CN102226839A - Estimation method for time delay of line scanning pulse with low sampling rate - Google Patents

Abstract

The invention relates to an estimation method for time delay of a line scanning pulse with a low sampling rate, belonging to the field of radar signal processing. In the invention, a simplified fractional Fourier transform is performed on a line scanning pulse echo, and a region in which the average phase difference of the neighbour adjacent points of a peak value point is located is determined to realize a pulse time delay defuzzification, thereby realizing the estimation of the pulse time delay. By using the estimation method for time delay of the line scanning pulse in the invention, the problem of signal time delay estimation fuzziness in a condition of low sampling rate can be solved, the sampling rate of receiving signals and the computation quantity of the follow-up signal processing can be efficiently decreased, and estimation can be realized by a fast Fourier transform algorithm, with a low calculation complexity; an efficient tool is provided for the radar signal processing of the line scanning pulse systems of ship-based radar, synthetic aperture radar and the like.

Description

A kind of low sampling rate line scanning frequency pulse delay time estimation method

Technical field

The present invention relates to a kind of low sampling rate line scanning frequency pulse delay time estimation method, belong to radar signal processing field.

Background technology

The active service shipborne radar mostly is line scanning frequency pulse system radar greatly.This system radar is under the limited condition of transmitter peak power, made full use of the average power of transmitter, often adopt matched filter to realize the detection of target by pulse compression in processing line scanning frequency pulse echoed signal, solved this a pair of contradiction that in normal pulsed system radar, is difficult to solve of radar horizon and range resolution preferably, improved the Signal Processing gain simultaneously, be at present on engineering is used the most widely, a kind of pulse-compression radars that technology is the most ripe.

Fourier Transform of Fractional Order is the generalized form of Fourier transform, it with signal decomposition to the line frequency sweep orthogonal basis function of the different initial frequencies of same frequency modulation rate, therefore, Fourier Transform of Fractional Order has the excellent energy focus characteristics to linear FM signal, is the effective tool of LFM Signal Detection and parameter estimation.People such as happy and carefree, LI XUEMEI are at article " Time delay estimation of Chirp signals in the fractional Fourier domain " (IEEE Trans.Signal Processing, 2009,57 (7): 2852-2856.) based on the time-frequency coupled characteristic of linear FM signal, by detecting the position of linear FM signal, realized estimation to line scanning frequency pulse time delay at coupling fractional number order Fourier focusing peak value.In addition, since fractional number order Fourier filtering can suppress some Fourier can't filtering interference and noise, therefore, adopt Fourier Transform of Fractional Order to carry out line scanning frequency pulse time delay estimation approach, advantage that can also be by fractional number order Fourier filtering, mutual interference when effectively suppressing the shipborne radar marshalling.

But, because the line scanning frequency pulse delay time estimation method based on Fourier Transform of Fractional Order is to estimate by the impulse time delay that the Doppler shift of estimating to be caused by signal time delay is realized, therefore, when impulse time delay is excessive, the Doppler shift of its generation can surpass the signals sampling frequency, cause the Doppler shift ambiguous estimation, and then produce the impulse time delay ambiguous estimation.In addition, only need to estimate the amplitude of detection signal fractional order Fourier spectrum to get final product based on the line scanning frequency pulse time delay of Fourier Transform of Fractional Order, therefore, transform domain phase modulation (PM) product term in the Fourier Transform of Fractional Order can not produce any meaning, increased the complexity of system, can reduce the complexity of system by adopting the Fourier Transform of Fractional Order of simplifying.

Summary of the invention

The present invention is directed to line scanning frequency pulse radar signal time delay ambiguous estimation problem, proposed a kind of low sampling rate line scanning frequency pulse delay time estimation method.This method utilization is simplified Fourier Transform of Fractional Order and has been solved signal time delay ambiguous estimation problem under the low sampling rate condition, effectively reduce the sampling rate of received signal and the operand that follow-up signal is handled, and can realize by fast fourier transform algorithm, computation complexity is low, for line scanning frequency pulse system Radar Signal Processing such as shipborne radar, synthetic-aperture radar provide effective instrument.

A kind of low sampling rate line scanning frequency pulse delay time estimation method of the present invention, at first according to the frequency modulation rate-a (a＞0) of line scanning frequency pulse radar signal, pulse-recurrence time T, pulse width is Δ T, selected simplification Fourier Transform of Fractional Order conversion order p=2arccot (a)/π that adopts.

The present invention includes following steps:

Step 1, serve as to carry out time-domain sampling at interval with Δ t, obtain sample sequence x (n), wherein the line frequency-scan radar echoed signal that receives -a is the frequency modulation rate of line scanning frequency pulse radar signal, a＞0; By pulse-recurrence time T and pulse width be that N=T/ Δ t, pulsewidth length are M=Δ T/ Δ t for the sequence length that Δ T obtains this sample sequence x (n);

The sequence length N of step 2, the x (n) that determined by step 1, the sample sequence x (n) that step 1 is obtained carries out p rank N point simplification Fourier Transform of Fractional Order, obtains X _p(m), promptly

$X_p\left(m\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{e}^{j\&CenterDot;\frac{1}{2}\&CenterDot;\cot \left(\frac{1}{2}\mathrm{p\&pi;}\right)\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000066634490000012.png"\; state="\{\{state\}\}">n</figure-callout>}}^2\&CenterDot;\mathrm{\&Delta;}{t}^2-j\&CenterDot;\frac{2\mathrm{\&pi;}}{N}\&CenterDot;\mathrm{mn}}x\left(n\right);---\left(1\right)$

Wherein, p=2arccot (a)/π;

The X that step 3, search step two obtain _p(m) amplitude is promptly in | X _p(m) | maximum point, and obtain the coordinate m of this point ₀,, obtain the fuzzy time delay n of nothing of line scanning frequency pulse according to following formula by burst length N, the time-domain sampling interval of delta t that simplification fraction order Fourier transform order p that is adopted and step 1 are determined ₀, promptly

$n_0=\frac{2\mathrm{\&pi;}\&CenterDot;m_0}{N\&CenterDot;\cot \left(\frac{1}{2}\mathrm{p\&pi;}\right)\&CenterDot;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000066634490000012.png"\; state="\{\{state\}\}">t</figure-callout>}}^2};---\left(2\right)$

Step 4, the X that obtains in step 3 _p(m ₀) the right and left respectively gets near X _p(m ₀) b point, ask X then _p(m ₀-b) ..., X _p(m ₀-1), X _p(m ₀), X _p(m ₀+ 1) ..., X _p(m ₀+ b) the phase differential between per two adjacent points in this (2b+1) individual point is averaged to this 2b phase differential then

As preferably, b=2; When b increased, in fact performance improvement was little, but calculated amount has increased; When b=2, said process can be with mathematical notation: the X that is obtained by step 2 _p(m) calculate X _p(m ₀-2+l) and X _p(m ₀-1+l), l=0,1 ..., 3, phase differential

Promptly

Ang[wherein] expression gets the phase bit arithmetic, and the phase place codomain is 0 to 2 π, calculates

Mean value

The phase differential mean value that step 5, the sample sequence length N, signal pulsewidth M, the step 4 that are obtained by step 1 obtain The nothing that step 3 obtains is blured time delay n ₀Calculate the average phase-difference of revising according to following formula:

Wherein, [] _{Mod 2 π}Expression is about the complementation computing of 2 π;

Step 6, the signal time-domain sampling interval of delta t of being determined by the simplification fraction order Fourier transform order p that is adopted and step 1 are determined the sequence fuzzy interval length Δ N under this sampling rate condition, promptly

$\mathrm{\&Delta;N}=\frac{2\mathrm{\&pi;}}{\cot \left(\frac{1}{2}\mathrm{p\&pi;}\right)\&CenterDot;\mathrm{\&Delta;}{t}^2}---\left(5\right)$

Step 7, the sequence length N that determines by step 1, the correction average phase-difference that step 5 obtains

The fuzzy interval length Δ N that step 6 is determined calculates the fuzzy interval sequence number A at impulse time delay place, promptly

Wherein, Expression is rounding operation down;

Step 8, the signal time-domain sampling interval of delta t of determining by the simplification fraction order Fourier transform order p that is adopted, step 1, the fuzzy time delay n of nothing that step 3 obtains ₀, the fuzzy interval sequence number A that obtains of the step 7 time delay that obtains pulse is

τ＝n ₀·Δt+A·Δτ (7)

Δ τ=2 π/[cot (p pi/2) Δ t] wherein.

The contrast prior art, beneficial effect of the present invention is:

1. a kind of low sampling rate line scanning frequency pulse delay time estimation method of proposing of the present invention can effectively solve the time delay fuzzy problem that the Doppler shift that causes because of impulse time delay causes greater than signal sampling rate under the low sampling rate condition;

2. a kind of low sampling rate line scanning frequency pulse delay time estimation method of the present invention's proposition can realize that computation complexity is low by fast fourier transform algorithm;

3. a kind of low sampling rate line scanning frequency pulse delay time estimation method of the present invention's proposition can be applicable to line scanning frequency pulse system radars such as synthetic-aperture radar, the sampling rate and the operand of effective reduction system, and system complexity is significantly less than the method for reduction signal sampling rates such as compression sampling.

Description of drawings

Fig. 1-sampling pulse time domain synoptic diagram

Fig. 2-low sampling rate line scanning frequency pulse time delay is estimated realization flow figure;

The fuzzy False Rate of time delay is separated in Fig. 3-pulse accumulation for 16 times;

The fuzzy False Rate of time delay is separated in Fig. 4-pulse accumulation for 32 times.

Embodiment

Below in conjunction with drawings and Examples technical solution of the present invention is made an explanation.

The low sampling rate line scanning frequency pulse delay time estimation method realization flow figure that the present invention proposes as shown in Figure 2.At first according to the frequency modulation rate-a (a＞0) of echo pulse signal, pulse-recurrence time T, pulse width be Δ T, selected conversion order p=2arccot (a)/π that simplifies Fourier Transform of Fractional Order;

On this basis, specific implementation step of the present invention is as follows:

(1) serve as to carry out at interval time-domain sampling to line frequency-scan radar echoed signal with Δ t, by pulse-recurrence time T to obtain length be that N=T/ Δ t, pulsewidth length are the sample sequence x (n) of M=Δ T/ Δ t; Parameters relationship as shown in Figure 1.

(2) according to formula (1) x (n) of step () gained is carried out p rank N point and simplify Fourier Transform of Fractional Order, obtain X _p(m);

(3) X that obtains of search step (two) _p(m) peak point obtains corresponding point coordinate m ₀, and calculate the fuzzy time delay n of nothing of line scanning frequency pulse according to formula (2) ₀

(4) in the present embodiment, b=2, the X that obtains in step (three) _p(m ₀) the right and left respectively gets two points, calculates the phase differential of consecutive point according to formula (3)

And obtain its mean value

(5) obtain by step (four)

Calculate the average phase-difference of revising according to formula (4)

(6), determine sequence fuzzy interval length Δ N by the signal time-domain sampling interval of delta t that simplification fraction order Fourier transform order p that is adopted and step () are determined according to formula (5);

(7) according to formula (6), by the definite sequence length N of step (), the correction average phase-difference that step (five) obtains

The fuzzy interval length Δ N that step (six) is determined calculates the fuzzy interval sequence number A at impulse time delay place;

(8), determine the fuzzy time delay n of nothing that signal time-domain sampling interval of delta t, step (three) obtain by the simplification fraction order Fourier transform order p that is adopted, step () according to formula (7) ₀, the fuzzy interval sequence number A that obtains of step (seven) obtains the time delay of pulse.

Below in conjunction with definition and the character of simplifying Fourier Transform of Fractional Order, embodiment is carried out theoretical explanation.

Suppose that pulsewidth is T, frequency modulation rate and for the form of transmitting of the LFM system pulsed radar of-a is

Wherein, g _T(t) for the time domain width be the rectangular window function of Δ T, so, time delay is that the radar target signal of τ can be expressed as

$x\left(t\right)=g_T(t-\mathrm{\&tau;})e^{-j\&CenterDot;\frac{1}{2}\&CenterDot;a\&CenterDot;{(t-\mathrm{\&tau;})}^2}$

Echoed signal is sampled with the time-domain sampling interval of delta t, and Δ T=M Δ t, τ=n _τΔ t, corresponding N point long echo sample sequence can be expressed as so

$x\left(n\right)=g_M(n-n_{\mathrm{\&tau;}})e^{-j\&CenterDot;\frac{1}{2}\&CenterDot;a\&CenterDot;{(n-n_{\mathrm{\&tau;}})}^2\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000066634490000012.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}$

According to formula (1), the simplification Fourier Transform of Fractional Order of x (n) being carried out p=2arccot (a)/π order can have

$X_p\left(m\right)=e^{j\&CenterDot;\frac{1}{2}\&CenterDot;a\&CenterDot;n_{\mathrm{\&tau;}}^2\&CenterDot;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000066634490000012.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}\&CenterDot;e^{-j\&CenterDot;\frac{2\mathrm{\&pi;}}{N}\&CenterDot;{\mathrm{mn}}_{\mathrm{\&tau;}}}\&CenterDot;e^{-j\&CenterDot;\frac{1}{2}(M-1)(\frac{2\mathrm{\&pi;}}{N}m-a\&CenterDot;n_{\mathrm{\&tau;}}\&CenterDot;\mathrm{\&Delta;}{t}^2)}\&CenterDot;\mathrm{Sinc}(\frac{2\mathrm{\&pi;}}{N}m-a\&CenterDot;n_{\mathrm{\&tau;}}\&CenterDot;\mathrm{\&Delta;}{t}^2)---\left(8\right)$

Wherein,

$\mathrm{Sinc}\left(\frac{2\mathrm{\&pi;}}{N}m\right)=\frac{\sin (\frac{1}{2}M\&CenterDot;\frac{2\mathrm{\&pi;}}{N}m)}{\sin (\frac{1}{2}\&CenterDot;\frac{2\mathrm{\&pi;}}{N}m)}$

Excessive when the time delay of signal, promptly the Doppler shift that is caused by time delay is greater than the sample frequency f of system _sThe time, i.e. a τ＞2 π f _sThe time, system delay can be expressed as τ=τ ₀+ A Δ τ, wherein Δ τ=2 π f _s/ a, and τ ₀＜Δ τ, A ∈ Z ⁺The time, echoed signal focuses on peak value at fractional number order Fourier position is τ=τ with time-delay ₀Shi Xiangtong, system will blur because of the Frequency Estimation of fractional number order Fourier and bring the time delay ambiguous estimation of pulse.

The simplification fractional order Fourier spectrum of signal comprises amplitude and two information of phase place, and under the same prerequisite in signal amplitude position, we can come the different information in the signal are distinguished by the phase information of detection signal fractional order Fourier spectrum.Find by formula (8), when system delay is τ=τ ₀During+A Δ τ, i.e. n _τ=n ₀+ A2 π/(a Δ t ²) time, X _p(m) focusing peak point position is m ₀=Nan ₀Δ t ²/ (2 π), then X _p(m ₀-l) phase information is for being expressed as

$\mathrm{ang}\left[X_p(m_0-l)\right]=\mathrm{ang}[e^{j\&CenterDot;\frac{1}{2}\&CenterDot;a\&CenterDot;n_0^2\&CenterDot;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000066634490000012.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}\&CenterDot;e^{-j\&CenterDot;a\&CenterDot;n_0^2\&CenterDot;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000066634490000012.png"\; state="\{\{state\}\}">t</figure-callout>}}^2+j\&CenterDot;\frac{2\mathrm{\&pi;}}{N}\&CenterDot;l\&CenterDot;n_0+j\&CenterDot;l\&CenterDot;A\&CenterDot;\frac{\mathrm{\&Delta;N}}{N}\&CenterDot;2\mathrm{\&pi;}}\&CenterDot;e^{j\&CenterDot;\frac{1}{2}\&CenterDot;l\&CenterDot;(M-1)\frac{2\mathrm{\&pi;}}{N}}]$ (9)

$=\mathrm{ang}[e^{-j\&CenterDot;\frac{1}{2}\&CenterDot;\cot \left(\frac{\mathrm{p\&pi;}}{2}\right)\&CenterDot;n_0^2\&CenterDot;\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000066634490000012.png"\; state="\{\{state\}\}">t</figure-callout>}}^2}\&CenterDot;e^{j\&CenterDot;\frac{2\mathrm{\&pi;}}{N}\&CenterDot;l\&CenterDot;n_0}\&CenterDot;e^{j\&CenterDot;\frac{1}{2}\&CenterDot;l\&CenterDot;(M-1)\frac{2\mathrm{\&pi;}}{N}}\&CenterDot;e^{j\&CenterDot;l\&CenterDot;A\&CenterDot;\frac{\mathrm{\&Delta;N}}{N}\&CenterDot;2\mathrm{\&pi;}}]$

Wherein, Δ N=2 π/(a Δ t ²).Can find by formula (9), we can simplify the fuzzy interval of the phase information differentiation pulse of fractional order Fourier spectrum by signal, but this method is easy to be subjected to The noise, for example, under the low signal-to-noise ratio environment, the signal focus peak value is easy to be offset, and then the frequency displacement error will cause the error of phase estimation.Composing adjacent phase place at 2 by the observation signal fractional order Fourier can have

Can find that by formula (10) influence of signal peak skew obviously is weaker than formula (9).Further, for offsetting the influence of the interval sequence number item of non-fuzzy, the phase differential that can obtain revising is

And then, based on the MPSK demodulation principle, can obtain signal time delay fuzzy interval sequence number and be

Thus, the time delay that obtains pulse of can instead spreading out is

τ＝n ₀·Δt+A·Δτ

Δ τ=2 π/[cot (p pi/2) Δ t] wherein.

Below in conjunction with the concrete signal example the present invention is elaborated:

In this emulation experiment, we adopt bandwidth is 5MHz, and pulse width is that 100 μ s, frequency modulation rate are 5 * 10 ¹⁰Hz/s, pulse repetition time are the line scanning frequency pulse signal of 1ms.We sample to echo-pulse with 10MHz, 5MHz, 2.5MHz respectively, and the signal time delay fuzzy interval of three sampling rate correspondences is respectively 2 * 10 ^-4S, 1 * 10 ^-4S, 0.5 * 10 ^-4S is under 16 and 32 the condition, to carry out Monte Carlo emulation experiment 1000 times at pulse accumulation number, and we can obtain adopting algorithm that this patent is carried, and are 7.9 * 10 for impulse time delay ^-4The False Rate of the time delay fuzzy interval of s as shown in Figure 3, Figure 4.By simulation result as can be seen, under the situation of threshold sampling, this algorithm can correctly be realized the time delay ambiguity solution under the condition of-30dB, and along with the reduction of signal sampling rate, the signal to noise ratio (S/N ratio) lower limit that this algorithm satisfied improves constantly; In addition, along with improving constantly of pulse accumulation number, the algorithm signal to noise ratio (S/N ratio) lower limit under the same sampling rate condition constantly reduces.Therefore, the MPSK demodulating algorithm is similar with communicating by letter, and under signal to noise ratio (S/N ratio) environment good conditions, we can effectively reduce the sampling rate of system guaranteeing that the ambiguity solution False Rate satisfies under the prerequisite of system requirements, and then reduce the operand that follow-up signal is handled; Under signal to noise ratio (S/N ratio) environment rugged environment, we can when reducing the systematic sampling rate, make and separate the primary demand that the fuzzy False Rate of time delay reaches system by the number of the pulse of increasing accumulation.

Above-described specific descriptions; purpose, technical scheme and beneficial effect to invention further describe; institute is understood that; the above only is specific embodiments of the invention; and be not intended to limit the scope of the invention; within the spirit and principles in the present invention all, any modification of being made, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. a low sampling rate line scanning frequency pulse delay time estimation method is characterized in that, comprises the steps:

Step 1, serve as to carry out time-domain sampling at interval with Δ t, obtain sample sequence x (n), wherein the line frequency-scan radar echoed signal that receives

-a is the frequency modulation rate of line scanning frequency pulse radar signal, a＞0; By pulse-recurrence time T and pulse width be that N=T/ Δ t, pulsewidth length are M=Δ T/ Δ t for the sequence length that Δ T obtains this sample sequence x (n);

The sequence length N of step 2, the x (n) that determined by step 1, the sample sequence x (n) that step 1 is obtained carries out p rank N point simplification Fourier Transform of Fractional Order, obtains X _p(m), promptly

$X_p\left(m\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}{e}^{j\&CenterDot;\frac{1}{2}\&CenterDot;\cot \left(\frac{1}{2}\mathrm{p\&pi;}\right)\&CenterDot;n^2\&CenterDot;\mathrm{\&Delta;}{t}^2-j\&CenterDot;\frac{2\mathrm{\&pi;}}{N}\&CenterDot;\mathrm{mn}}x\left(n\right);---\left(1\right)$

Wherein, p=2arccot (a)/π;

The X that step 3, search step two obtain _p(m) amplitude is promptly in | X _p(m) | maximum point, and obtain the coordinate m of this point ₀,, obtain the fuzzy time delay n of nothing of line scanning frequency pulse according to following formula by burst length N, the time-domain sampling interval of delta t that simplification fraction order Fourier transform order p that is adopted and step 1 are determined ₀, promptly

$n_0=\frac{2\mathrm{\&pi;}\&CenterDot;m_0}{N\&CenterDot;\cot \left(\frac{1}{2}\mathrm{p\&pi;}\right)\&CenterDot;\mathrm{\&Delta;}{t}^2};---\left(2\right)$

Step 4, the X that obtains in step 3 _p(m ₀) the right and left respectively gets near X _p(m ₀) b point, ask X then _p(m ₀-b) ..., X _p(m ₀-1), X _p(m ₀), X _p(m ₀+ 1) ..., X _p(m ₀+ b) the phase differential between per two adjacent points in this (2b+1) individual point is averaged to this 2b phase differential then

The phase differential mean value that step 5, the sample sequence length N, signal pulsewidth M, the step 4 that are obtained by step 1 obtain

The nothing that step 3 obtains is blured time delay n ₀Calculate the average phase-difference of revising according to following formula:

Wherein, [] _{Mod 2 π}Expression is about the complementation computing of 2 π;

Step 6, the signal time-domain sampling interval of delta t of being determined by the simplification fraction order Fourier transform order p that is adopted and step 1 are determined the sequence fuzzy interval length Δ N under this sampling rate condition, promptly

$\mathrm{\&Delta;N}=\frac{2\mathrm{\&pi;}}{\cot \left(\frac{1}{2}\mathrm{p\&pi;}\right)\&CenterDot;\mathrm{\&Delta;}{t}^2}---\left(4\right)$

Step 7, the sequence length N that determines by step 1, the correction average phase-difference that step 5 obtains

The fuzzy interval length Δ N that step 6 is determined calculates the fuzzy interval sequence number A at impulse time delay place, promptly

Wherein,

Expression is rounding operation down;

The time delay that step 8, the signal time-domain sampling interval of delta t of being determined by the simplification fraction order Fourier transform order p that is adopted, step 1, the fuzzy time delay n0 of nothing that step 3 obtains, the fuzzy interval sequence number A that step 7 obtains obtain pulse is

τ＝n ₀·Δt+A·Δτ (6)

Δ τ=2 π/[cot (p pi/2) Δ t] wherein.

2. according to the described a kind of low sampling rate line scanning frequency pulse delay time estimation method of claim 1, it is characterized in that, in the step 4, b=2.

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