CN113514798A - A Time Difference/Scale Difference Estimation Method for Wideband Nonlinear FM Signal Based on Fourier Merlin Transform - Google Patents
A Time Difference/Scale Difference Estimation Method for Wideband Nonlinear FM Signal Based on Fourier Merlin Transform Download PDFInfo
- Publication number
- CN113514798A CN113514798A CN202110786412.2A CN202110786412A CN113514798A CN 113514798 A CN113514798 A CN 113514798A CN 202110786412 A CN202110786412 A CN 202110786412A CN 113514798 A CN113514798 A CN 113514798A
- Authority
- CN
- China
- Prior art keywords
- scale
- time
- difference
- signal
- transform
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 55
- 238000005314 correlation function Methods 0.000 claims description 23
- 238000012545 processing Methods 0.000 abstract description 6
- 241000272186 Falco columbarius Species 0.000 abstract 1
- 238000004364 calculation method Methods 0.000 description 19
- 238000001228 spectrum Methods 0.000 description 16
- 238000005070 sampling Methods 0.000 description 9
- 238000004088 simulation Methods 0.000 description 5
- 230000005855 radiation Effects 0.000 description 4
- 238000007796 conventional method Methods 0.000 description 3
- 238000013459 approach Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 230000003595 spectral effect Effects 0.000 description 2
- 230000009466 transformation Effects 0.000 description 2
- 238000000342 Monte Carlo simulation Methods 0.000 description 1
- 241000801924 Sena Species 0.000 description 1
- 230000003044 adaptive effect Effects 0.000 description 1
- 230000003471 anti-radiation Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004422 calculation algorithm Methods 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 230000006835 compression Effects 0.000 description 1
- 238000007906 compression Methods 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 230000001360 synchronised effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
本发明属于信号处理领域，针对双星无源定位系统中的时差/尺度差估计问题，提出基于傅里叶梅林变换的宽带非线性调频信号时差/尺度差估计方法，核心思想是利用傅里叶变换“时移不变性”、梅林变换“尺度不变性”对时差/尺度差进行级联估计。结果表明，相比传统基于宽带互模糊函数的时差/尺度差估计方法，所提方法计算复杂度更低；相比基于分数阶傅里叶变换的时差/尺度差估计方法，所提方法可适用线性调频(LFM)、二次调频(QFM)、指数调频(EFM)、双曲调频(HFM)及高斯噪声脉冲信号。
The invention belongs to the field of signal processing, and aims at the time difference/scale difference estimation problem in a dual-star passive positioning system, and proposes a time difference/scale difference estimation method based on Fourier Merlin transform for a broadband nonlinear frequency modulation signal. The core idea is to use Fourier transform "Time shift invariance", Merlin transform "scale invariance" cascade estimation of time difference/scale difference. The results show that the proposed method has lower computational complexity than the traditional time difference/scale difference estimation method based on broadband mutual ambiguity function; compared with the time difference/scale difference estimation method based on fractional Fourier transform, the proposed method is applicable Linear Frequency Modulation (LFM), Quadratic Frequency Modulation (QFM), Exponential Frequency Modulation (EFM), Hyperbolic Frequency Modulation (HFM) and Gaussian Noise Pulse Signals.
Description
Technical Field
The invention belongs to the field of signal processing, and is suitable for solving the time difference/scale difference estimation problem in a double-satellite passive positioning system.
Background
Electronic warfare is an important component of information-based warfare, and accurate positioning of targets is an important content of electronic warfare. The target positioning system can be generally divided into an active positioning system and a passive positioning system, wherein the typical active positioning system is a radar, and the target echo is acquired by externally radiating an electromagnetic signal, so that the target echo is easily detected by an enemy on a battlefield and is struck by an anti-radiation weapon. Compared with the prior art, the passive positioning system does not radiate electromagnetic signals, has good concealment, and is typically double-satellite passive positioning. Under the broadband condition, the double-satellite passive positioning system estimates Time Difference (TDOA) and Scale Difference (SDOA) according to two paths of received signals, and then accurately positions a radiation source by utilizing the geometrical relationship among satellites, targets and the earth. In order to estimate the time difference/scale difference, the traditional method is to calculate a wideband mutual-ambiguity function (WBCAF) of two paths of received signals, the method can estimate 2 parameters simultaneously, and is suitable for various source signal forms, and the problem is that the calculation amount is large. The WBCAF calculation process comprises two steps, firstly, a scale version of one path of signal is calculated, then the scale version and the other path of signal are subjected to related processing, and since the 2 nd step can be quickly realized in a frequency domain by FFT and IFFT, the difficulty restricting the quick realization of WBCAF is the 1 st step, and aiming at the problem, a multi-rate sampling reconstruction filtering method is proposed in documents [ Wangzhao, Wangbangyi, Suweimin, and the like. Part of the research considers computing WBCAF only in the transform domain to avoid the scale version computation problem, wherein the document [ NIU X, CHING P C. wavelet based adaptive approach for joint time delay and Doppler stretch measures [ J ]. IEEE transformation on Aerospace and Electronic Systems,1999,35(3): 1111-. The document [ Wangjun, Liyaan, wideband underwater acoustic signal processing research [ J ] based on Mellin transform, war institute, 2007,28(1):87-90] proposes a WBCAF implementation method based on Mellin transform, but the numerical calculation methods of the Mellin transform are various, and the calculation precision of the used method is not high. In addition, if the source signal form is known, the time difference/scale difference estimation problem becomes relatively easy, for example, for chirp source signals, documents [ guo pay yang, zhangyao, yanlinson ] wideband chirp time difference/scale difference estimation algorithm [ J ] electric wave science report, 2017,32(4): 441-. The improved method reduces the overall complexity of operation through two-step cascade processing, the time difference/scale difference estimation mean square error approaches the lower boundary of Cramer under the condition of low signal-to-noise ratio, and unfortunately, the method cannot be applied when the source signal is a nonlinear frequency modulation signal.
Aiming at the problems, the invention provides a method for estimating the time difference/scale difference of the broadband nonlinear frequency modulation signal based on Fourier Mellin transform by utilizing the characteristic that the spectral envelopes of two paths of signals are mutually scaled versions. The core idea is to utilize Fourier transform 'time shift invariance' and Mellin scale transform 'scale invariance' to carry out cascade estimation on the scale difference/time difference. Simulation results show that when the SNR is larger than 5dB, the method can accurately estimate time difference and scale difference of 4 broadband nonlinear frequency modulation signals of Quadratic Frequency Modulation (QFM), Exponential Frequency Modulation (EFM), Hyperbolic Frequency Modulation (HFM) and Sinusoidal Frequency Modulation (SFM), the average relative error of time difference estimation is smaller than 1%, and the average relative error of scale difference estimation is smaller than 5%.
Disclosure of Invention
The invention aims to provide a time difference/scale difference estimation method of a broadband nonlinear frequency modulation signal based on Fourier Mellin transform, so as to solve the problem of time difference/scale difference estimation in a double-satellite passive positioning system. To illustrate the present invention, first, a conventional time difference/scale difference estimation method and an improved method are briefly introduced; secondly, 2 basic concepts, Time Scale (TS) and Scale Estimation (SE), are introduced; thirdly, the basic principle of the invention is introduced; then, compared with the traditional time difference/scale difference estimation method based on the broadband mutual fuzzy function, the calculation complexity of the method is analyzed; finally, the method steps of the invention are presented.
(1) Traditional time difference/scale difference estimation method and improvement method
Under the broadband condition, a double-star passive positioning system is utilized to position a fixed radiation source on the ground, and the 1 st path of signal is taken as a reference, so that the signals received by 2 independent receivers can be expressed as follows:
in the formula: x is the number of1(t)、x2(t) are respectively the 1 st path and the 2 nd path receiving signals, t is more than or equal to 0 and is a time independent variable, A1、A2For the path gain of the source signal s (t) to 2 receivers, Δ t is the time difference of two paths (TDOA), Δ α is the Scale Difference (SDOA) related to the radial velocity of the satellite relative to the source and the speed of light, n1(t)、n2(t) is complex white gaussian noise at the base of the receiver. The traditional time difference/scale difference estimation method is implemented using a wideband mutual ambiguity function (WBCAF). The WBCAF of the successive signals z (t) and x (t) is defined as:
in the formula: γ is the WBCAF scale factor, τ is the time shift, and x is the conjugate sign. Let z (t) be x2(t)、x(t)＝x1(t), it is easy to know that | X when γ ═ 1+ Δ α and τ ═ Δ tzxThe (gamma, tau) | takes the maximum value, and the peak search can obtain the time difference and the scale difference (needs to be reduced by 1). WBCAF can be expressed as a fast implementation in the frequency domain in the form of a convolution, i.e.:
in the formula:
is a convolution symbol, F [ ·]、F-1[·]Is a FuThe interior and inverse transforms represent symbols. In order to calculate the WBCAF of the two received signals, a scale factor search interval needs to be set, and then the 1 st signal is "stretched" or "compressed" according to different scale factors, and the expansion of the search interval can result in the multiplication of the calculation amount. When the source signal form is known, the time difference/scale difference estimation problem becomes relatively easy, if the source signal is a single-frequency signal, the difference in scale reflects the difference in the frequency of the received signal, if the source signal is an LFM signal, the difference in the frequency modulation slope reflects the difference in the frequency modulation slope, SDOA can be obtained by estimating the frequency of the two paths of signals or the frequency modulation slope, and then x is corrected according to the estimated SDOA1(t) is "stretched" or "compressed" and then reacted with x2(t) the time-domain correlation process can obtain TDOA, and this improved method, although capable of significantly reducing the amount of computation, cannot be applied when the source signal is an NLFM signal. Commonly used NLFM signals in radar and communication systems comprise Quadratic Frequency Modulation (QFM), Exponential Frequency Modulation (EFM), Hyperbolic Frequency Modulation (HFM), Sinusoidal Frequency Modulation (SFM) and the like, and the complex forms are as follows in sequence:
in the formula: t is time width, f1、f2Starting and cut-off frequencies, T, of the 4 signals, respectively0HFM latency. The QFM, EFM, HFM, SFM instantaneous frequencies obtained by phase derivation are:
(2) time scale and scale estimation
The Time Scale (TS), i.e. the mapping process of the continuous signals x (t) to y (t), can be expressed as:
in the formula: TS (transport stream)α[·]Denotes the symbol for TS, α ∈ R+Is a function of the scale factor, and is,
to keep the signal energy before and after TS the same, namely:
when alpha is more than 0 and less than 1, the TS post-signal time domain expands, and when alpha is more than 1, the TS post-signal time domain contracts. According to the Fourier transform scale property, the following steps are carried out:
in the formula: y (f), X (f) are Fourier transforms of y (t) and x (t), respectively, and f is a frequency independent variable. It can be seen that performing TS on the signal also results inThe bandwidth is proportionally decreased (0 < alpha < 1) or increased (alpha > 1). Setting continuous signals
α1Is z (t) scale factor. So-called Scale Estimation (SE), i.e. z (t), x (t) when known for alpha1Can be expressed as:
in the formula:
is alpha1Estimated value of phizx(α) is the scale cross-correlation function (SCF) of z (t) with x (t), i.e.:
in the formula: is the scale cross correlation symbol. When τ is 0, WBCAF is similar to SCF, differing by different integration intervals. The Scale Transform (ST) is a special case where the real part of the complex argument of the Mellin Transform (MT) takes 0.5, and is expressed as:
in the formula: s {. is ST denotes symbol, Df(c) ST, c for signal f (t) are scale independent variables. Inverse Scale Transform (IST) is:
in the formula: s-1Symbol for IST. Let t be euObtaining:
it can be seen that ST is actually
The fourier transform of (f), (t) can be performed exponentially and then quickly by FFT, i.e., Fast Scale Transform (FST), which is generally called as exponential sampling FST. Literature [ SENA D A, ROCHESSO D.A fast Mellin and Scale transform [ J ]].EURASIP Journal on Advances in Signal Processing,2007:089170]By analyzing each implementation link, obtaining the index sampling type FST with the calculation complexity of O [ (N ln N) log2(N ln N)]N is the number of equally spaced sampling points of the original signal, and the total required complex multiplication times is N ln N +0.5N ln Nlog2(N ln N). The following are easy to know:
it can be seen that IST can also be quickly implemented by IFFT to obtain fast inverse scale transform (IFST), and the calculation process is opposite to FST, and D is calculated firstf(c) And performing inverse Fourier transform and then performing logarithmic sampling. To solve the problem of fast implementation of TS, reference is made to ST scale invariance, i.e.:
in the formula: dx(c)、Dz(c) ST of x (t), z (t), respectively, has the same envelope and different phase. Computing the equation IST, we readily obtain:
the above formula is used to obtain the after-TS signal of x (t) at a certain scale factor. SE is also rapidly implemented using ST, specifically:
(3) basic principle of the invention
For the purpose of introducing the present invention, receiver noise is not considered for the moment, and is readily available:
in the formula: x1(f)、X2(f) Are respectively x1(t)、x2(t) Fourier transform, f ≧ 0 is the frequency independent variable. The following are easy to know:
as can be seen, | X2(f) Actual is | X1(f) The scale version of l, the scale factor is 1/(1+ Δ α), independent of the source signal form. When | X1(f)|、|X2(f) When | is known, the estimation of 1/(1+ Δ α) belongs to a scale estimation concept, the spectral envelope scale cross-correlation function of two paths of signals is calculated, 1/(1+ Δ α) can be estimated, further, the scale difference Δ α is obtained, and then, for x, the scale difference Δ α is obtained1(t) carrying out time scale (scale factor takes 1+ delta alpha) to obtain the 1 st path signal after the time scale
Calculating x2(t) and
time domain cross correlation function of
Tau is a time delay independent variable and is obtained by taking envelope
Searching peak value to obtain corresponding time delay tau0I.e. the estimated time difference at. The time domain cross-correlation function calculation formula is as follows:
therein, Ψzx(τ) is the time-domain cross-correlation function of the continuous signal z (t) and x (t), □ is the time-domain cross-correlation sign. Ψzx(τ) is implemented using FFT and IFFT, i.e.:
Ψzx(τ)＝F-1{F[z(t)]F*[x(γt)]；τ}
(4) computational complexity analysis
First, the Time Scale (TS) computation complexity is analyzed. The TS implementation process comprises three links of 'FST + phase correction + IFST', and the calculation complexity is O [ (N ln N) log2(N ln N)]Total 3N ln N + N ln Nlog2(N ln N) complex multiplications. Second, the Scale Estimation (SE) computational complexity is analyzed. The key point of SE realization is that the calculation of the scale cross-correlation function specifically needs 2 FST, 1 complex product and 1 IFST, and the calculation complexity is O [ (N ln N) log2(N ln N)]Total 4N ln N +1.5N ln Nlog is required2(N ln N) complex multiplications. And thirdly, analyzing the calculation complexity of the traditional time difference/scale difference estimation method based on the broadband mutual fuzzy function. For 1 scale factor, 1 TS, 2 FFT, 1 IFFT and 1 dot product are needed for WBCAF calculation, and MN +1.5MNlog is needed in total2N+3MN ln N+MNln Nlog2(N ln N) times complex multiplication operation, and the calculation complexity is O [ (MN ln N) log2(N ln N)]And M is the numeric value of the scale factor. Finally, the computational complexity of the present invention is analyzed. 2 FFT and 1 SE are needed for estimating the scale difference, and 1 TS and 1 time domain correlation (2 FFT, 1 IFFT and 1 dot product) are needed for estimating the time difference, and N +2.5Nlog is needed in total2N+7N ln N+2.5N·lnNlog2(N ln N) times complex multiplication operation, and the calculation complexity is O [ (N ln N) log2(N ln N)]. Because the traditional method needs to perform 1 two-dimensional search (the invention needs to perform 2 one-dimensional searches), the actual computation amount is larger.
(5) Method steps of the invention
The invention mainly comprises the following steps:
calculating Fourier transform of two paths of signals, and obtaining two paths of signal frequency spectrums by using a packet;
step two, calculating a scale cross-correlation function of the 2 nd path signal spectrum and the 1 st path signal spectrum, and searching and estimating a scale difference by a peak value;
step three, performing time scale on the 1 st path of signal according to the estimated scale difference;
and step four, calculating a time domain cross-correlation function of the 2 nd path signal and the 1 st path signal after the time scale, and searching and estimating the time difference by the peak value.
The steps are as follows:
step (I) of calculating the 1 st path signal x1(t) and 2 nd path signal x2(t) Fourier transform, taking envelope to obtain | X1(f)|、|X2(f) Where t ≧ 0 is the time independent variable, f ≧ 0 is the frequency independent variable, X1(f)、X2(f) Are respectively x1(t)、x2(t) Fourier transform;
step (two) of calculating | X2(f) I and | X1(f) Scale cross correlation function of |
α∈R+Is a scale factor independent variable and is obtained by envelope taking
Searching peak value to obtain corresponding scale factor alpha0And the estimated scale difference delta alpha is 1/alpha0-1；
Step (three) making alpha be 1+ delta alpha and making said signal be matched with 1 st channel signal x1(t) performing time scale to obtain the 1 st path signal after time scale operation as
TSα[·]Representing symbols for a time scale;
step (four) of calculating x2(t) and
time domain cross correlation function of
Tau is a time delay independent variable and is obtained by taking envelope
Searching peak value to obtain corresponding time delay tau0I.e. the estimated time difference at.
The beneficial effects of the invention are illustrated as follows:
compared with the traditional time difference/scale difference estimation method based on WBCAF, the time difference/scale difference estimation method based on the FRFT is lower in calculation complexity, and compared with the time difference/scale difference estimation improvement method based on the FRFT, the time difference/scale difference estimation method based on the FRFT is applicable to signal forms such as broadband LFM and NLFM.
Drawings
FIG. 1 is a flow chart of the method steps of the present invention;
FIG. 2 is a graph showing the variation of the number of complex multiplications with the number of sampling points;
FIG. 3 is a time domain waveform of an NLFM signal;
FIG. 4 is a time-frequency distribution of NLFM signals;
FIG. 5 is a received signal time domain waveform and spectrum;
FIG. 6 is a scale cross correlation function of the received signal spectrum;
FIG. 7 is a time domain waveform and spectrum of a received signal after a time scale;
FIG. 8 is a time-domain cross-correlation function of the 2 nd signal and the 1 st signal after time scaling;
FIG. 9 is a plot of mean relative error of scale difference estimation as a function of signal to noise ratio;
figure 10 is a plot of the mean relative error of the time difference estimate versus the signal to noise ratio.
Detailed description of the invention
The present invention will be described in detail below with reference to the accompanying drawings. FIG. 1 is a flow chart of the method steps of the present invention. The method comprises the following specific steps:
calculating Fourier transform of two paths of signals, and obtaining two paths of signal frequency spectrums by using a packet;
step (2) calculating a scale cross-correlation function of the 2 nd path signal spectrum and the 1 st path signal spectrum, and searching and estimating a scale difference by a peak value;
step (3) time scale is carried out on the 1 st path of signal according to the estimated scale difference;
and (4) calculating a time domain cross-correlation function of the 2 nd path signal and the 1 st path signal after the time scale, and searching and estimating a time difference by a peak value.
The values of WBCAF scale factors in the traditional method are respectively 10, 100 and 1000, and the figure 2 is a curve of the variation of the multiplication times of the method and the traditional method along with the number of sampling points, the calculated amount of the traditional method is multiplied along with the values of the scale factors, and the calculated amount of the method is obviously lower than that of the traditional method.
The implementation conditions are as follows: the simulation experiment was performed under the following parameter conditions:
TABLE 1 radiation source and receive signal
A radiation source is arranged to emit 4 NLFM signals of QFM, EFM, HFM and SFM, the time width is 2.5 mu s, the bandwidth is 250MHz, the starting frequency and the cut-off frequency are respectively 10MHz and 260MHz, the HFM delay time is 1 time domain sampling interval, the sampling frequency of the double-satellite passive positioning system is 1GHz, and the time difference/scale difference of two received signals is respectively 3.75 mu s and 0.1. Fig. 3 shows time domain waveforms of 4 NLFM signals, and fig. 4 shows time-frequency distribution of NLFM signals obtained by synchronous compression transformation. The source signal is an SFM signal, the time duration of the received signal is 10 μ s, and the feasibility of the invention is verified according to the flow of fig. 1. The time domain waveform and the frequency spectrum of the two paths of received signals are shown in fig. 5. And calculating the scale cross-correlation function of the two signal spectrums to estimate the scale difference, and the result is shown in fig. 6. According to the estimated scale difference, the 1 st path signal is subjected to time scale, and the time domain waveform and the frequency spectrum of the received signal after the time scale are shown in fig. 7. The time-domain cross-correlation function of the 2 nd path signal and the 1 st path signal after the time scale is shown in fig. 8. LFM signals (the initial frequency and the cut-off frequency are the same as the initial frequency) and 4 NLFM signals and zero-mean Gaussian white noise are respectively selected as source signals, and the average relative error (MRE) is used as an index to evaluate the anti-noise performance of the traditional method and the anti-noise performance of the invention. The SNR takes a value of-10 dB, the interval is 1dB, Monte Carlo simulation is operated for 500 times, a curve of the average relative error of the scale difference estimation along with the signal-to-noise ratio is obtained, and is shown in figure 9, and figure 10 is a curve of the average relative error of the time difference estimation along with the signal-to-noise ratio. As can be seen from fig. 5, due to the existence of the scale difference, the SFM signal in the 2 nd path signal has time-domain shrinkage and spectrum expansion phenomena compared with the SFM signal in the 1 st path signal; as can be seen from fig. 6, when the spectrum is enveloped, the estimated scale factor is 0.9092, the scale difference is 0.0999, which is consistent with the scale difference 0.1 set by the simulation, and if the spectrum is not enveloped, the estimation result is completely wrong; as can be seen from fig. 7, the SFM signals in the two paths of received signals have substantially the same time width and bandwidth, and do not contract or expand; as can be seen from the attached figure 8, the time domain cross-correlation function is approximate to a sine function, and the time difference obtained by peak value search and estimation is 3.75 mus and is completely consistent with the parameters set by simulation; as can be seen from fig. 9 and 10, the estimation efficiency of the conventional method and the estimation efficiency of the invention for the time difference/scale difference of different signal forms are different, and in general, the conventional method is more suitable for the low SNR condition, when the SNR is greater than-4 dB, the MRE of 4 signal scale differences of LFM, QFM, EFM, and SFM is less than 5%, and the MRE of the time difference estimation is less than 1%, but the SNR of the invention is required to be greater than 5dB, it should be noted that the estimation accuracy of the invention is higher than that of the conventional method under the high SNR condition because the calculation of WBCAF requires manual setting of the scale factor value range and the interval (the scale factor value range is set to be 0.5-1.5 in the simulation, and the interval is 0.01), and when the value range is fixed, the interval is reduced, the estimation accuracy can be improved, but a larger calculation amount is also required. The traditional method has extremely poor estimation effect on the HFM scale difference, the scale difference estimation MRE under different SNR conditions is more than 13%, and the estimation error is obviously higher than that of the method, because the HFM has Doppler invariance, the ridge line of the broadband fuzzy function is approximately linear, the ridge line amplitude is relatively close, the peak value search cannot accurately estimate the time difference/scale difference, but the method performs scale estimation on the signal spectrum envelope, and the problem does not exist. Meanwhile, the critical SNR of the noise signal scale difference estimation MRE less than 5% is respectively 2dB and 3dB, the critical SNR of the time difference estimation MRE less than 1% is respectively 1dB and 2dB, and the estimation efficiency is not greatly different.
Claims (4)
1. The method for estimating the time difference/scale difference of the broadband nonlinear frequency modulation signal based on Fourier Mellin transform is characterized by comprising the following steps of:
step (I) of calculating the 1 st path signal x1(t) and 2 nd path signal x2(t) Fourier transform, taking envelope to obtain | X1(f)|、|X2(f) Where t ≧ 0 is the time independent variable, f ≧ 0 is the frequency independent variable, X1(f)、X2(f) Are respectively x1(t)、x2(t) Fourier transform;
step (two) of calculating | X2(f) I and | X1(f) Scale cross correlation function of |
α∈R+Is a scale factor independent variable and is obtained by envelope taking
Searching peak value to obtain corresponding scale factor alpha0Estimated to obtain a difference in scale of 1/alpha0-1；
Step (three) making alpha be 1+ delta alpha and making said signal be matched with 1 st channel signal x1(t) performing time scale to obtain the 1 st path signal after time scale operation as
TSα[·]Representing symbols for a time scale;
step (four) of calculating x2(t) and
time domain cross correlation function of
Tau is a time delay independent variable and is obtained by taking envelope
Searching peak value to obtain corresponding time delay tau0I.e. the estimated time difference.
2. The fourier-mellin-transform-based method for estimating moveout/scale difference of a wideband non-chirp signal according to claim 1, wherein the scale cross-correlation function in step (two) is calculated as:
wherein phizxAnd (α) is the scale cross-correlation function of the continuous signal z (t) with x (t), and the symbol of scale cross-correlation, and the symbol of conjugate. Phizx(α) is implemented using a Scale Transform (ST) and an Inverse Scale Transform (IST), namely:
wherein S is-1{. is IST denotes symbol, Dx(c)、Dz(c) ST for x (t), z (t), respectively.
3. The fourier-mellin-transform-based method for estimating moveout/scale difference of a wideband non-chirp signal according to claim 1, wherein the time scale in step (three) is operated as
4. The fourier-mellin-transform-based method for estimating moveout/scale difference of a wideband non-chirp signal according to claim 1, wherein the time-domain cross-correlation function in step (iv) is calculated by the following formula:
therein, Ψzx(τ) is the time-domain cross-correlation function of the continuous signal z (t) with x (t),
is a time domain cross correlation symbol. Ψzx(τ) is implemented using Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT), namely:
Ψzx(τ)＝F-1[F[z(t)]F*[x(γt)]]
wherein F [. C]For FFT representation of symbols, F-1[·]The symbols are represented for an IFFT.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110786412.2A CN113514798A (en) | 2021-07-12 | 2021-07-12 | A Time Difference/Scale Difference Estimation Method for Wideband Nonlinear FM Signal Based on Fourier Merlin Transform |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110786412.2A CN113514798A (en) | 2021-07-12 | 2021-07-12 | A Time Difference/Scale Difference Estimation Method for Wideband Nonlinear FM Signal Based on Fourier Merlin Transform |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN113514798A true CN113514798A (en) | 2021-10-19 |
Family
ID=78067246
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110786412.2A Pending CN113514798A (en) | 2021-07-12 | 2021-07-12 | A Time Difference/Scale Difference Estimation Method for Wideband Nonlinear FM Signal Based on Fourier Merlin Transform |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113514798A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115022145A (en) * | 2022-07-01 | 2022-09-06 | 舟山美通信息技术有限责任公司 | LFM signal and HFM signal distinguishing method based on time delay autocorrelation |
Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4073010A (en) * | 1976-07-23 | 1978-02-07 | The United States Of America As Represented By The Secretary Of The Navy | Correlation methods and apparatus utilizing mellin transforms |
| US5874916A (en) * | 1996-01-25 | 1999-02-23 | Lockheed Martin Corporation | Frequency selective TDOA/FDOA cross-correlation |
| WO2000069198A1 (en) * | 1999-05-06 | 2000-11-16 | Cell-Loc Inc. | Wireless location system |
| JP2009192516A (en) * | 2008-01-16 | 2009-08-27 | Mitsubishi Electric Corp | Propagation delay time measuring device and radar device |
| CN106931973A (en) * | 2017-03-14 | 2017-07-07 | 杭州电子科技大学 | High accuracy indoor locating system and method based on nonlinear FM pulse signal |
| CN107271955A (en) * | 2017-07-25 | 2017-10-20 | 西安电子科技大学 | A kind of time difference of wideband correlation and the poor method of estimation of yardstick |
| CN107870316A (en) * | 2017-11-10 | 2018-04-03 | 中国电子科技集团公司第四十研究所 | A TDOA positioning method, device and system based on time difference calculation |
| CN110808934A (en) * | 2019-11-01 | 2020-02-18 | 中国电子科技集团公司第二十九研究所 | Time difference estimation method and device for chirp signal |
| CN112346010A (en) * | 2020-09-28 | 2021-02-09 | 中国人民解放军海军航空大学 | Dual-machine passive localization method based on scale difference and time difference |
| CN112688716A (en) * | 2020-11-06 | 2021-04-20 | 西安电子科技大学 | Time-frequency difference estimation method for time-frequency aliasing signals |
-
2021
- 2021-07-12 CN CN202110786412.2A patent/CN113514798A/en active Pending
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4073010A (en) * | 1976-07-23 | 1978-02-07 | The United States Of America As Represented By The Secretary Of The Navy | Correlation methods and apparatus utilizing mellin transforms |
| US5874916A (en) * | 1996-01-25 | 1999-02-23 | Lockheed Martin Corporation | Frequency selective TDOA/FDOA cross-correlation |
| WO2000069198A1 (en) * | 1999-05-06 | 2000-11-16 | Cell-Loc Inc. | Wireless location system |
| JP2009192516A (en) * | 2008-01-16 | 2009-08-27 | Mitsubishi Electric Corp | Propagation delay time measuring device and radar device |
| CN106931973A (en) * | 2017-03-14 | 2017-07-07 | 杭州电子科技大学 | High accuracy indoor locating system and method based on nonlinear FM pulse signal |
| CN107271955A (en) * | 2017-07-25 | 2017-10-20 | 西安电子科技大学 | A kind of time difference of wideband correlation and the poor method of estimation of yardstick |
| CN107870316A (en) * | 2017-11-10 | 2018-04-03 | 中国电子科技集团公司第四十研究所 | A TDOA positioning method, device and system based on time difference calculation |
| CN110808934A (en) * | 2019-11-01 | 2020-02-18 | 中国电子科技集团公司第二十九研究所 | Time difference estimation method and device for chirp signal |
| CN112346010A (en) * | 2020-09-28 | 2021-02-09 | 中国人民解放军海军航空大学 | Dual-machine passive localization method based on scale difference and time difference |
| CN112688716A (en) * | 2020-11-06 | 2021-04-20 | 西安电子科技大学 | Time-frequency difference estimation method for time-frequency aliasing signals |
Non-Patent Citations (3)
| Title |
|---|
| JOEL B. HARLEY: "Scale Transform Signal Processing for Optimal Ultrasonic Temperature Compensation", IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FR 2226 EQUENCY CONTROL * |
| 李阳;龙腾;: "基于Keystone变换的相位编码信号长时间积累方法", 北京理工大学学报 * |
| 郭付阳;张子敬;杨林森;: "基于尺度变换的宽带线性调频信号时差/尺度差估计算法", 电波科学学报 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115022145A (en) * | 2022-07-01 | 2022-09-06 | 舟山美通信息技术有限责任公司 | LFM signal and HFM signal distinguishing method based on time delay autocorrelation |
| CN115022145B (en) * | 2022-07-01 | 2023-09-29 | 舟山美通信息技术有限责任公司 | LFM signal and HFM signal distinguishing method based on delay autocorrelation |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Su et al. | High-speed multi-target detection with narrowband radar | |
| Sun et al. | A novel weighted mismatched filter for reducing range sidelobes | |
| CN109471095A (en) | FMCW radar range estimation algorithm based on fast iterative interpolation | |
| CN108931766B (en) | Non-uniform STAP interference target filtering method based on sparse reconstruction | |
| Pang et al. | High-speed target detection algorithm based on sparse Fourier transform | |
| CN114488049B (en) | A frequency offset compensation method based on full-phase FFT amplitude | |
| CN111159888A (en) | Covariance matrix sparse iteration time delay estimation method based on cross-correlation function | |
| CN108802716A (en) | CW with frequency modulation landing radar distance measuring method based on center of gravity correction | |
| CN107271955B (en) | Time difference and scale difference estimation method for broadband linear frequency modulation signal | |
| CN106950532A (en) | United delay time estimation method is compared with wave-form similarity based on cross ambiguity function | |
| Zheng et al. | Radar detection and motion parameters estimation of maneuvering target based on the extended keystone transform (July 2018) | |
| CN112130138B (en) | An ionospheric phase pollution correction method for over-the-horizon radar | |
| CN113514798A (en) | A Time Difference/Scale Difference Estimation Method for Wideband Nonlinear FM Signal Based on Fourier Merlin Transform | |
| CN116165619A (en) | A Method of Motion Parameter Estimation and Coherent Accumulation Detection for Highly Maneuvering Targets | |
| JP4834370B2 (en) | Correlation reception processing device | |
| Arya et al. | Pulse compression using linear frequency modulation technique | |
| JP2005128011A (en) | Pulse compression processor | |
| CN106209715A (en) | A kind of amplitude modulated jamming suppressing method offseted based on time domain | |
| CN105548987B (en) | A kind of continuous wave radar aimed acceleration blind estimating method | |
| CN113358931A (en) | Time difference calculation method and system based on cross-power spectrum | |
| CN112014807A (en) | An adaptive clutter suppression method for frequency agile radar | |
| CN115480228B (en) | Nanosecond time difference estimation method based on integrated time difference and phase difference analysis | |
| Chen et al. | Anti-jamming approach based on radar transmitted waveform matching | |
| CN114488054B (en) | Computationally efficient synthetic aperture radar ground moving target focusing method | |
| Ashtekar et al. | Study of generalized cross correlation techniques for direction finding of wideband signals |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20211019 |
|
| WD01 | Invention patent application deemed withdrawn after publication |