CN102624657A - Frequency difference estimation method - Google Patents

Abstract

The invention discloses a frequency difference estimation method, which belongs to the technical field of signal parameter estimation. The frequency difference estimation method includes the following steps: (S1) the data segment number m, the data segment duration Tp and the data segment interval Tr are selected, and m is greater than or equal to 1; (S2) starting from the same time, the data in each data segment of two channels of signals is acquired and the cross ambiguity functions of the data segments are computed; (S3) the cross ambiguity functions of the m data segments are coherently added, so that the cross ambiguity function of the whole data is obtained; (S4) the cross ambiguity function of the whole data is calculated modulo, peak search is carried out, and the frequency value corresponding to a maximum point is the estimated value reaching frequency difference. The invention adopts the method of spreading the root mean square time to replace the method of spreading the integral time, and therefore the frequency difference estimation method can better be applied to a real-time processing system and can come up to the precision requirement of the system with less computational quantity.

Description

The frequency difference estimation method

Technical field

The present invention relates to signal parameter estimation technique field, particularly a kind of frequency difference estimation method.

Background technology

The passive location technology of confirming its position through the radiation signal in receiver radiation source has a wide range of applications in radar, sonar and the communications field, and method commonly used is to use the space geometry position that time difference of taking things philosophically measuring point or Doppler frequency difference information are confirmed the target emanation source.The time difference that arrives between the observation station is called step-out time, and the Doppler frequency difference is called the arrival frequency difference.Passive location technology based on time difference/frequency difference combined estimation with its characteristics that observation station quantity is few, positioning accuracy is high, becomes a kind of important passive location method.Wherein, the estimated accuracy of the frequency difference parameter brought of the dynamic variation characteristic of observation station is an important decisive factor of system accuracy.

Mutual ambiguity function (Cross Ambiguity function based on relative theory; CAF) algorithm is to estimate step-out time and the classical way that arrives frequency difference; Under the condition of certain signal to noise ratio and signal bandwidth, the theoretical precision lower limit of frequency difference parameter Estimation is decided by the signal integration time.Raising frequency difference estimation precision methods commonly used mainly is to increase the time of integration, but the also corresponding increase of amount of calculation only is applicable to the narrow band signal condition simultaneously.For the broadband signal condition; Merely increase when arriving the time of integration to a certain degree; Can worsen based on the CAF estimated performance of relative theory and to cause the estimated performance variation; Existing solution be through calculate contiguous segmentation in short-term the method for CAF coherent accumulation compensate the loss performance of CAF, existing contiguous segmentation method sketch map is as shown in Figure 1.Frequency difference estimation theory by classics can know that the estimated accuracy lower limit expression formula of frequency difference is following:

${\mathrm{\σ}}_{\mathrm{\υ}}=\frac{1}{T_e\sqrt{B_n\mathrm{T\γ}}}---\left(1\right)$

B wherein _nBe noise bandwidth (relevant with signal bandwidth) that T is the time of integration, γ is an effective signal-to-noise ratio, T _eBe root mean square (Root Mean Square, RMS) time of integration.

The root mean square T time of integration _eDefinition following:

$T_e=2\mathrm{\&pi;}{\left(\frac{{\&Integral;}_{-\&infin;}^{\&infin;}{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">t</figure-callout>}}^2{\left|u\left(t\right)\right|}^2\mathrm{dt}}{{\&Integral;}_{-\&infin;}^{\&infin;}{\left|u\left(t\right)\right|}^2\mathrm{dt}}\right)}^{1/2}---\left(2\right)$

Be without loss of generality, establishing complex envelope u (t) is constant envelope signal, and its envelope expression formula is following:

$\left|u\left(t\right)\right|=\mathrm{rect}\left(\frac{t}{T_p}\right)=\left\{\begin{array}{cc}1,& -\frac{{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}{2}<t<\frac{{\mathrm{<figure-callout\; id="2"\; label="T\; p"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_p}{2}\\ 0,& \mathrm{others}\end{array}\right.---\left(3\right)$

Can know that by Fig. 1 the complex envelope signal of existing method is used u ₁(t) expression, its envelope expression formula is:

$\left|u_1\left(t\right)\right|=\mathrm{rect}\left(\frac{t}{{\mathrm{mT}}_p}\right)---\left(4\right)$

(4) formula substitution (2) formula is got the RMS T time of integration of existing method _E1Expression formula is following:

$T_{\mathrm{el}}=\frac{\mathrm{\&pi;m}{T}_p}{\sqrt{3}}=\frac{\mathrm{\&pi;T}}{\sqrt{3}}---\left(5\right)$

T wherein _pBe each data segment duration, m is the data segment number, and T is the time of integration.Formula (5) substitution (1) formula is got:

${\mathrm{\&sigma;}}_{\mathrm{\&upsi;}}=\frac{\sqrt{3}}{\mathrm{\&pi;T}\sqrt{B_n\mathrm{T\&gamma;}}}---\left(6\right)$

Being known that by above for existing contiguous segmentation method, there are fixing proportionate relationship in the root mean square time of integration and the time of integration, promptly mainly is the estimated accuracy that improves frequency difference the time of integration through increasing.Yet along with the increase of the time of integration, amount of calculation also increases, and under the requirement of system's degree of precision, the increase of amount of calculation tends to cause satisfying the processing requirements of real-time.

Summary of the invention

The technical problem that (one) will solve

The technical problem that the present invention will solve is: how to improve the estimated accuracy that arrives frequency difference.

(2) technical scheme

For solving the problems of the technologies described above, the invention provides a kind of frequency difference estimation method, may further comprise the steps:

S1: selected data section segmentation number m, data segment duration T _pAnd data segment interval T _r, m>=1;

S2: begin at synchronization, obtain data and the mutual ambiguity function of calculated data section in each data segment of two paths of signals;

S3: the mutual ambiguity function that m the mutual ambiguity function coherent accumulation of data segment is obtained whole data;

S4: to the mutual ambiguity function delivery of whole data, and carry out peak value searching, the maximum of points frequency value corresponding is the estimated value that arrives frequency difference.

Wherein, said data segment interval T _rBe μ T _p, μ is the temporal extension factor.

Among the said step S2, the formula of the mutual ambiguity function of calculated data section k is following:

${\mathrm{CAF}}_k({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})={\&Integral;}_{(k-1)T_r}^{T_p+(k-1)T_r}{s}_1\left(t-{\mathrm{\&tau;}}_k\right){\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2^{*}\left(t\right){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j\mathrm{dt}$

Wherein, ${\mathrm{\&tau;}}_k={\mathrm{\&tau;}}_1+\frac{\mathrm{\&upsi;}}{f_0}(k-1)T_r$

τ ₁Be two paths of signals s ₁() and s ₂The time of advent in () first segment data section is poor, τ _kBe two paths of signals s ₁() and s ₂The time of advent in () k segment data section is poor, and υ is the arrival frequency difference that two-way receives signal, f ₀Be the radiation source rf frequency.

Wherein, the formula of coherent accumulation is following among the said step S3:

${\mathrm{CAF}}_c({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})=\underset{k}{\mathrm{\&Sigma;}}{\mathrm{CAF}}_k({\mathrm{\&tau;}}_1,\mathrm{\&upsi;}){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j$

Wherein, CAF _c(τ ₁, υ) be the mutual ambiguity function of whole data.

(3) beneficial effect

Frequency difference estimation method of the present invention is through increasing root mean square time of integration; Under the situation of identical calculations amount; The estimated accuracy of frequency difference is high, is reaching under the same precision condition, has overcome existing method and has fetched data continuously and calculate the big problem of CAF operand; Alleviated the prominent contradiction between precision raising and the amount of calculation; The present invention adopts expansion root mean square time method to replace the expansion method of the time of integration, can be applied to real time processing system better, can reach the required precision of system with smaller calculation.

Description of drawings

Fig. 1 is the data extract sketch map in the existing method;

Fig. 2 is a kind of frequency difference estimation method flow diagram of the embodiment of the invention;

Fig. 3 is the data extract sketch map comparison diagram in Fig. 2 and Fig. 1 method.

Embodiment

Below in conjunction with accompanying drawing and embodiment, specific embodiments of the invention describes in further detail.Following examples are used to explain the present invention, but are not used for limiting scope of the present invention.

The present invention proposes discontinuous segmentation and calculate the method for estimation of coherent accumulation CAF, improve the estimated accuracy that arrives frequency difference the time of integration through increasing root mean square, idiographic flow is as shown in Figure 2, comprising:

Step S201, selected data section segmentation number m, data segment duration T _pAnd data segment interval T _r, m>=1.Adopted discontinuous segment data extracting mode in this step, shown in (b) among Fig. 3.

Step S202 begins at synchronization, preferably samples the initial moment at two paths of signals, gets the mutual ambiguity function of data computation data segment in each data segment of two paths of signals.Get two paths of signals s ₁(t) and s ₂(t) at time [(k-1) T _r, (k-1) T _r+ T _p] in data computation CAF, wherein data segment interval T in short-term _r=μ T _p, 1≤k≤m, μ are the temporal extension factor.

Step-out time in each data segment thinks in the short time and remains unchanged, and arrives the rate of change that frequency difference depends on step-out time between the data segment, and therefore the two paths of signals step-out time can be expressed as τ in the k segment data section _k

${\mathrm{\&tau;}}_k={\mathrm{\&tau;}}_1+\frac{\mathrm{\&upsi;}}{f}(k-1)T_r---\left(7\right)$

Wherein, τ ₁The time of advent that is the interior two paths of signals of the first segment data section is poor, and υ is the arrival frequency difference that two-way receives signal, f ₀Be the radiation source rf frequency.

Then the calculation expression of the CAF in short-term of each data segment is following:

${\mathrm{CAF}}_k({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})={\&Integral;}_{(k-1)T_r}^{T_p+(k-1)T_r}{s}_1\left(t-{\mathrm{\&tau;}}_k\right){\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_2^{*}\left(t\right){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j\mathrm{dt}---\left(8\right)$

Step S203 obtains m the mutual ambiguity function coherent accumulation of data segment the mutual ambiguity function of whole data.The CAF of coherent accumulation wherein _cExpression formula following:

${\mathrm{CAF}}_c({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})=\underset{k}{\mathrm{\&Sigma;}}{\mathrm{CAF}}_k({\mathrm{\&tau;}}_1,\mathrm{\&upsi;}){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j---\left(9\right)$

Step S204 to the mutual ambiguity function delivery of whole data, and carries out peak value searching, that is:

$({\widehat{\mathrm{\&tau;}}}_1,\widehat{\mathrm{\&upsi;}})=\underset{({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})}{\mathrm{Max}}\left(\right|{\mathrm{CAF}}_c({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})\left|\right)---\left(10\right)$

Mutual ambiguity function theory by classics can know that the corresponding υ of maximal peak point is the estimated value that arrives frequency difference.

The method of above-mentioned steps S201～S204 and existing method are following, as (a) among Fig. 3 (b) shown in, the known data volume that both are adopted is identical, under the situation that promptly amount of calculation is identical.

If the complex envelope signal is used u ₂(t) expression, its envelope expression formula is:

$\left|u_2\left(t\right)\right|=\underset{n=-k}{\overset{k}{\mathrm{\&Sigma;}}}\mathrm{rect}\left(\frac{{t-\mathrm{nT}}_r}{T_p}\right)---\left(11\right)$

Can know that by formula (2) the RMS expression formula time of integration of the inventive method is distinguished as follows:

${\mathrm{<figure-callout\; id="2"\; label="T\; e"\; filenames="HDA0000139524510000011.png,HDA0000139524510000021.png"\; state="\{\{state\}\}">T</figure-callout>}}_e=\mathrm{\&pi;}{T}_p\sqrt{\frac{u^2(m^2-1)+1}{3}}---\left(12\right)$

Wherein, T _pBe each data segment duration, m is the data segment number, and μ is the temporal extension factor of definition.Formula (12) substitution (1) formula is got:

${\mathrm{\&sigma;}}_{\mathrm{\&upsi;}}^{\&prime;}=\frac{\sqrt{3}}{\mathrm{\&pi;}{T}_p\sqrt{{\mathrm{\&mu;}}^2(m^2-1)+1}\sqrt{B_n\mathrm{T\&gamma;}}}---\left(13\right)$

Definition improvement factor I can be known by (6) and (13) two formulas for the ratio of existing method and the inventive method estimation root-mean-square error

$I=\frac{{\mathrm{\&sigma;}}_{\mathrm{\&upsi;}}}{{\mathrm{\&sigma;}}_{\mathrm{\&upsi;}}^{\&prime;}}=\sqrt{\frac{{\mathrm{\&mu;}}^2(m^2-1)+1}{m^2}}---\left(14\right)$

Wherein, σ _vBe the estimation root-mean-square error of existing method frequency difference, σ ' _vRoot-mean-square error for the inventive method.When μ＞＞1, m＞1 o'clock, improvement factor I＞＞1, the root mean square time of the inventive method, the estimate variance of frequency difference reduced I doubly obviously greater than existing method, and promptly the estimated accuracy of frequency difference improves I doubly.Can know that under the identical calculations amount, the inventive method precision is higher than existing method.In other words, reaching under the same precision condition, the required amount of calculation of the inventive method is obviously less, is more suitable in real time processing system.

Above execution mode only is used to explain the present invention; And be not limitation of the present invention; The those of ordinary skill in relevant technologies field under the situation that does not break away from the spirit and scope of the present invention, can also be made various variations and modification; Therefore all technical schemes that are equal to also belong to category of the present invention, and scope of patent protection of the present invention should be defined by the claims.

Claims (4)

1. a frequency difference estimation method is characterized in that, may further comprise the steps:

S1: selected data section segmentation number m, data segment duration T _pAnd data segment interval T _r, m>=1;

S2: begin at synchronization, obtain data and the mutual ambiguity function of calculated data section in each data segment of two paths of signals;

S3: the mutual ambiguity function that m the mutual ambiguity function coherent accumulation of data segment is obtained whole data;

S4: to the mutual ambiguity function delivery of whole data, and carry out peak value searching, the maximum of points frequency value corresponding is the estimated value that arrives frequency difference.

2. frequency difference estimation method as claimed in claim 1 is characterized in that, said data segment interval T _rBe μ T _p, μ is the temporal extension factor.

3. frequency difference estimation method as claimed in claim 1 is characterized in that, among the said step S2, the formula of the mutual ambiguity function of calculated data section k is following:

${\mathrm{CAF}}_k({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})={\&Integral;}_{(k-1)T_r}^{T_p+(k-1)T_r}{s}_1\left(t-{\mathrm{\&tau;}}_k\right)s_2^{*}\left(t\right)e^{j2\mathrm{\&pi;\&upsi;}(t-(k-1)T_r)}\mathrm{dt}$

Wherein, ${\mathrm{\&tau;}}_k={\mathrm{\&tau;}}_1+\frac{\mathrm{\&upsi;}}{f_0}(k-1)T_r$

τ ₁Be two paths of signals s ₁() and S ₂The time of advent in () first segment data section is poor, τ _kBe two paths of signals s ₁() and S ₂The time of advent in () k segment data section is poor, and υ is the arrival frequency difference that two-way receives signal, f ₀Be the radiation source rf frequency.

4. frequency difference estimation method as claimed in claim 1 is characterized in that, the formula of coherent accumulation is following among the said step S3:

${\mathrm{CAF}}_c({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})=\underset{k}{\mathrm{\&Sigma;}}{\mathrm{CAF}}_k({\mathrm{\&tau;}}_1,\mathrm{\&upsi;})e^{j2\mathrm{\&pi;\&upsi;}(k-1)T_r}$

Wherein, CAF _c(τ ₁, υ) be the mutual ambiguity function of whole data.

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