Radar echo phase correlation accumulation method and device based on third-order time scale transformation

Abstract

This invention discloses a method and apparatus for coherent accumulation of radar echo wavelengths based on a third-order time-scale transform. The method first performs a fast time-domain Fourier transform on the radar echo to the range-frequency domain, and obtains basic data through matched filtering. Then, it determines the range of acceleration ratio and jerk ratio based on the observed target's velocity, acceleration, and jerk. Next, it calculates and discretizes the new slow time range for each acceleration ratio and jerk ratio, and derives the original slow time in reverse. Subsequently, it combines the basic data and performs interpolation using a set interpolation algorithm to obtain echo data under the new slow time. Then, it performs inverse range-to-Fourier transform and azimuth-to-Fourier transform to obtain range-Doppler domain coherent accumulation echo data. Finally, it iterates through all acceleration ratios and jerk ratios to obtain the corresponding accumulated echo data. This invention can simultaneously correct first-order, second-order, and third-order range travel, eliminate Doppler diffusion, improve coherent accumulation gain and signal-to-noise ratio, assist in the detection of weak targets, and has strong applicability.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, specifically to a radar backwave coherent accumulation method and apparatus based on third-order time-scale transformation. Background Technology

[0002] Long-time accumulation algorithms are an effective method for improving the signal-to-noise ratio (SNR) in radar detection of weak targets. They are often used to significantly increase the accumulation gain when the SNR is low, so as to achieve an SNR exceeding the detection threshold. Existing commonly used short-time accumulation algorithms all have an implicit assumption that the target does not move across range cells or spread across Doppler cells during its movement time.

[0003] However, in practical applications, as the observation period lengthens, target movement inevitably leads to cross-range cell movement and cross-Doppler cell diffusion. This cross-range cell movement and cross-Doppler cell diffusion cause energy to accumulate in multiple different range cells and Doppler cells, making it difficult to achieve a sustained increase in signal-to-noise ratio gain.

[0004] Therefore, there is an urgent need to invent a more robust accumulation algorithm that enables target echoes to coherently accumulate into a range-Doppler unit over a long period of time, thereby achieving the goal of increasing accumulation gain over a long accumulation time and providing sufficient signal-to-noise ratio for target detection. Summary of the Invention

[0005] To address this, the present invention provides a radar echo wavelength coherent accumulation method and apparatus based on third-order time-scale transformation. By using third-order time-scale transformation, the traditional method cannot efficiently detect targets with velocity and acceleration in long-term radar coherent accumulation. This achieves effective convergence of echo energy in the range-Doppler domain, improving the signal-to-noise ratio to meet the requirements for weak target detection.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a radar back wavelength coherent accumulation method based on third-order time-scale transformation, comprising:

[0007] The radar echo is transformed into the range frequency domain by performing a fast time-domain Fourier transform on the radar echo; matched filtering is then performed on the radar echo in the range frequency domain without performing an inverse range-to-Fourier transform, resulting in the basic radar echo data after frequency domain matched filtering.

[0008] Based on the possible ranges of velocity, acceleration, and jerk of the observed target, the ranges of acceleration ratio and jerk ratio are set.

[0009] For each acceleration ratio and rapid ratio within the range of the acceleration ratio and rapid ratio, the new slow time range after the third-order time scale transformation is calculated according to the third-order time scale transformation principle; the new slow time range is discretized according to the radar pulse repetition frequency to obtain the discrete new slow time.

[0010] For each new slow time and the acceleration ratio and the rapid ratio, the original slow time before the third-order time scale transformation is obtained by inverse calculation using the third-order time scale transformation formula.

[0011] Based on the original slow time, and combined with the radar echo base data after frequency domain matched filtering, interpolation calculation is performed by setting an interpolation algorithm to obtain the radar echo data under the new slow time.

[0012] Perform a range-to-Fourier inverse transform on the radar echo data under the new slow time domain to obtain echo data in the range-to-new slow time domain; based on the echo data in the range-to-new slow time domain, perform an azimuth-to-Fourier transform to obtain coherently accumulated echo data in the range-to-Doppler domain.

[0013] Repeated calculations are performed on all acceleration ratios and rapid ratios within their respective ranges to obtain coherent accumulated echo data in the range-Doppler domain corresponding to all acceleration ratios and rapid ratios.

[0014] As a preferred scheme for the radar echo wavelength coherent accumulation method based on third-order time-scale transformation, the expression for the basic radar echo data after frequency-domain matched filtering is as follows:

[0015]

[0016] In the formula, S(f,η) m ) represents the basic radar echo data; K represents the frequency modulation; T represents the basic radar echo data. p For time width; f c τ is the carrier frequency of the transmitted signal; A is the amplitude of the echo; τ is the echo time delay of the target; T m η is the total coherent accumulation time. m The slow-time variable is discretized according to the pulse repetition frequency (PRF), with a value of m / PRF, a minimum value of 0, and a maximum value of M / PRF, where m∈Z and Z is the set of integers; f is the range frequency; j is the imaginary unit; v is the target velocity; a is the target acceleration; k is the target jerk; c is the electromagnetic wave propagation speed; and R0 is the distance between the target and the radar at time 0.

[0017] As a preferred scheme for radar backwave coherent accumulation method based on third-order time-scale transformation, the range of acceleration ratio and speed ratio is set. Based on the radar parameters and the acceleration ratio and speed ratio to be searched, the range of the new slow time (i.e., the minimum and maximum values) is calculated according to the third-order time-scale transformation, and then discretized according to PRF. The minimum value of the new slow time is 0, and the expression for the maximum value is:

[0018]

[0019] In the formula, r av For the acceleration ratio, r kv For rapidity ratio;

[0020] exist The new slow time expression after discretization according to PRF within the range is as follows:

[0021]

[0022] In the formula, For new slow time; This is the new slow time index after discretization.

[0023] As a preferred scheme for the radar back wavelength coherent accumulation method based on third-order time-scale transformation, the original slow time is calculated based on the new slow time after PRF quantization. The expression for the original slow time is as follows:

[0024]

[0025] in,

[0026]

[0027] In the formula, Y1, Y2, A, B, and C are the terms used for calculation. Intermediate variables.

[0028] As a preferred scheme for the radar echo wavelength coherent accumulation method based on third-order time-scale transformation, in the process of obtaining the radar echo data under the new slow time through interpolation calculation using the interpolation algorithm, the expression for the radar echo data under the new slow time is:

[0029]

[0030] In the formula, S(f,η) m () represents the original slow-time radar echo data, P is the interpolation kernel length, and i is the summation index. To The integer obtained by rounding to the nearest whole number.

[0031] As a preferred scheme for the radar echo wavelength coherent accumulation method based on third-order time-scale transformation, range-to-new-slow-time-domain echo data is obtained by performing an inverse Fourier transform of the range-frequency-to-new-slow-time-domain echo data with respect to the range frequency. The expression for the range-to-new-slow-time-domain echo data is as follows:

[0032]

[0033] In the formula, Echo data in the distance-new slow time domain;

[0034] Range-Doppler coherently accumulated echo data is obtained by performing a Fourier transform of the range-new-slow time domain echo data with respect to the new-slow time. The expression for the range-Doppler coherently accumulated echo data is as follows:

[0035]

[0036] In the formula, Coherently accumulate echo data for the range-Doppler domain.

[0037] This invention also provides a radar back wavelength coherent accumulation device based on a third-order time-scale transformation, employing the aforementioned radar back wavelength coherent accumulation method based on a third-order time-scale transformation, comprising:

[0038] The radar echo basic data acquisition module is used to transform the radar echo to the range frequency domain by performing a fast time-domain Fourier transform on the radar echo; and to perform matched filtering on the radar echo in the range frequency domain without performing an inverse range-to-Fourier transform to obtain the frequency-domain matched-filtered radar echo basic data.

[0039] The acceleration ratio and jerk ratio value range setting module is used to set the acceleration ratio and jerk ratio value range based on the possible value range of the observed target's velocity, acceleration, and jerk.

[0040] The new slow time acquisition module is used to calculate the new slow time range after the third-order time scale transformation for each acceleration ratio and rapid ratio within the range of the acceleration ratio and rapid ratio values, based on the principle of third-order time scale transformation; and to quantize the new slow time range according to the radar pulse repetition frequency to obtain the discrete new slow time.

[0041] The original slow time acquisition module is used to calculate the original slow time before the third-order time scale transformation for each new slow time and the speedup ratio by performing a reverse calculation using the third-order time scale transformation formula.

[0042] The new slow time radar echo data acquisition module is used to obtain the radar echo data under the new slow time by performing interpolation calculations based on the original slow time and the radar echo basic data after frequency domain matched filtering, through a set interpolation algorithm.

[0043] The range-Doppler domain coherent accumulation echo data acquisition module is used to perform range-to-Fourier inverse transform on the radar echo data under the new slow time to obtain echo data in the range-to-new slow time domain; and to perform azimuth-to-Fourier transform on the echo data in the range-to-new slow time domain to obtain coherent accumulation echo data in the range-Doppler domain.

[0044] The repeated calculation module is used to repeatedly calculate all acceleration ratios and rapid ratios within the range of the acceleration ratio and rapid ratio, and obtain the coherent accumulated echo data of the range-Doppler domain corresponding to all acceleration ratios and rapid ratios.

[0045] As a preferred embodiment of a radar echo wavelength coherent accumulation device based on a third-order time-scale transformation, the expression for the radar echo fundamental data after frequency-domain matched filtering in the radar echo fundamental data acquisition module is as follows:

[0046]

[0047] In the formula, S(f,η) m ) represents the basic radar echo data; K represents the frequency modulation; T represents the basic radar echo data. p For time width; f c τ is the carrier frequency of the transmitted signal; A is the amplitude of the echo; τ is the echo time delay of the target; T m η is the total coherent accumulation time. m The slow-time variable is discretized according to the pulse repetition frequency (PRF), with a value of m / PRF, a minimum value of 0, and a maximum value of M / PRF, where m∈Z and Z is the set of integers; f is the range frequency; j is the imaginary unit; v is the target velocity; a is the target acceleration; k is the target jerk; c is the electromagnetic wave propagation speed; and R0 is the distance between the target and the radar at time 0.

[0048] As a preferred embodiment of the radar back wavelength coherent accumulation device based on third-order time-scale transformation, the acceleration ratio and rapidity ratio value range setting module sets the value range of acceleration ratio and rapidity ratio. Based on the radar parameters and the acceleration ratio and rapidity ratio to be searched, the value range of the new slow time is calculated according to the third-order time-scale transformation, i.e., the minimum and maximum values, and discretized according to PRF. The minimum value of the new slow time is 0, and the maximum value expression is:

[0049]

[0050] In the formula, r av For the acceleration ratio, rkv This is the speed ratio.

[0051] exist The new slow time expression after discretization according to PRF within the range is as follows:

[0052]

[0053] In the formula, For new slow time; This is the new slow time index after discretization.

[0054] As a preferred embodiment of a radar back wavelength coherent accumulation device based on a third-order time scale transformation, the original slow time acquisition module calculates the original slow time by inversely performing a third-order time transformation based on the new slow time after PRF quantization. The expression for the original slow time is as follows:

[0055]

[0056] in,

[0057]

[0058] In the formula, Y1, Y2, A, B, and C are the terms used for calculation. Intermediate variables.

[0059] As a preferred embodiment of a radar echo wavelength coherent accumulation device based on a third-order time scale transformation, in the radar echo data acquisition module under the new slow time, during the process of obtaining the radar echo data under the new slow time through interpolation calculation using the set interpolation algorithm, the expression for the radar echo data under the new slow time is:

[0060]

[0061] In the formula, S(f,η) m () represents the original slow-time radar echo data, P is the interpolation kernel length, and i is the summation index. To The integer obtained by rounding to the nearest whole number.

[0062] As a preferred embodiment of a radar echo wavelength coherent accumulation device based on a third-order time-scale transformation, the range-Doppler domain coherent accumulation echo data acquisition module obtains range-new-slow-time domain echo data by performing an inverse Fourier transform of the range-frequency domain-new-slow-time domain echo data with respect to the range frequency. The expression for the range-new-slow-time domain echo data is as follows:

[0063]

[0064] In the formula, This is the echo data in the distance-new slow time domain.

[0065] As a preferred embodiment of a radar echo wavelength coherent accumulation device based on a third-order time-scale transformation, the range-Doppler domain coherent accumulation echo data acquisition module obtains range-Doppler domain coherent accumulation echo data through a Fourier transform of the range-new-slow-time domain echo data with respect to the new-slow-time. The expression for the range-Doppler domain coherent accumulation echo data is as follows:

[0066]

[0067] In the formula, Coherently accumulate echo data for the range-Doppler domain.

[0068] This invention has the following advantages: It transforms the radar echo into the range frequency domain by performing a fast time-domain Fourier transform on the radar echo; within the range frequency domain, it performs matched filtering on the radar echo without performing an inverse range-to-Fourier transform, obtaining the basic radar echo data after frequency-domain matched filtering; based on the possible ranges of the observed target's velocity, acceleration, and jerk information, it sets the ranges for acceleration ratio and jerk ratio; for each acceleration ratio and jerk ratio within the ranges, it calculates the new slow time range after the third-order time-scale transformation according to the principle of third-order time-scale transformation; it discretizes the new slow time range according to the radar's pulse repetition frequency to obtain discrete new slow times; for each new slow time and the acceleration ratio and jerk ratio, it uses a third-order time-scale transformation... The transformation formula is solved in reverse to obtain the original slow time before the third-order timescale transformation corresponding to the new slow time. Based on the original slow time and combined with the radar echo base data after frequency domain matched filtering, interpolation calculation is performed using a set interpolation algorithm to obtain the radar echo data under the new slow time. The radar echo data under the new slow time is subjected to range-to-Fourier inverse transform to obtain echo data in the range-new slow time domain. Based on the echo data in the range-new slow time domain, an azimuth-to-Fourier transform is performed to obtain coherent accumulation echo data in the range-Doppler domain. All acceleration ratios and velocity ratios within the range of the acceleration ratio and velocity ratio are repeatedly calculated to obtain the coherent accumulation echo data in the range-Doppler domain corresponding to all acceleration ratios and velocity ratios. This invention utilizes a core technology of third-order time-scale transformation to simultaneously correct for first-, second-, and third-order range migrations caused by target motion, and eliminates Doppler diffusion caused by second- and third-order motions. It avoids the energy dispersion problem caused by neglecting second- and third-order range migrations in traditional methods, allowing radar echo energy to converge efficiently in the range-Doppler domain. Compared to traditional range-Doppler algorithms and Keystone Transform-Fractional Fourier Transform (KT-FrFT) coherent accumulation methods, it achieves higher coherent accumulation gain, significantly improves the signal-to-noise ratio, and is more conducive to the detection of weak targets. Furthermore, the method has a clear process, strong operability, and a reasonable division of corresponding device modules, facilitating engineering implementation. It can be widely adapted to various radar systems that need to detect targets containing velocity, acceleration, and jerkiness, demonstrating significant practical value and promising prospects for widespread application. Attached Figure Description

[0069] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0070] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0071] Figure 1 This is a flowchart illustrating the radar back wavelength coherent accumulation method based on third-order time-scale transformation provided in Embodiment 1 of the present invention.

[0072] Figure 2 This is a schematic diagram illustrating the specific implementation process of the radar back wavelength coherent accumulation method based on third-order time-scale transformation provided in Embodiment 1 of the present invention.

[0073] Figure 3 This is a schematic diagram of the cross-range cell and cross-Doppler movement phenomena in the radar back wavelength coherent accumulation method based on third-order time-scale transformation provided in Embodiment 1 of the present invention; wherein, (a) is noise-free; (b) is noisy;

[0074] Figure 4 This is a schematic diagram of the range-Doppler domain result after a third-order time scaling transform (TOTST) in the radar back wavelength coherent accumulation method based on third-order time scaling transformation provided in Embodiment 1 of the present invention; wherein, (a) is noise-free; (b) is noisy;

[0075] Figure 5 This is a schematic diagram comparing the signal-to-noise ratio outputs of the radar back wavelength coherent accumulation method based on third-order time-scale transformation and the KT-FrFT method in Embodiment 1 of the present invention; where (a) is TOTST; (b) is KT-FrFT;

[0076] Figure 6 This is a schematic diagram of the architecture of the radar back wavelength coherent accumulation device based on third-order time-scale transformation provided in Embodiment 2 of the present invention. Detailed Implementation

[0077] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] Example 1

[0079] See Figure 1 and Figure 2 Embodiment 1 of the present invention provides a radar back wavelength coherent accumulation method based on third-order time-scale transformation, comprising the following steps:

[0080] S1. The radar echo is transformed to the range frequency domain by performing a fast time-domain Fourier transform on the radar echo; the radar echo is matched and filtered in the range frequency domain without performing a range-to-Fourier inverse transform to obtain the basic data of the radar echo after frequency domain matching and filtering.

[0081] S2. Based on the possible range of values ​​for the velocity, acceleration, and jerk of the observed target, set the range of values ​​for the acceleration ratio and jerk ratio.

[0082] S3. For each acceleration ratio and rapid ratio within the range of the acceleration ratio and rapid ratio, calculate the new slow time range after the third-order time scale transformation according to the third-order time scale transformation principle; quantize the new slow time range according to the radar pulse repetition frequency to obtain the discrete new slow time.

[0083] S4. For each new slow time and the acceleration ratio and the rapid ratio, the original slow time before the third-order time scale transformation is obtained by inverse calculation using the third-order time scale transformation formula.

[0084] S5. Based on the original slow time and combined with the radar echo base data after frequency domain matched filtering, interpolation calculation is performed by setting an interpolation algorithm to obtain the radar echo data under the new slow time.

[0085] S6. Perform range-to-Fourier inverse transform on the radar echo data under the new slow time domain to obtain echo data in the range-new slow time domain; based on the echo data in the range-new slow time domain, perform azimuth-to-Fourier transform to obtain coherent accumulation echo data in the range-Doppler domain.

[0086] S7. Repeatedly calculate all acceleration ratios and rapid ratios within the range of the acceleration ratio and rapid ratio to obtain coherent accumulated echo data of the range-Doppler domain corresponding to all acceleration ratios and rapid ratios.

[0087] In this embodiment, in step S1, the radar echo is transformed to the range frequency domain by performing a fast time-domain Fourier transform on the radar echo; in the range frequency domain, the radar echo is matched and filtered without performing a range-to-Fourier inverse transform to obtain the basic data of the radar echo after frequency domain matching and filtering.

[0088] Specifically, radar echoes consist of target echoes and Gaussian white noise, where the white noise n is generally considered to be a zero-mean complex Gaussian random vector, independent of the target echo. Pulse-based radars transmit coherent pulses multiple times within the coherent accumulation time, thus receiving multiple echoes that constitute a radar echo sequence with a long coherent accumulation time.

[0089] Assuming the signal-to-noise ratio (SNR) of a single-pulse echo is SNR0, the ideal SNR value after pulse compression and pulse accumulation, without considering accumulation loss, is:

[0090] SNR output (dB)=SNR0+10log10(TBP)+10log10(N a )

[0091] In the formula, SNR output (dB) is the ideal signal-to-noise ratio; TBP is the time-bandwidth product; N a This represents the total number of pulses within the pulse accumulation time; the longer the pulse accumulation time, the larger this value becomes.

[0092] Taking the LFM waveform commonly used in radar as an example, let the carrier frequency of the transmitted signal be f. c The time width is T p The frequency modulation is K. The transmitted signal reaches the receiver after distance delay and attenuation. The received echo signal is:

[0093]

[0094] In the formula, A is the amplitude of the echo signal; τ = 2R / c is the time delay of the target's echo signal; R is the distance between the target and the radar; c is the electromagnetic wave propagation speed; j is the imaginary unit; and t is the fast time.

[0095] In this embodiment, to improve the signal-to-noise ratio gain, the radar uses multiple transmissions of pulses with the same waveform and performs coherent accumulation to increase the gain. Let the total number of pulses be M, then the total coherent accumulation time is T. m Let the pulse repetition frequency be PRF, the radar transmits and receives at intervals of 1 / PRF, let the pulse sequence number be m, and define the slow time variable as:

[0096] η m =m / PRF

[0097] During the accumulation time, the distance between the target and the radar changes continuously with the target's movement. Let the target distance at time η be R(η). m If ), then the time delay is:

[0098]

[0099] Considering the varying echo delays over longer time periods, radar echoes should be recorded using a longer time dimension variable. Therefore, the radar echo signal should be denoted as:

[0100]

[0101] In the formula, the second window function represents the pulse accumulation time length windowing.

[0102] In this embodiment, to describe the change in target distance over the long-coherence accumulation time, the distance between the target and the radar can be expressed by the following formula:

[0103]

[0104] In the formula, v is the target velocity; a is the acceleration; k is the jerk; o(η) m 4 ) indicates a higher-order component of order 4 or above.

[0105] In this embodiment, modern radar typically uses short CPI for accumulation, that is, controlling the total number of accumulated pulses or the coherent accumulation time in a single operation. This coherent accumulation time is usually in the range of tens of milliseconds (ms). Within a short time, high-order changes in the target distance can be ignored. That is, the distance between the target and the radar can be expressed by the following formula:

[0106] R(η m )=R0+vη m

[0107] In this embodiment, considering acceleration and jerk, the distance equation between the target and the radar can be expressed as follows:

[0108]

[0109] Substituting the echo delay corresponding to the above equation into the echo model, performing a Fourier transform along the fast time domain to transform it to the range frequency domain, and compensating for the second phase to complete the range-directed matched filtering (without performing the range-directed inverse Fourier transform), the frequency domain echo after matched filtering is:

[0110]

[0111] In the formula, S(f,η) m ) represents the basic radar echo data; K represents the frequency modulation; T represents the basic radar echo data. p For time width; f cτ is the carrier frequency of the transmitted signal; A is the amplitude of the echo; τ is the echo time delay of the target; T m η is the total coherent accumulation time. m The slow-time variable is discretized according to the pulse repetition frequency (PRF), with a value of m / PRF, a minimum value of 0, and a maximum value of M / PRF, where m∈Z and Z is the set of integers; f is the range frequency; j is the imaginary unit; v is the target velocity; a is the target acceleration; k is the target jerk; c is the electromagnetic wave propagation speed; and R0 is the distance between the target and the radar at time 0.

[0112] In this embodiment, in step S2, the range of acceleration ratio and jerk ratio values ​​is set based on the possible values ​​of the observed target's velocity, acceleration, and jerk.

[0113] Specifically, based on the possible range of motion of the radar-detected target—for example, in aerospace detection scenarios, the target's speed may range from hundreds of meters per second to thousands of meters per second, its acceleration may range from several meters per square second to tens of meters per square second, and its jerk may range from 0.1 meters per cubic second to several meters per cubic second—the acceleration ratio r is set in conjunction with the radar system parameters. av The range of values ​​and the rate of change r kv The range of values ​​for:

[0114]

[0115] In the formula, r av,min r av,max r kv,min r kv,max Determined based on the actual situation.

[0116] In this embodiment, in step S3, for each acceleration ratio and rapid ratio within the range of the acceleration ratio and rapid ratio, the new slow time range after the third-order time scale transformation is calculated according to the third-order time scale transformation principle; the new slow time range is discretized according to the radar pulse repetition frequency to obtain the discrete new slow time.

[0117] Specifically, to obtain high coherent accumulation gain under long accumulation time conditions, a timescale transformation is first performed, defining a new slow time. Perform the third-order time-scale transformation SOTST according to the following formula:

[0118]

[0119] Where r av For the acceleration ratio, r kv This is the speed ratio.

[0120] In this embodiment, when transforming from s(f,η) to The process has a one-to-one mapping relationship in the continuous time domain, but due to the discrete mapping in the digital domain, it becomes... The discrete observations cannot be directly obtained from the discrete observations of S(f,η) (η=m / PRF, m∈Z). Considering exist The digital sampling on the surface is also discrete, and must be... Discretize the time; the new slow time after discretization is:

[0121]

[0122] In the formula, For new slow time; This is the new slow time index after discretization.

[0123] In this embodiment, in step S4, for each new slow time and the acceleration ratio and the rapid ratio, the original slow time before the third-order time scale transformation is obtained by inverse calculation using the third-order time scale transformation formula.

[0124] Specifically, since the original data is obtained in the original slow time η m For the sampled data, it is necessary to calculate the corresponding η for a given data. m Thus from s(f,η) m )get

[0125] For acceleration ratio r av And the speed ratio r kv According to the second-order time-scale transformation formula, we can obtain:

[0126]

[0127] in,

[0128]

[0129] In the formula, Y1, Y2, A, B, and C are the terms used for calculation. Intermediate variables.

[0130] In this embodiment, in step S5, based on the original slow time and combined with the radar echo baseline data after frequency domain matched filtering, interpolation calculation is performed using a set interpolation algorithm to obtain the radar echo data under the new slow time; since the time scale transformation is different from the discrete... Sampling location The corresponding η sampling position m is not an integer. It cannot be directly obtained in the range m∈Z At this point, interpolation is required. Interpolation involves using observation data from surrounding integer sampling positions to obtain data from non-integer sampling positions. Considering that complex data interpolation algorithms need to ensure undistorted spectra, a suitable interpolation method is to use a sinc interpolation kernel. The expression for interpolating to obtain the new slow-time radar echo data is as follows:

[0131]

[0132] In the formula, S(f,η) m () represents the original slow-time radar echo data, P is the interpolation kernel length, and i is the summation index. To The integer obtained by rounding to the nearest whole number.

[0133] The relationship between the transformed target echo and the original echo is as follows:

[0134]

[0135] Right now:

[0136]

[0137] In the formula, After mapping The maximum value in the range of values.

[0138] In this embodiment, in step S6, the radar echo data under the new slow time is subjected to range-to-Fourier inverse transform to obtain echo data in the range-to-new slow time domain; based on the echo data in the range-to-new slow time domain, the azimuth-to-Fourier transform is performed to obtain coherent accumulation echo data in the range-to-Doppler domain.

[0139] Specifically, an inverse range-to-Fourier transform is performed on the transformed echo to obtain the echo in the range-new slow time domain, as shown in the following equation:

[0140]

[0141] In the formula, This is the echo data in the distance-new slow time domain.

[0142] Further azimuth-to-Fourier transform yields the coherent accumulated echo in the range-Doppler domain, as shown in the following equation:

[0143]

[0144] In the formula, Coherently accumulate echo data for the range-Doppler domain.

[0145] In this embodiment, in step S7, all acceleration ratios and rapid ratios within the range of the acceleration ratio and rapid ratio are repeatedly calculated to obtain the coherent accumulated echo data of the range-Doppler domain corresponding to all acceleration ratios and rapid ratios.

[0146] Specifically, repeat steps S4 to S6 to process each acceleration ratio and rapidity ratio within its range, and finally obtain the coherent cumulative echo data of the range-Doppler domain corresponding to all acceleration ratios and rapidity ratios.

[0147] In this embodiment, short-time coherent accumulation processing is relatively simple. When the target velocity is low, pulse-Doppler (PD) processing is usually sufficient. To overcome the low signal-to-noise ratio gain caused by short-time CPI processing, the accumulation time needs to be further increased. Long coherent accumulation times bring two problems: first, the target travels a large distance, causing the post-pulse compression echo to appear across multiple range cells over a slower time; second, the target's higher-order motion over a long period makes the Doppler echo's Doppler value non-constant, meaning that a cross-Doppler cell phenomenon occurs in the Doppler domain. The manifestation of these two phenomena in the range-Doppler domain is as follows: Figure 3 As shown in (a), this phenomenon makes it difficult to achieve the expected signal-to-noise ratio gain with pulse Doppler-based coherent processing, as the target is submerged in noise, such as... Figure 3 As shown in (b).

[0148] To achieve the desired signal-to-noise ratio (SNR) gain over long coherent processing times, a common approach is to first perform a Keystone Transform (KT) to eliminate linear distance travel, and then perform a Fractional Fourier Transform (FrFT) to eliminate Doppler diffusion caused by second-order motion, thus obtaining the coherent accumulation gain. However, this method still has drawbacks, primarily because it ignores second-order distance travel caused by second-order motion, making it difficult to achieve the ideal SNR output value after accumulation.

[0149] This invention provides a method for processing long-coherent accumulation when a target exhibits third-order motion (velocity, acceleration, and jerk), which can simultaneously correct first-order, second-order, and third-order distance movement and eliminate Doppler diffusion phenomena caused by second-order and third-order motion. Figure 4 As shown, it has a higher coherent accumulation gain, such as Figure 5 As shown.

[0150] The application scenarios of this invention are as follows:

[0151] In the military field, aerial target (such as fighter jets and missiles) detection and tracking can improve the signal-to-noise ratio through efficient coherent accumulation when the target is maneuvering at high speed and has acceleration and jerk, so as to achieve accurate capture of long-range or stealthy weak targets.

[0152] In the civil aviation field, it can monitor air traffic targets such as civil airliners and drones, and can cope with the motion state of targets during take-off and landing or sudden trajectory changes, ensuring the stability of target identification and tracking in complex airspace. In the maritime field, it can handle the non-uniform motion of ships sailing in wind and waves, and enhance the detection capability of long-range, low radar cross-section ship targets. It can also be used in low-altitude security monitoring scenarios, targeting the maneuvering motion of small targets flying at low altitudes (such as light helicopters and multi-rotor drones), and overcome the low signal-to-noise ratio limitation through long-term coherent accumulation, thereby improving the accuracy and timeliness of security early warning.

[0153] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0154] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0155] Example 2

[0156] See Figure 6 Embodiment 2 of the present invention also provides a radar back wavelength coherent accumulation device based on a third-order time-scale transformation, comprising:

[0157] The radar echo basic data acquisition module 001 is used to transform the radar echo to the range frequency domain by performing a fast time-domain Fourier transform on the radar echo; and to perform matched filtering on the radar echo in the range frequency domain without performing range-to-Fourier inverse transform to obtain the frequency domain matched-filtered radar echo basic data.

[0158] The acceleration ratio and jerk ratio value range setting module 002 is used to set the acceleration ratio and jerk ratio value range based on the possible value range of the observed target's velocity, acceleration, and jerk.

[0159] The new slow time acquisition module 003 is used to calculate the new slow time range after the third-order time scale transformation for each acceleration ratio and rapid ratio within the range of the acceleration ratio and rapid ratio values, based on the principle of third-order time scale transformation; and to quantize the new slow time range according to the radar pulse repetition frequency to obtain the discrete new slow time.

[0160] The original slow time acquisition module 004 is used to calculate the original slow time before the third-order time scale transformation for each new slow time and the acceleration ratio and the rapid ratio by performing a reverse calculation using the third-order time scale transformation formula.

[0161] The new slow time radar echo data acquisition module 005 is used to obtain the radar echo data under the new slow time by performing interpolation calculations based on the original slow time and the radar echo basic data after frequency domain matched filtering, through a set interpolation algorithm.

[0162] The range-Doppler domain coherent accumulation echo data acquisition module 006 is used to perform range-to-Fourier inverse transform on the radar echo data under the new slow time to obtain echo data in the range-to-new slow time domain; and to perform azimuth-to-Fourier transform on the echo data in the range-to-new slow time domain to obtain coherent accumulation echo data in the range-Doppler domain.

[0163] The repeat calculation module 007 is used to repeatedly calculate all acceleration ratios and rapid ratios within the range of the acceleration ratio and rapid ratio, and obtain the coherent accumulated echo data of the range-Doppler domain corresponding to all acceleration ratios and rapid ratios.

[0164] In this embodiment, the expression for the frequency-domain matched-filtered radar echo basic data in the radar echo basic data acquisition module 001 is as follows:

[0165]

[0166] In the formula, S(f,η) m ) represents the basic radar echo data; K represents the frequency modulation; T represents the basic radar echo data. p For time width; f c τ is the carrier frequency of the transmitted signal; A is the amplitude of the echo; τ is the echo time delay of the target; T m η is the total coherent accumulation time. mThe slow-time variable is discretized according to the pulse repetition frequency (PRF), with a value of m / PRF, a minimum value of 0, and a maximum value of M / PRF, where m∈Z and Z is the set of integers; f is the range frequency; j is the imaginary unit; v is the target velocity; a is the target acceleration; k is the target jerk; c is the electromagnetic wave propagation speed; and R0 is the distance between the target and the radar at time 0.

[0167] In this embodiment, the acceleration ratio and speed ratio value range setting module 002 sets the value range of acceleration ratio and speed ratio. Based on radar parameters and the acceleration ratio and speed ratio to be searched, the value range of the new slow time is calculated according to a third-order time scale transformation, i.e., the minimum and maximum values. This is then discretized according to the PRF (Pressure Realm Function). The minimum value of the new slow time is 0, and the maximum value expression is:

[0168]

[0169] In the formula, r av For the acceleration ratio, r kv This is the speed ratio.

[0170] exist The new slow time expression after discretization according to PRF within the range is as follows:

[0171]

[0172] In the formula, For new slow time; This is the new slow time index after discretization.

[0173] In this embodiment, the original slow time acquisition module 004 calculates the original slow time based on the new slow time after PRF quantization through the inverse process of third-order time transformation. The expression for the original slow time is:

[0174]

[0175] in,

[0176]

[0177] In the formula, Y1, Y2, A, B, and C are the terms used for calculation. Intermediate variables.

[0178] In this embodiment, in the radar echo data acquisition module 005 under the new slow time, during the process of obtaining the radar echo data under the new slow time through interpolation calculation using the set interpolation algorithm, the expression for the radar echo data under the new slow time is:

[0179]

[0180] In the formula, S(f,η) m () represents the original slow-time radar echo data, P is the interpolation kernel length, and i is the summation index. To The integer obtained by rounding to the nearest whole number.

[0181] In this embodiment, the range-Doppler domain coherent accumulation echo data acquisition module 006 obtains range-new slow time domain echo data by performing an inverse Fourier transform of the range frequency domain-new slow time domain echo data with respect to the range frequency. The expression for the range-new slow time domain echo data is:

[0182]

[0183] In the formula, This is the echo data in the distance-new slow time domain.

[0184] In this embodiment, the range-Doppler domain coherent accumulation echo data acquisition module 006 obtains range-Doppler domain coherent accumulation echo data by performing a Fourier transform of the range-new-slow-time domain echo data with respect to the new-slow time. The expression for the range-Doppler domain coherent accumulation echo data is as follows:

[0185]

[0186] In the formula, Coherently accumulate echo data for the range-Doppler domain.

[0187] The method embodiments in Example 1 are based on the same concept, and the technical effects they bring are the same as those in the method embodiments of this application. For details, please refer to the description in the method embodiments shown above in this application, which will not be repeated here.

[0188] Example 3

[0189] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code for a radar back wavelength coherent accumulation method based on a third-order time-scale transformation. The program code includes instructions for executing the radar back wavelength coherent accumulation method based on a third-order time-scale transformation as described in Embodiment 1 or any possible implementation thereof.

[0190] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives, SSDs).

[0191] Example 4

[0192] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0193] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can call the program instructions to execute the radar back wavelength coherent accumulation method based on third-order time-scale transformation in Embodiment 1 or any possible implementation thereof.

[0194] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0195] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0196] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0197] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A radar backwavelength coherent accumulation method based on third-order time-scale transformation, characterized in that, include: The radar echo is transformed into the range frequency domain by performing a fast time-domain Fourier transform on the radar echo; matched filtering is then performed on the radar echo in the range frequency domain without performing an inverse range-to-Fourier transform, resulting in the basic radar echo data after frequency domain matched filtering. Based on the possible ranges of velocity, acceleration, and jerk of the observed target, the ranges of acceleration ratio and jerk ratio are set. For each acceleration ratio and rapid ratio within the range of the acceleration ratio and rapid ratio, the new slow time range after the third-order time scale transformation is calculated according to the third-order time scale transformation principle; the new slow time range is discretized according to the radar pulse repetition frequency to obtain the discrete new slow time. For each new slow time, acceleration ratio, and rapid ratio, the original slow time before the third-order time scale transformation is obtained by inverse calculation using the third-order time scale transformation formula. Based on the original slow time, and combined with the radar echo base data after frequency domain matched filtering, interpolation calculation is performed by setting an interpolation algorithm to obtain the radar echo data under the new slow time. Perform a range-to-Fourier inverse transform on the radar echo data under the new slow time domain to obtain echo data in the range-to-new slow time domain; based on the echo data in the range-to-new slow time domain, perform an azimuth-to-Fourier transform to obtain coherently accumulated echo data in the range-to-Doppler domain. Repeated calculations are performed on all acceleration ratios and rapid ratios within their respective ranges to obtain coherent accumulated echo data in the range-Doppler domain corresponding to all acceleration ratios and rapid ratios.

2. The radar back wavelength coherent accumulation method based on third-order time-scale transformation according to claim 1, characterized in that, The expression for the basic radar echo data after frequency domain matched filtering is: In the formula, S(f,η) m ) represents the basic radar echo data; K represents the frequency modulation; T represents the basic radar echo data. p For time width; f c τ is the carrier frequency of the transmitted signal; A is the amplitude of the echo; τ is the echo time delay of the target; T m For the total coherent accumulation time; η m The slow-time variable is discretized according to the pulse repetition frequency (PRF), with a value of m / PRF, a minimum value of 0, and a maximum value of M / PRF, where m∈Z and Z is the set of integers; f is the range frequency; j is the imaginary unit; v is the target velocity; a is the target acceleration; k is the target jerk; c is the electromagnetic wave propagation speed; and R0 is the distance between the target and the radar at time 0.

3. The radar back wavelength coherent accumulation method based on third-order time-scale transformation according to claim 2, characterized in that, The acceleration ratio and speed ratio are set within a certain range. Based on the radar parameters and the acceleration ratio and speed ratio to be searched, the range of the new slow time (i.e., the minimum and maximum values) is calculated using a third-order time scale transformation. This is then discretized according to the PRF (Pressure, Power, and Reduction) algorithm. The minimum value of the new slow time is 0, and the maximum value is expressed as: In the formula, r av For the acceleration ratio, r kv For rapidity ratio; exist The new slow time expression after discretization according to PRF within the range is as follows: In the formula, For new slow time; This is the new slow time index after discretization.

4. The radar back wavelength coherent accumulation method based on third-order time-scale transformation according to claim 3, characterized in that, The original slow time is calculated based on the new slow time after PRF quantization. The expression for the original slow time is as follows: in, In the formula, Y1, Y2, A, B, and C are the terms used for calculation. Intermediate variables.

5. The radar back wavelength coherent accumulation method based on third-order time-scale transformation according to claim 4, characterized in that, In the process of obtaining the radar echo data under the new slow time using the interpolation algorithm, the expression for the radar echo data under the new slow time is: In the formula, S(f,η) m () represents the original slow-time radar echo data, P is the interpolation kernel length, and i is the summation index. To The integer obtained by rounding to the nearest whole number.

6. The radar back wavelength coherent accumulation method based on third-order time-scale transformation according to claim 5, characterized in that, The distance-to-new-slow-time domain echo data is obtained by performing an inverse Fourier transform on the distance-frequency-to-new-slow-time domain echo data with respect to the distance frequency. The expression for the distance-to-new-slow-time domain echo data is as follows: In the formula, Echo data in the distance-new slow time domain; Range-Doppler coherently accumulated echo data is obtained by performing a Fourier transform of the range-new-slow time domain echo data with respect to the new-slow time. The expression for the range-Doppler coherently accumulated echo data is as follows: In the formula, Coherently accumulate echo data for the range-Doppler domain.

7. A radar back wavelength coherent accumulation device based on third-order time-scale transformation, employing the radar back wavelength coherent accumulation method based on third-order time-scale transformation as described in any one of claims 1-6, characterized in that, include: The radar echo basic data acquisition module is used to transform the radar echo to the range frequency domain by performing a fast time-domain Fourier transform on the radar echo; and to perform matched filtering on the radar echo in the range frequency domain without performing an inverse range-to-Fourier transform to obtain the frequency-domain matched-filtered radar echo basic data. The acceleration ratio and jerk ratio value range setting module is used to set the acceleration ratio and jerk ratio value range based on the possible value range of the observed target's velocity, acceleration, and jerk. The new slow time acquisition module is used to calculate the new slow time range after the third-order time scale transformation for each acceleration ratio and rapid ratio within the range of the acceleration ratio and rapid ratio values, based on the principle of third-order time scale transformation; and to quantize the new slow time range according to the radar pulse repetition frequency to obtain the discrete new slow time. The original slow time acquisition module is used to calculate the original slow time before the third-order time scale transformation for each new slow time, the acceleration ratio, and the rapid ratio by performing a reverse calculation using the third-order time scale transformation formula. The new slow time radar echo data acquisition module is used to obtain the radar echo data under the new slow time by performing interpolation calculations based on the original slow time and the radar echo basic data after frequency domain matched filtering, through a set interpolation algorithm. The range-Doppler domain coherent accumulation echo data acquisition module is used to perform range-to-Fourier inverse transform on the radar echo data under the new slow time to obtain echo data in the range-to-new slow time domain; and to perform azimuth-to-Fourier transform on the echo data in the range-to-new slow time domain to obtain coherent accumulation echo data in the range-Doppler domain. The repeated calculation module is used to repeatedly calculate all acceleration ratios and rapid ratios within the range of the acceleration ratio and rapid ratio, and obtain the coherent accumulated echo data of the range-Doppler domain corresponding to all acceleration ratios and rapid ratios.

8. The radar back wavelength coherent accumulation device based on third-order time-scale transformation according to claim 7, characterized in that, In the radar echo basic data acquisition module, the expression for the frequency-domain matched-filtered radar echo basic data is: In the formula, S(f,η) m ) represents the basic radar echo data; K represents the frequency modulation; T represents the basic radar echo data. p For time width; f c τ is the carrier frequency of the transmitted signal; A is the amplitude of the echo; τ is the echo time delay of the target; T m For the total coherent accumulation time; η m The slow-time variable is discretized according to the pulse repetition frequency (PRF), with a value of m / PRF, a minimum value of 0, and a maximum value of M / PRF, where m∈Z and Z is the set of integers; f is the range frequency; j is the imaginary unit; v is the target velocity; a is the target acceleration; k is the target jerk; c is the electromagnetic wave propagation speed; and R0 is the distance between the target and the radar at time 0.

9. The radar back wavelength coherent accumulation device based on third-order time-scale transformation according to claim 8, characterized in that, In the acceleration ratio and speed ratio value range setting module, the value range of acceleration ratio and speed ratio is set. Based on the radar parameters and the acceleration ratio and speed ratio to be searched, the value range of the new slow time is calculated according to the third-order time scale transformation, that is, the minimum and maximum values, and discretized according to PRF. The minimum value of the new slow time is 0, and the expression for the maximum value is: In the formula, r av For the acceleration ratio, r kv This is the speed ratio. exist The new slow time expression after discretization according to PRF within the range is as follows: In the formula, For new slow time; This is the new slow time index after discretization. In the original slow time acquisition module, the original slow time is calculated by inverse process of third-order time transformation based on the new slow time after PRF quantization. The expression for the original slow time is: in, In the formula, Y1, Y2, A, B, and C are the terms used for calculation. Intermediate variables.

10. The radar back wavelength coherent accumulation device based on third-order time-scale transformation according to claim 9, characterized in that, In the radar echo data acquisition module under the new slow time, during the process of obtaining the radar echo data under the new slow time by performing interpolation calculations using the set interpolation algorithm, the expression for the radar echo data under the new slow time is: In the formula, S(f,η) m () represents the original slow-time radar echo data, P is the interpolation kernel length, and i is the summation index. To The integer obtained by rounding to the nearest integer; In the range-Doppler domain coherent accumulation echo data acquisition module, range-new slow-time domain echo data is obtained by performing an inverse Fourier transform of the range-frequency domain-new slow-time domain echo data with respect to the range frequency. The expression for the range-new slow-time domain echo data is as follows: In the formula, Echo data in the distance-new slow time domain; In the range-Doppler domain coherent accumulation echo data acquisition module, range-Doppler domain coherent accumulation echo data is obtained by performing a Fourier transform of the range-new-slow-time domain echo data with respect to the new-slow time. The expression for the range-Doppler domain coherent accumulation echo data is as follows: In the formula, Coherently accumulate echo data for the range-Doppler domain.

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