CN102226839B - 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 is line scanning frequency pulse system radar mostly.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 through 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 practical applications 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; Through detecting the position of linear FM signal Fourier focusing peak value, realized estimation to line scanning frequency pulse time delay on the matching fractional rank.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, can also be through the advantage of 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 through the impulse time delay that the Doppler shift of estimating to be caused by signal time delay is realized; Therefore, when impulse time delay was 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, has increased the complexity of system, can reduce the complexity of system through 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 operand that receives signals sampling rate and follow-up signal processing; And can realize through 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 to the line frequency-scan radar echoed signal that receives; Obtain sample sequence x (n); Wherein

-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 confirmed 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

$X_p\left(m\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{e}^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·n^2\·\mathrm{\Δ}{t}^2-j\·\frac{2\mathrm{\π}}{N}\·\mathrm{mn}}x\left(n\right);---\left(1\right)$

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 confirmed ₀, promptly

$n_0=\frac{2\mathrm{\π}\·m_0}{N\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·\mathrm{\Δ}{t}^2};---\left(2\right)$

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

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

Wherein the phase bit arithmetic is got in ang [] expression; The phase place codomain is 0 to 2 π, the mean value

that calculates

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 ₀Average phase-difference according to the computes correction:

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 confirmed by the simplification fraction order Fourier transform order p that is adopted and step 1 are confirmed the sequence fuzzy interval length Δ N under this sampling rate condition, promptly

$\mathrm{\ΔN}=\frac{2\mathrm{\π}}{\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·\mathrm{\Δ}{t}^2}---\left(5\right)$

The fuzzy interval length Δ N that step 7, the sequence length N that is confirmed by step 1, correction average phase-difference

step 6 that step 5 obtains are confirmed; Calculate the fuzzy interval sequence number A at impulse time delay place, promptly

Wherein, rounding operation under

expression;

Step 8, the signal time-domain sampling interval of delta t of confirming 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 does

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 under the low sampling rate condition, causes because of impulse time delay causes greater than signal sampling rate;

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 through 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 accompanying drawing and embodiment technical scheme 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 is shown in accompanying drawing 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, concrete performing step of the present invention is following:

(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 is shown in accompanying drawing 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) by step; (4)

that obtain is according to formula; (4) calculate the average phase-difference of revising

(6), confirm 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 confirmed according to formula (5);

(7) according to formula (6); The fuzzy interval length Δ N that the sequence length N that is confirmed by step (), correction average phase-difference

step (six) that step (five) obtains are confirmed calculates the fuzzy interval sequence number A at impulse time delay place;

(8), confirm 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 does

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

$x\left(t\right)=g_T(t-\mathrm{\τ})e^{-j\·\frac{1}{2}\·a\·{(t-\mathrm{\τ})}^2}$

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

$x\left(n\right)=g_M(n-n_{\mathrm{\τ}})e^{-j\·\frac{1}{2}\·a\·{(n-n_{\mathrm{\τ}})}^2\mathrm{\Δ}{t}^2}$

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

$X_p\left(m\right)=e^{j\·\frac{1}{2}\·a\·n_{\mathrm{\τ}}^2\·\mathrm{\Δ}{t}^2}\·e^{-j\·\frac{2\mathrm{\π}}{N}\·{\mathrm{mn}}_{\mathrm{\τ}}}\·e^{-j\·\frac{1}{2}(M-1)(\frac{2\mathrm{\π}}{N}m-a\·n_{\mathrm{\τ}}\·\mathrm{\Δ}{t}^2)}\·\mathrm{Sinc}(\frac{2\mathrm{\π}}{N}m-a\·n_{\mathrm{\τ}}\·\mathrm{\Δ}{t}^2)---\left(8\right)$

Wherein,

$\mathrm{Sinc}\left(\frac{2\mathrm{\π}}{N}m\right)=\frac{\sin (\frac{1}{2}M\·\frac{2\mathrm{\π}}{N}m)}{\sin (\frac{1}{2}\·\frac{2\mathrm{\π}}{N}m)}$

Excessive when the time delay of signal, the Doppler shift that is promptly caused by time delay is greater than the SF 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 through 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

$\mathrm{ang}\left[X_p(m_0-l)\right]=\mathrm{ang}[e^{j\·\frac{1}{2}\·a\·n_0^2\·\mathrm{\Δ}{t}^2}\·e^{-j\·a\·n_0^2\·\mathrm{\Δ}{t}^2+j\·\frac{2\mathrm{\π}}{N}\·l\·n_0+j\·l\·A\·\frac{\mathrm{\ΔN}}{N}\·2\mathrm{\π}}\·e^{j\·\frac{1}{2}\·l\·(M-1)\frac{2\mathrm{\π}}{N}}]$ (9)

$=\mathrm{ang}[e^{-j\·\frac{1}{2}\·\cot \left(\frac{\mathrm{p\π}}{2}\right)\·n_0^2\·\mathrm{\Δ}{t}^2}\·e^{j\·\frac{2\mathrm{\π}}{N}\·l\·n_0}\·e^{j\·\frac{1}{2}\·l\·(M-1)\frac{2\mathrm{\π}}{N}}\·e^{j\·l\·A\·\frac{\mathrm{\ΔN}}{N}\·2\mathrm{\π}}]$

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 through signal; But this method is easy to receive The noise, for example, and under the low signal-to-noise ratio environment; The signal focus peak value is easy to squint, and then the frequency displacement error will cause the error of phase estimation.Composing adjacent phase place at 2 through 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 does

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

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

τ＝n ₀·Δt+A·Δτ

Δ τ=2 π/[cot (p pi/2) Δ t] wherein.

Below in conjunction with the concrete signal instance 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 three corresponding signal time delay fuzzy intervals of sampling rate are 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 such as Fig. 3, shown in Figure 4.Can be found out that by simulation result under the situation of threshold sampling, this algorithm can correctly be realized the time delay ambiguity solution under the condition of-30dB, 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 through the number of the pulse of increasing accumulation.

Above-described specific descriptions; Purpose, technical scheme and beneficial effect to invention have carried out further explain, and institute it should be understood that the above is merely specific embodiment of the present invention; And be not used in qualification protection scope of the present invention; All within spirit of the present invention and principle, 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 △ t to the line frequency-scan radar echoed signal that receives; Obtain sample sequence x (n); Wherein -a is the frequency modulation rate of line scanning frequency pulse radar signal, a>0; Sequence length by pulse-recurrence time, T and pulse width △ T obtained this sample sequence x (n) is that N=T/ Δ t, pulsewidth length are M=△ T/ Δ t;

The sequence length N of step 2, the x (n) that confirmed 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

$X_p\left(m\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}{e}^{j\·\frac{1}{2}\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·n^2\·\mathrm{\Δ}{t}^2-j\·\frac{2\mathrm{\π}}{N}\·\mathrm{mn}}x\left(n\right);$

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 sequence length N, the time-domain sampling interval △ t that simplification fraction order Fourier transform order p that is adopted and step 1 are confirmed ₀, promptly

$n_0=\frac{2\mathrm{\π}\·m_0}{N\·\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·\mathrm{\Δ}{t}^2};$

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 point is averaged to this 2b phase differential then

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

The nothing that step 3 obtains is blured time delay n ₀Average phase-difference according to the computes correction:

Wherein, [] _{Mod2 π}Expression is about the complementation computing of 2 π;

Step 6, the time-domain sampling interval △ t that is confirmed by simplification fraction order Fourier transform order p that is adopted and step 1 confirm the fuzzy interval length △ N under this time-domain sampling interval △ t condition, promptly

$\mathrm{\ΔN}=\frac{2\mathrm{\π}}{\cot \left(\frac{1}{2}\mathrm{p\π}\right)\·\mathrm{\Δ}{t}^2}$

The fuzzy interval length △ N that step 7, the sequence length N that is confirmed by step 1, correction average phase-difference

step 6 that step 5 obtains are confirmed; Calculate the fuzzy interval sequence number A at impulse time delay place, promptly

Wherein, rounding operation under expression;

Step 8, the time-domain sampling interval of delta t of confirming 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 does

τ=n ₀·Δt+A·Δτ

Δ τ=2 π/[cot (p pi/2) △ t] wherein.

2. according to the said 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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