlation function calculated according to formula (16) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then Δt d The calculation formula is as follows:

[0170]

[0171] 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 method for measuring speed using a triangular linear frequency modulation continuous wave radar, characterized in that: The radar periodically transmits an equilateral triangle linear frequency modulation continuous wave transmission signal, wherein the equilateral triangle linear frequency modulation continuous wave transmission signal includes a transmission signal of a frequency increase section and a transmission signal of a frequency decrease section, and controls the duration of the transmission signal of the frequency increase section to be equal to the duration of the transmission signal of the frequency decrease section, the lowest instantaneous frequency of the transmission signal of the frequency increase section to be equal to the lowest instantaneous frequency of the transmission signal of the frequency decrease section, and the highest instantaneous frequency of the transmission signal of the frequency increase section to be equal to the highest instantaneous frequency of the transmission signal of the frequency decrease section; the radial velocity between the target and the radar is calculated by using the time difference when the instantaneous frequency of the transmission signal of the frequency increase section is equal to the instantaneous frequency of its echo signal, and the time difference when the instantaneous frequency of the transmission signal of the frequency decrease section is equal to the instantaneous frequency of its echo signal, and 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, f1 represents the lowest instantaneous frequency of the transmitted signal in the frequency increase segment and the lowest instantaneous frequency of the transmitted signal in the frequency decrease segment, f2 represents the highest instantaneous frequency of the transmitted signal in the frequency increase segment and the highest instantaneous frequency of the transmitted signal in the frequency decrease segment, represents the frequency slope of the transmitted signal in the frequency rising section, T represents the duration of the transmitted signal in the frequency rising section and the duration of the transmitted signal in the frequency falling section, Δt u Represents the time difference when the instantaneous frequency of the transmitted signal in the frequency rising section is equal to the instantaneous frequency of its echo signal, Δt d The time difference when the instantaneous frequency of the transmitted signal representing the frequency drop segment is equal to the instantaneous frequency of its echo signal.

2. The speed measurement method of the triangular linear frequency modulation continuous wave radar according to claim 1 is characterized in that: The cross-correlation function between the transmitted signal in the frequency rising section and its echo signal is used to calculate Δt u The specific method is as follows: Use s u (t) represents the replica signal of the transmitted signal in the frequency rising section within a transmission cycle, and r u (t) represents the echo signal of the frequency rising section of the transmission signal in the same transmission cycle after being amplified by the receiver. u (t) The digital signal obtained by sampling at equal intervals is s u (n) means, then R u (t) The digital signal obtained by equal-interval sampling is represented by r u (n) means, then Where t represents s u (t), r u (t) is the time variable, n represents s u (n), r u (n) is the independent variable, Representatives u (t), r u (t) is the sampling time interval, f s Representatives u (t), r u The sampling frequency of (t), f s The value of must meet the following conditions: Where B = f H -f L , f H Take u (t) The highest cutoff frequency and r u The larger value of the highest cutoff frequency of (t), f L Take u (t) the lowest cutoff frequency and r u (t) and the minimum cutoff frequency, L represents the smaller value. The integer part of The decimal part of Use x u (m) means s u (n) and r u (n), m represents x u The independent variable of (m), x u (m) is calculated according to the following formula: in represents the rotation factor of IDFT, S u [k] stands for s u The discrete Fourier transform of (n) is represent The discrete Fourier transform of Represents r u The conjugate signal of (n), the superscript "*" represents the conjugate operation, and k represents S u [k], The independent variable, N represents s u (t), r u The number of sampling points (t), the value of N must meet the following conditions: The cross-correlation function x calculated according to formula (13) u (m) is a function with the largest peak value, and M represents x u (m) The m value corresponding to the maximum peak value, then Δt u The calculation formula is as follows: Δt u =MT s 。 3. The speed measurement method of the triangular linear frequency modulation continuous wave radar according to claim 1, characterized in that: The cross-correlation function of the baseband signal corresponding to the transmitted signal in the frequency rising section and the baseband signal corresponding to its echo signal is used to calculate Δt u The specific method is as follows: Use s u (t) represents the replica signal of the transmitted signal in the frequency rising section within a transmission cycle, and r u (t) represents the echo signal of the frequency rising segment of the transmission signal in the same transmission cycle after being amplified by the receiver, and is expressed as Indicates u (t) The baseband signal obtained by down-conversion, then use Represents r u (t) The baseband signal obtained by down-conversion, then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; The digital signal obtained by equal-interval sampling is used Indicates that right The digital signal obtained by equal-interval sampling is used Indicates that Where t represents s u (t) r u (t) The time variable, n represents The independent variable, 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, Calculated according to the following formula: in represent The discrete Fourier transform of represent The discrete Fourier transform of represent The conjugate signal of The independent variable, N represents The number of sampling points, N must meet the following conditions: The cross-correlation function calculated according to formula (14) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then Δt u The calculation formula is as follows:

4. The method for measuring speed using a triangular 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 in the frequency drop section is used to calculate Δt d The specific method is as follows: Use s d (t) represents the replica signal of the transmitted signal in the frequency reduction segment within a transmission cycle, and r d (t) represents the echo signal of the transmitted signal in the frequency drop section within the same transmission cycle after being amplified by the receiver. d (t) The digital signal obtained by sampling at equal intervals is s d (n) means, then R d (t) The digital signal obtained by equal-interval sampling is represented by r d (n) means, then Where t represents s d (t), r d (t) is the time variable, n represents s d (n), r d (n) is the independent variable, Representatives d (t), r d (t) is the sampling time interval, f s Representatives d (t), r d The sampling frequency of (t), f s The value of must meet the following conditions: Where B = f H -f L , f H Take d (t) The highest cutoff frequency and r d The larger value of the highest cutoff frequency of (t), f L Take d (t) the lowest cutoff frequency and r d (t) and the minimum cutoff frequency, L represents the smaller value. The integer part of The decimal part of Use x d (m) means s d (n) and r d (n), m represents x d The independent variable of (m), x d (m) is calculated according to the following formula: Where S d [k] stands for s d The discrete Fourier transform of (n) is represent The discrete Fourier transform of Represents r d The conjugate signal of (n), the superscript "*" represents the conjugate operation, and k represents S d [k], The independent variable, N represents s d (t), r d The number of sampling points (t), the value of N must meet the following conditions: The cross-correlation function x calculated according to formula (15) is d (m) is a function with the largest peak value, and I represents x d (m) The m value corresponding to the maximum peak value, then Δt d The calculation formula is as follows: Δt d =IT s 。 5. The speed measurement method of the triangular linear frequency modulation continuous wave radar according to any one of claims 1 to 3, characterized in that: The cross-correlation function of the baseband signal corresponding to the transmitted signal in the frequency drop section and the baseband signal corresponding to its echo signal is used to calculate Δt d The specific method is as follows: Use s d (t) represents the replica signal of the transmitted signal in the frequency reduction segment within a transmission cycle, and r d (t) represents the echo signal of the transmitted signal in the frequency drop section within the same transmission cycle after being amplified by the receiver, and is expressed as Indicates d (t) The baseband signal obtained by down-conversion, then use Represents r d (t) The baseband signal obtained by down-conversion, then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; The digital signal obtained by equal-interval sampling is used Indicates that right The digital signal obtained by equal-interval sampling is used Indicates that Where t represents s d (t) r d (t) The time variable, n represents The independent variable, 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, Calculated according to the following formula: in represent The discrete Fourier transform of represent The discrete Fourier transform of represent The conjugate signal of The independent variable, N represents The number of sampling points, N must meet the following conditions: The cross-correlation function calculated according to formula (16) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then Δt d The calculation formula is as follows:

6. A ranging method for a triangular linear frequency modulation continuous wave radar, characterized in that: The radar periodically transmits an equilateral triangle linear frequency modulation continuous wave transmission signal, wherein the equilateral triangle linear frequency modulation continuous wave transmission signal includes a transmission signal of a frequency increase section and a transmission signal of a frequency decrease section, and controls the duration of the transmission signal of the frequency increase section to be equal to the duration of the transmission signal of the frequency decrease section, the lowest instantaneous frequency of the transmission signal of the frequency increase section to be equal to the lowest instantaneous frequency of the transmission signal of the frequency decrease section, and the highest instantaneous frequency of the transmission signal of the frequency increase section to be equal to the highest instantaneous frequency of the transmission signal of the frequency decrease section; the distance between the target and the radar is calculated by using the time difference when the instantaneous frequency of the transmission signal of the frequency increase section is equal to the instantaneous frequency of its echo signal, and the time difference when the instantaneous frequency of the transmission signal of the frequency decrease section is equal to the instantaneous frequency of its echo signal, and the specific calculation formula is as follows: Where R represents the distance between the target and the radar, c represents the speed of light, Δt u Represents the time difference when the instantaneous frequency of the transmitted signal in the frequency rising section is equal to the instantaneous frequency of its echo signal, Δt d The time difference when the instantaneous frequency of the transmitted signal representing the frequency drop segment is equal to the instantaneous frequency of its echo signal.

7. The distance measurement method of the triangular linear frequency modulation continuous wave radar according to claim 6 is characterized in that: The cross-correlation function between the transmitted signal in the frequency rising section and its echo signal is used to calculate Δt u The specific method is as follows: Use s u (t) represents the replica signal of the transmitted signal in the frequency rising section within a transmission cycle, and r u (t) represents the echo signal of the frequency rising section of the transmission signal in the same transmission cycle after being amplified by the receiver. u (t) The digital signal obtained by sampling at equal intervals is s u (n) means, then R u (t) The digital signal obtained by equal-interval sampling is represented by r u (n) means, then Where t represents s u (t), r u (t) is the time variable, n represents s u (n), r u (n) is the independent variable, Representatives u (t), r u (t) is the sampling time interval, f s Representatives u (t), r u The sampling frequency of (t), f s The value of must meet the following conditions: Where B = f H -f L , f H Take u (t) The highest cutoff frequency and r u The larger value of the highest cutoff frequency of (t), f L Take u (t) the lowest cutoff frequency and r u (t) is the smaller value of the lowest cutoff frequency, l represents The integer part of The decimal part of Use x u (m) means s u (n) and r u (n), m represents x u The independent variable of (m), x u (m) is calculated according to the following formula: Where S u [k] stands for s u The discrete Fourier transform of (n) is represent The discrete Fourier transform of Represents r u The conjugate signal of (n), the superscript "*" represents the conjugate operation, and k represents S u [k], The independent variable, N represents s u (t), r u The number of sampling points (t), the value of N must meet the following conditions: The cross-correlation function x calculated according to formula (13) u (m) is a function with the largest peak value, and M represents x u (m) The m value corresponding to the maximum peak value, then Δt u The calculation formula is as follows: Δt u =MT s 。 8. The distance measurement method of the triangular linear frequency modulation continuous wave radar according to claim 6, characterized in that: The cross-correlation function of the baseband signal corresponding to the transmitted signal in the frequency rising section and the baseband signal corresponding to its echo signal is used to calculate Δt u The specific method is as follows: Use s u (t) represents the replica signal of the transmitted signal in the frequency rising section within a transmission cycle, and r u (t) represents the echo signal of the frequency rising segment of the transmission signal in the same transmission cycle after being amplified by the receiver, and is expressed as Indicates u (t) The baseband signal obtained by down-conversion, then use Represents r u (t) The baseband signal obtained by down-conversion, then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; The digital signal obtained by equal-interval sampling is used Indicates that right The digital signal obtained by equal-interval sampling is used Indicates that Where t represents s u (t) r u (t) The time variable, n represents The independent variable, 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, Calculated according to the following formula: in represent The discrete Fourier transform of represent The discrete Fourier transform of represent The conjugate signal of The independent variable, N represents The number of sampling points, N must meet the following conditions: The cross-correlation function calculated according to formula (14) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then Δt u The calculation formula is as follows:

9. The distance measurement method of the triangular 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 in the frequency drop section is used to calculate Δt d The specific method is as follows: Use s d (t) represents the replica signal of the transmitted signal in the frequency reduction segment within a transmission cycle, and r d (t) represents the echo signal of the transmitted signal in the frequency drop section within the same transmission cycle after being amplified by the receiver. d (t) The digital signal obtained by sampling at equal intervals is s d (n) means, then R d (t) The digital signal obtained by equal-interval sampling is represented by r d (n) means, then Where t represents s d (t), r d (t) is the time variable, n represents s d (n), r d (n) is the independent variable, Representatives d (t), r d (t) is the sampling time interval, f s Representatives d (t), r d The sampling frequency of (t), f s The value of must meet the following conditions: Where B = f H -f L , f H Take d (t) The highest cutoff frequency and r d The larger value of the highest cutoff frequency of (t), f L Take d (t) the lowest cutoff frequency and r d (t) and the minimum cutoff frequency, L represents the smaller value. The integer part of The decimal part of Use x d (m) means s d (n) and r d (n), m represents x d The independent variable of (m), x d (m) is calculated according to the following formula: Where S d [k] stands for s d The discrete Fourier transform of (n) is represent The discrete Fourier transform of Represents r d The conjugate signal of (n), the superscript "*" represents the conjugate operation, and k represents S d [k], The independent variable, N represents s d (t), r d The number of sampling points (t), the value of N must meet the following conditions: The cross-correlation function x calculated according to formula (15) is d (m) is a function with the largest peak value, and I represents x d (m) The m value corresponding to the maximum peak value, then Δt d The calculation formula is as follows: Δt d =IT s 。 10. The distance measurement method of the triangular linear frequency modulation continuous wave radar according to any one of claims 6 to 8, characterized in that: The cross-correlation function of the baseband signal corresponding to the transmitted signal in the frequency drop section and the baseband signal corresponding to its echo signal is used to calculate Δt d The specific method is as follows: Use s d (t) represents the replica signal of the transmitted signal in the frequency reduction segment within a transmission cycle, and r d (t) represents the echo signal of the transmitted signal in the frequency drop section within the same transmission cycle after being amplified by the receiver, and is expressed as Indicates d (t) The baseband signal obtained by down-conversion, then use Represents r d (t) The baseband signal obtained by down-conversion, then Where f0 represents the frequency of the local sine wave oscillator for down-conversion; The digital signal obtained by equal-interval sampling is used Indicates that right The digital signal obtained by equal-interval sampling is used Indicates that Where t represents s d (t) r d (t) The time variable, n represents The independent variable, 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, Calculated according to the following formula: in represent The discrete Fourier transform of represent The discrete Fourier transform of represent The conjugate signal of The independent variable, N represents The number of sampling points, N must meet the following conditions: The cross-correlation function calculated according to formula (16) is is a function with a maximum peak value, express The m value corresponding to the maximum peak value, then Δt d The calculation formula is as follows:

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