CN1566985A - Linear frequency modulation continuous wave system moving destination parameter estimation method - Google Patents

Abstract

It is an estimation method for frequency-modulation continuous wave parameter of target motion and is characterized by the following: to establish accurate target echo mathematical model to calculate echo spectrum of multiple groups of ideal targets through searching the distance r and speed v of the target with 50-300 meters searching step length; to compare the ideal echo spectrum of target with real echo spectrum of target, wherein, the relevant r and v values of the ideal echo spectrum of target which is most matchable are the estimations of gamma and nu of the target distance and speed.

Description

Linear frequency modulation continuous wave system moving target method for parameter estimation

Technical field

The present invention relates to a kind of linear frequency modulation continuous wave (FMCW) system moving target method for parameter estimation, particularly in high-frequency ground wave radar, can significantly improve the target component estimated accuracy.

Background technology

High-frequency ground wave radar is a kind ofly to utilize high frequency (3～30MHz) electromagnetic waves are surveyed the New Type Radar of distant object (naval vessel, low altitude aircraft, cruise missile, ocean surface etc.) along earth surface diffraction, have detection range antiradiation missile far away, anti-stealthy, anti-, anti-low-level penetration, can survey outstanding advantages (comparing) such as ocean surface state, have very big development potentiality with normal radar.

High-frequency ground wave radar generally adopts the FMCW system, under the situation that transmitting-receiving is stood altogether, is interrupted becoming FMICW (linear frequency modulation interruption continuous wave) system for solving the transmitting-receiving isolating problem.How under the FMCW system, to extract target components such as distance, speed, people such as Rafaat Khan deliver is entitled as " high-frequency ground wave radar target detection and tracking " (Target Detection andTracking With a High Frequency Ground Wave Radar.IEEE Journal of Oceanic Engineering, 1994,19 (4): in the paper 540～548) this is had a detailed description, now be described below:

Radar Signal Generator produces the FMCW local oscillation signal, can be expressed as

f _oBe Carrier Frequency on Radar Signal, α is a sweep rate, and T is a frequency sweep cycle, and A and are respectively signal amplitude and first phase.Local oscillation signal is had no progeny to become in gating pulse and is transmitted

S _T(t)＝S(t)g(t) (2)

Gating pulse g (t) can be expressed as

$g\left(t\right)=\underset{p=0}{\overset{P-1}{\mathrm{\Σ}}}\mathrm{rect}\left[\frac{t-\mathrm{pq}-\frac{T_0}{2}}{T_0}\right]---\left(3\right)$

P is the gating pulse number in the frequency sweep cycle T, T ₀, q is respectively pulse width and cycle. Representing width is T ₀, the center is at the rect.p. of initial point.

If target is sentenced radial velocity v (away from radar for just) motion at distance r, then the time delay of the target echo of radar reception is

$\mathrm{\τ}=\frac{2(r+\mathrm{vt})}{c}---\left(4\right)$

Wherein c is the light velocity.The radar received signal is

S _R(t)＝K _RS _T(t-τ) (5)

K _RBe the propagation attenuation factor.After received signal and the local oscillation signal mixing, obtain baseband signal through the low-pass filtering demodulation and be

$S_I\left(t\right)=\mathrm{lowpass}\{S\left(t\right)\·S_R\left(t\right)\}$

$=A_I\cos \left(2\mathrm{\π}(\mathrm{\α\τt}-f_0\mathrm{\τ}-\frac{{\mathrm{\α\τ}}^2}{2})\right)---\left(6\right)$

A _IIt is the baseband signal amplitude.Low-pass filtering has been removed pulsed modulation and has been made baseband signal become continuous wave, therefore do not had in (6) formula gating pulse g (t) this.To launch after (4) formula substitution (6) formula, omitting some very little phase masses can get

$S_I\left(t\right)\≈A_I\cos \left(2\mathrm{\π}(2\left(\frac{\mathrm{\αr}-f_{0}v}{c}\right)t+\frac{2\mathrm{\αv}}{c}{t}^2-\frac{2f_{0}r}{c}-\frac{2\mathrm{\α}{r}^2}{c^2})\right)=A_I\cos \left({\mathrm{\φ}}_{\mathrm{\τ}}\right)---\left(7\right)$

The baseband signal instantaneous frequency is

$f_{\mathrm{\τ}}\left(t\right)=\frac{1}{2\mathrm{\π}}\frac{d{\mathrm{\φ}}_{\mathrm{\τ}}}{\mathrm{dt}}=\frac{2\mathrm{\αr}}{c}-\frac{2f_{0}v}{c}+\frac{4\mathrm{\αvt}}{c}---\left(8\right)$

Wherein first is caused that by target range second and third is caused by target radial speed.In higher-frequency radar

$\left|\frac{2\mathrm{\αr}}{c}\right|>>|-\frac{2f_{0}v}{c}+\frac{4\mathrm{\αvt}}{c}|,$ Thereby have $f_{\mathrm{\τ}}\left(t\right)\≈\frac{2\mathrm{\αr}}{c}.$

The analysis showed that more than can obtain the discrete spectrum corresponding with distance to carrying out FFT (fast fourier transform) after the baseband signal sampling, current FFT is called range conversion, the gained distance spectrum is

$R_I\left[m\right]=\mathrm{FFT}\left\{S_I\left(t\right)\right\}$

$=A_I\·\mathrm{FFT}\left\{\cos \left(2\mathrm{\π}(\mathrm{\α\τt}-f_0\mathrm{\τ}-\frac{{\mathrm{\α\τ}}^2}{2})\right)\right\}$

$=A_I\·R\left[m\right]---\left(9\right)$

With the distance spectrum that obtains in the frequency sweep cycle as delegation, l continuously then _MaxThe distance spectrum that individual frequency sweep cycle obtains can constitute a l _Max* m _MaxMatrix

m _MaxBe maximum distance unit ordinal number.

Analyze the Changing Pattern of the phase place of each row among the R now with frequency sweep cycle ordinal number (row ordinal number) l.During l frequency sweep cycle, target range is

r _l＝r+v(l-1)T (11)

Then l frequency sweep cycle baseband signal phase place is

${\mathrm{\φ}}_{\mathrm{l\τ}}=2\mathrm{\π}(2\left(\frac{{\mathrm{\αr}}_1-f_{0}v}{c}\right)t+\frac{2\mathrm{\αv}}{c}{t}^2-\frac{2f_0{r}_l}{c}-\frac{{{2\mathrm{\αr}}_l}^2}{c^2})---\left(12\right)$

In 100 frequency sweep cycles, i.e. l _Max≤ 100 o'clock, omit some little phase terms, continuous two frequency sweep cycle baseband signal phase differential are

$\mathrm{\Δ\φ}\≈2\mathrm{\π}(-\frac{2f_{0}v}{c})T---\left(13\right)$

Approximate according to this, l is capable among the R only differs a phase factor with the 1st row

Can approximate representation be

Each row to (14) formula carry out a FFT again and just can obtain the Doppler frequency spectrum corresponding with speed, and FFT is called Doppler-shift specifically.This shows, to getting the discrete two-dimensional echo spectrum through twice FFT processing after a plurality of frequency sweep cycle baseband signal samplings

P _2D(m，n)＝FFT{FFT{S ₁(t)}} (15)

Wherein m is the discrete frequency on the distance dimension, and n is the discrete frequency on speed (Doppler frequency) dimension.Target echo is f in the frequency that peak value appears in the distance dimension _τ=2ar/c, the frequency that occurs peak value in the speed dimension is f _v=-2f ₀V/c carries out the peak value detection to two-dimentional echo spectrum and can obtain target range and speed.

In the FMCW system, adopt twice FFT to extract distance and speed parameter, itself be exactly a kind of approximation method, can cause certain systematic error; In addition, what FFT obtained is discrete spectrum, extracts target component according to the spectrum peak and can produce quantization error again, and maximum can reach half of resolution.Higher-frequency radar is operated in short-wave band, and frequency is lower, disturbs morely, and modulating bandwidth B can not be too big, range resolution $\mathrm{\Δr}=\frac{c}{2B}$ Can not show a candle to normal radar, be generally several kilometers even tens kilometers, the range finding quantization error is very big, has brought exceptional hardship for target detection and tracking.How to improve the target component estimated accuracy and become the key issue that the higher-frequency radar target detection will solve.

Summary of the invention

The objective of the invention is to improve FMCW system target component estimated accuracy, be beneficial to motion target detection and tracking.

To achieve these goals, target component method of estimation of the present invention is: set up accurate target echo mathematical model, by to the searching for of target apart from r and speed v, calculate many group dreamboat echo spectrums (noiseless), the step-length of range search is a 50-300 rice; Again dreamboat echo spectrum and realistic objective echo spectrum are compared the r of that group dreamboat echo spectrum correspondence when both mate the most, the estimation that the v value is target range and speed

Observe (4), (6) formula as can be known, radar running parameter f ₀After determining with α, the functional form of echo baseband signal is known, only contains two variable r and v, can be expressed as

$S_I\left(t\right)=A_I\cos \left(2\mathrm{\π}(\mathrm{\α\τt}-f_0\mathrm{\τ}-\frac{{\mathrm{\α\τ}}^2}{2})\right)=A_I\·f(r,v,t)---\left(16\right)$

(15) the two-dimentional echo spectrum in the formula can be expressed as again

P _2D(m，n，r，v)＝FFT{FFT{S _I(t)}}＝A _I·FFT{FFT{f(r，v，t)}} (17)

＝A _I·P(m，n，r，v)

Wherein (r v) is the unit strength ideal baseband signal handles gained two dimension echo spectrum through twice FFT to P, is the function of r and v for m, n, can directly calculate when r and v determine.

Desirable echo spectrum that can directly calculate and actual ghosts spectrum compare the estimation that the r of the dreamboat echo spectrum correspondence when both mate the most, v value are target range and speed

Compare with twice traditional FFT method, the present invention has adopted accurate target echo mathematical model, eliminated the systematic error that approximation method causes, the searching method of the long 50-300 rice of small step has been eliminated the discrete quantization error that produces of echo spectrum again, the parameter estimation precision improves greatly, the range finding quantization error only is tens to hundreds of rice, improves an order of magnitude than prior art, helps motion target detection and tracking; On the other hand, high-precision distance estimations has reduced by increasing the necessity that modulating bandwidth B improves range resolution, has relaxed the requirement to Waveform Design, helps optimization system design, improves the radar overall performance.

Below in conjunction with drawings and Examples, the present invention is done more detailed explanation.

Description of drawings

Fig. 1 is the high-frequency ground wave radar fundamental diagram

Fig. 2 is that distance-speed two dimension is united estimation embodiment synoptic diagram

Fig. 3 is the one-dimensional estimated embodiment synoptic diagram of distance

Embodiment

Can directly calculate desirable echo spectrum according to (16), (17) formula, key be how by with relatively target component being estimated of actual ghosts spectrum.

Actual two-dimentional echo spectrum can be expressed as

P′ _2D(m，n)＝A′ _I·P(m，n，r′，v′)+N(m，n) (18)

A ' _IBe echo baseband signal amplitude, r ', v ' are respectively the actual range and the radial velocities of target, and (m n) is the echo spectrum noise contribution to N.Two-dimentional echo spectrum is carried out target peak detect, the discrete frequency of spectrum peak correspondence is m _rAnd n _v, then definition

${\mathrm{\β}}_1=\frac{P(m_r-1,n_v,r,v)}{P(m_r,n_v,r,v)}---\left(19\right)$

${\mathrm{\β}}_1^{\′}=\frac{P_{2D}^{\′}(m_r-1,n_v)}{P_{2D}^{\′}(m_r,n_v)}=\frac{A_I^{\′}\·P(m_r-1,n_v,r^{\′},v^{\′})+N(m_r-1,n_v)}{A_I^{\′}\·P(m_r,n_v,r^{\′},v^{\′})+N(m_r,n_v)}---\left(20\right)$

${\mathrm{\β}}_2=\frac{P(m_r+1,n_v,r,v)}{P(m_r,n_v,r,v)}---\left(21\right)$

${\mathrm{\β}}_2^{\′}=\frac{P_{2D}^{\′}(m_r+1,n_v)}{P_{2D}^{\′}(m_r,n_v)}=\frac{A_I^{\′}\·P(m_r-1,n_v,r^{\′},v^{\′})+N(m_r+1,n_v)}{A_I^{\′}\·P(m_r,n_v,r^{\′},v^{\′})+N(m_r,n_v)}---\left(22\right)$

${\mathrm{\γ}}_1=\frac{P(m_r,n_v-1,r,v)}{P(m_r,n_v,r,v)}---\left(23\right)$

${\mathrm{\γ}}_1^{\′}=\frac{P_{2D}^{\′}(m_r,n_v-1)}{P_{2D}^{\′}(m_r,n_v)}=\frac{A_I^{\′}\·P(m_r,n_v-1,r^{\′},v^{\′})+N(m_r,n_v-1)}{A_I^{\′}\·P(m_r,n_v,r^{\′},v^{\′})+N(m_r,n_v)}---\left(24\right)$

${\mathrm{\γ}}_2=\frac{P(m_r,n_v+1,r,v)}{P(m_r,n_v,r,v)}---\left(25\right)$

${\mathrm{\γ}}_2^{\′}=\frac{P_{2D}^{\′}(m_r,n_v+1)}{P_{2D}^{\′}(m_r,n_v)}=\frac{A_I^{\′}\·P(m_r,n_v+1,r^{\′},v^{\′})+N(m_r,n_v+1)}{A_I^{\′}\·P(m_r,n_v,r^{\′},v^{\′})+N(m_r,n_v)}---\left(26\right)$

P ' _2D(m n) is known actual ghosts spectrum, thereby β ' ₁, β ' ₂, γ ' ₁, γ ' ₂Known, β ₁, β ₂, γ ₁, γ ₂Be the function of r and v, can be expressed as β ₁(r, v), β ₂(r, v), γ ₁(r, v), γ ₂(r, v).

Fig. 2 has illustrated that distance-speed two dimension unites a kind of embodiment of estimation.Adopt the running parameter f identical with real system ₀And α, with suitable step-length r, v value to be searched for, simulation calculation goes out many group dreamboat echo spectrum P, and (r v) also preserves for m, n.Construct a two-dimensional search function

f _SEARCH(r, v)=| β ₁(r, v)-β ' ₁| ²+ | β ₂(r, v)-β ' ₂| ²+ | γ ₁(r, v)-γ ' ₁| ²+ | γ ₂(r, v)-γ ' ₂| ²(27) (r v) calculates, thereby β for m, n owing to P ₁(r, v), β ₂(r, v), γ ₁(r, v), γ ₂(r, v) also known.(m, n) ≡ 0, obviously had by (20), (22), (24), (26) formula for N in the ideal case

${\mathrm{\β}}_1^{\′}=\frac{P(m_r-1,n_v,r^{\′},v^{\′})}{P(m_r,n_v,r^{\′},v^{\′})}---\left(28\right)$

${\mathrm{\β}}_2^{\′}=\frac{P(m_r+1,n_v,r^{\′},v^{\′})}{P(m_r,n_v,r^{\′},v^{\′})}---\left(29\right)$

${\mathrm{\γ}}_1^{\′}=\frac{P(m_r,n_v-1,r^{\′},v^{\′})}{P(m_r,n_v,r^{\′},v^{\′})}---\left(30\right)$

${\mathrm{\γ}}_2^{\′}=\frac{P(m_r,n_v+1,r^{\′},v^{\′})}{P(m_r,n_v,r^{\′},v^{\′})}---\left(31\right)$

R, v are carried out two-dimensional search, when r → r ', v → v ', β ₁→ β ' ₁, β ₂→ β ' ₂, γ ₁→ γ ' ₁, γ ₂→ γ ' ₂, f _SEARCH(r, v) → 0, promptly desirable echo spectrum and actual ghosts spectrum have reached optimum matching.Noise is inevitable in the actual ghosts spectrum, gets f _SEARCH(r, the r of correspondence when v) reaching minimum value, v value are as the valuation of target range and speed This scheme adjust the distance and the estimated accuracy of speed all than higher, but the two-dimensional search calculated amount is bigger, can adopt when computing power allows.

Fig. 3 has illustrated the one-dimensional estimated a kind of embodiment of distance.For higher-frequency radar, higher rate accuracy can obtain by strengthening the signal Processing coherent accumulation time, and key is to improve distance accuracy, and therefore two dimension associating estimation approach can be reduced to one-dimensional estimated.According to detected Doppler frequency n _vCan obtain comparatively accurate velocity estimation

Adopt the running parameter f identical with real system ₀And α, with suitable step-length r to be searched for, simulation calculation goes out many group dreamboat echo spectrums And preserve.Re-construct a search function

$f_{\mathrm{SEARCH}}\left(r\right)=|{\mathrm{\β}}_1(r,\hat{v})-{\mathrm{\β}}_1^{\′}{|}^2+|{\mathrm{\β}}_2(r,\hat{v})-{\mathrm{\β}}_2^{\′}{|}^2---\left(32\right)$

This moment, search function was an one dimension, and the r of correspondence is the valuation of distance when reaching minimum value

It is slightly poor that the estimated accuracy ratio that this scheme is adjusted the distance is united estimation, but calculated amount is little a lot, practical.

When radar has a plurality of receiving cable, can obtain one group of β ' according to each passage echo ₁, β ' ₂, γ ' ₁, γ ' ₂, substitution after the statistical average (27) or (32) formula will improve the parameter estimation precision.

Two dimension is united estimation and can be referred to as the search matched method apart from one-dimensional estimated, proposes at the point target model.Because the range resolution of higher-frequency radar is generally several kilometers even tens kilometers, is far longer than the size of moving target (naval vessel, aircraft etc.), satisfies the point target model, so the present invention is well suited for the estimation of higher-frequency radar target component.In fact, the present invention can be applicable to satisfy in any FMCW detection system (comprising radar, sonar etc.) of point target model.For multiobject situation, as long as the difference of distance, speed between target is greater than the twice of resolution, target echo spectrum secondary lobe is very little to the influence of adjacent objects, and high estimation accuracy can be differentiated and keep to the search matched method just.

Claims (2)

1. linear frequency modulation continuous wave system target component method of estimation is characterized in that setting up accurate target echo mathematical model, by to the searching for apart from r and speed v of target, calculates many group dreamboat echo spectrums, and the step-length of range search is a 50-300 rice; Again dreamboat echo spectrum and realistic objective echo spectrum are compared the r of that group dreamboat echo spectrum correspondence when both mate the most, the estimation that the v value is target range and speed Described target echo mathematical model is

$S_I\left(t\right)=A_I\cos \left(2\mathrm{\π}(\mathrm{\α\τt}-f_0\mathrm{\τ}-\frac{{\mathrm{\α\τ}}^2}{2})\right)=A_I\·f(r,v,t)--\left(1\right)$

P _2D(m，n，r，v)＝FFT{FFT{S _I(t)}}＝A _I·FFT{FFT{f(r，v，t)}} (2)

＝A _I·P(m，n，r，v)

f _SEARCH(r，v)＝|β ₁(r，v)-β′ ₁| ²+|β ₂(r，v)-β′ ₂| ²+|γ ₁(r，v)-γ′ ₁| ²+|γ ₂(r，v)-γ′ ₂| ² (3)

Wherein, S _I(t) be the echo baseband signal;

P _2D(r v) is two-dimentional echo spectrum for m, n;

f _SEARCH(r is v) for being used for the search function of estimated distance and speed;

f ₀With α be the radar running parameter, (r v) is the unit strength ideal baseband signal handles gained two dimension echo spectrum through twice FFT to P, is the function of r and v for m, n, can directly calculate when r and v determine.

2. target component method of estimation as claimed in claim 1 only is characterized in that the searching for apart from r of target obtained comparatively accurate velocity estimation according to detected Doppler frequency nv With following formula estimating target distance:

$f_{\mathrm{SEARCH}}\left(r\right)={|{\mathrm{\β}}_1(r,\hat{v})-{\mathrm{\β}}_1^{\′}|}^2+{|{\mathrm{\β}}_2(r,\hat{v})-{\mathrm{\β}}_2^{\′}|}^2--\left(4\right)$

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