CN101776752B - Precise tracking and measuring method of high dynamic signal of air fleet link - Google Patents

Abstract

The invention relates to a precise tracking and measuring method of a high dynamic signal of an air fleet link, belonging to the technical field of aeronautical data links and radio navigation, and aiming at providing a precise tracking and measuring method of the high dynamic signal the an air fleet link and an implementation structure to solve the problems in the prior art. The invention provides a system framework of the precise tracking and measuring method of the high dynamic signal of the air fleet link, which can be implemented on a digital signal processor (DSP) and a FPGA (field programmable gate array) of a circuit board, and overcomes the defects of the unfavorable precision of a traditional high dynamic receiver by utilizing a double-loop structure of a frequency tracking loop of carrier tracking and a phase locking loop as well as a code phase locking loop to realize the high precise tracking under a high dynamic condition. The method can be widely applied to satellite navigation receivers, range measurement systems and communication systems based on a quiescent carrier modulation direct sequence spread spectrum system.

Description

The precision tracking of high dynamic signal of air fleet link and measuring method

Technical field:

The present invention relates to a kind of precision tracking and measuring method of high dynamic signal of air fleet link, belong to aeronautical data chain, technical field of aerial data chains.

Background technology:

Because link adopts suppressed carrier BPSK/QPSK phase-shift keying (PSK) modulation system and direct sequence spread spectrum pattern between member's aircraft of a group of planes, can run into the problem of signal capture and tracking:

1. under the suppressed carrier communication system, transmit leg-take over party's high dynamically relative motion causes to be caught and follows the tracks of difficulty and frequent losing lock, lose and catch;

2. the high difficulty that causes dynamically that the carrier track error increases, the regeneration pseudo-code phase is accurately alignd, range finding, range rate error increase;

3. losing lock, lose and to catch probability and increase greatly and will cause continuous carrier phase measurement difficulty and integrated Doppler measurements to be difficult to realization.Therefore, receive the emphasis and the difficult point of BPSK/QPSK modulated spread spectrum signal in the high dynamic environment, be that the high-quality of carrier wave and pseudo-code phase is followed the tracks of.

Summary of the invention

The object of the present invention is to provide a kind of precision tracking and measuring method of high dynamic signal of air fleet link, to solve the problems of the prior art.

The precision tracking of a kind of high dynamic signal of air fleet link of the present invention and measuring method, it can be realized on the digital signal processor DSP of circuit board and FPGA.This method is specific as follows:

(1) high dynamic carrier track loop

High dynamic carrier tracking cell of the present invention, adopted the dynamic carrier track strategy of suitable carrier, promptly undertaken by the FFT frequency domain algorithm after pseudo-code phase catches, adopt four phase frequency discriminators further to draw and catch Doppler frequency, the initial tracking, Doppler frequency is dropped to several hertz from the hundreds of hertz, make it to enter the working range of cross product automatic frequency tracking ring; Adopt the strong FLL ring of dynamic capability to eliminate dynamic, steady track; Adopt the little costas PLL of thermal noise error to improve carrier phase.Specific as follows:

[1] integration-remover and frequency, phase place decision algorithm

If sample frequency is $f_s=\frac{1}{T_s},$ T _sBe sampling interval, the received signal down coversion after if sampling obtain:

s(i)＝A _i·PN _I(i·T _s-τ)·cos[(ω _I，+ω _d)i+φ]+A _i·PN _Q(i·T _s-τ)·sin[(ω _I+ω _d)i+φ](1)

In the formula (1): ω _I=2 π f _IT _sBe the received signal IF-FRE; ω _d=2 π f _dT _sBe Doppler frequency; φ is a phase of received signal; PN _I(iT _s); PN _Q(jT _s) be respectively homophase pseudo-code and quadrature pseudo-code; τ is the received signal time-delay;

If the in-phase signal and the orthogonal signal of receiving cable carrier wave NCO output are respectively:

$\left\{\begin{array}{c}{I}_R\left(i\right)=A_R\·\cos [({\mathrm{\ω}}_I+{\widehat{\mathrm{\ω}}}_d)i+\widehat{\mathrm{\φ}}]\\ Q_R\left(i\right)=-A_R\·\sin [({\mathrm{\ω}}_I+{\widehat{\mathrm{\ω}}}_d)i+\widehat{\mathrm{\φ}}]\end{array}\right.---\left(2\right)$

In the formula (2): A _RAmplitude for NCO output cosine and sine signal; ${\widehat{\mathrm{\ω}}}_d=2\mathrm{\π}{\hat{f}}_d{T}_s$ ( Be Doppler frequency f in to received signal _dEstimation);

Be the estimation of phase to received signal;

I, Q branch road integration-remover in related interval end output result are:

$\left\{\begin{array}{c}{I}_{\mathrm{ps}}\left(k\right)\≈A\·R\left[\mathrm{\ϵ}\left(k\right)\right]\·\sin c[\mathrm{\Δ}{\mathrm{\ω}}_d\left(k\right)\·N/2]\cos {\mathrm{\θ}}_k+n_I\left(k\right)\\ Q_{\mathrm{ps}}\left(k\right)\≈A\·R\left[\mathrm{\ϵ}\left(k\right)\right]\·\sin c[\mathrm{\Δ}{\mathrm{\ω}}_d\left(k\right)\·N/2]\sin {\mathrm{\θ}}_k+n_Q\left(k\right)\end{array}\right.---\left(3\right)$

In the formula (3): A is a signal amplitude; Δ ω _d(k) estimate residual error for Doppler shift, $\mathrm{\Δ}{\mathrm{\ω}}_d\left(k\right)={\mathrm{\ω}}_d\left(k\right)-{\widehat{\mathrm{\ω}}}_d\left(k\right);$ ε (k) is code phase (time-delay) estimated bias (truly delays time and estimate to delay time poor), ε (k)=Δ τ; R () is two desirable level autocorrelation functions of pseudo-random code, is the function of time; N is that the integration of integration remover is counted; θ _kBe carrier phase error, θ _k=kN Δ w _d(k)-Δ w _d(k) N/2+ △ φ; n _I(k), n _Q(k) be random noise.Formula (3) is very important, is the foundation of carrying out frequency tracking error estimation, cross product frequency discrimination and arc tangent phase demodulation algorithm.

The frequency judgement adopts expression formula as follows:

$\mathrm{\Δ}{f}_k=\frac{1}{T_{\mathrm{ID}}}[I(k-1)Q\left(k\right)-I\left(k\right)Q(k-1)]---\left(4\right)$

In the formula (4), T _IDBe the integration checkout time.

In with four phase frequency discriminator frequency pulling processes, adopt Δ f _kJudge that whether current frequency is less than 10Hz.If current frequency Δ f _kLess than 10Hz, then change the FLL tracking loop over to and carry out frequency-tracking; Otherwise, continue the frequency pulling process.

When following the tracks of beginning, need frequency be drawn to below the 10Hz from the hundreds of hertz with the frequency pulling module, then according to carrier phase θ _kAdjudicate.If θ _kGreater than 10 °, receiver carries out frequency-tracking with the cross product frequency discriminator; If θ _kLess than 10 °, then adopt pure PLL ring to carry out Phase Tracking.

Phase place judgement expression formula is:

${\mathrm{\η}}_k=\left|\frac{Q_s\left(k\right)}{I_s\left(k\right)}\right|=\left|\frac{\sin {\mathrm{\θ}}_k}{\cos {\mathrm{\θ}}_s}\right|=\left|\mathrm{tg}{\mathrm{\θ}}_k\right|---\left(5\right)$

Work as θ in the following formula _kWhen very little, tg θ _kWith θ _kBe directly proportional.If θ _kIn the time of＜10 °, change phaselocked loop over to and follow the tracks of, θ _kBring following formula into for=10 °, obtain phase place decision threshold η _k=0.176.

[2] four phase frequency discriminators are realized frequency pulling

Behind the acquiring pseudo code, the carrier doppler frequency swing is directed into a Doppler frequency search unit scope, i.e. 500Hz, this moment, estimated frequency error was still very big, therefore, at first utilize the frequency pulling module with frequency pulling in the following range of cross product frequency discriminator; The present invention adopts four phase frequency discriminators to carry out the frequency pulling algorithm, needs after the repeatedly traction frequency pulling below 10Hz.In the frequency pulling process, adopt Δ f _kWhether judge current frequency less than 10Hz, if current frequency Δ f _kLess than 10Hz, then change the FLL tracking loop over to and carry out the high-frequency tracking; Otherwise, continue the frequency pulling process.

[3] cross product frequency discrimination automatic frequency tracking (CP-AFC) locking ring (FLL)

When frequency error during, adopt the cross product frequency discriminator to realize accurate frequency-tracking less than 10Hz.Wherein, T is the integration interval time of integration-remover.

Cross product frequency discriminator output e _FkFor:

e _fk＝I(k-1)Q(k)-I(k)Q(k-1)

＝0.25A ²D(k)D(k-1)R[ε(k)][ε(k-1)] (6)

·sinc[Δf _d(k)·πT]·sinc[Δf _d(k-1)·πT]·sin(φ _k-φ _k-1)

In the formula (6): T is the integration checkout time.Owing to catch when finishing, will receive pseudo-code and local pseudo-code is alignd substantially, establishing the time interval is the unit interval, modulating data invariant position in the measurement process continuously is so have D (k) D (k-1)=1, R[ε (k)] and ≈ 1, R[ε (k-1)] ≈ 1, φ _k=Δ f _d(k) t+ φ ₀, φ _k-φ _K-1=[Δ f _d(k)-Δ f _d(k-1)] T=Δ f _dT; When frequency pulling is finished, Doppler shift evaluated error Δ f _d＜10 °/Hz, phase error | Δ f _d(k). π T|＜＜during pi/2, sinc ²[Δ f _d(k) π T] → 1, sin (φ _k-φ _K-1) → φ _k-φ _K-1So the phase change (frequency) in controlled quentity controlled variable and unit interval is directly proportional, control the purpose that carrier wave NCO reaches frequency-tracking through wave filter with this.

The cross product frequency discriminator is output as

e _fk＝θ _k-θ _k-1＝2πΔf _d(k)·T (7)

[4] Phase Tracking locking ring (PLL)

Inphase quadrature phaselocked loop (Costas ring, i.e. section's Stas ring) is a kind of of PLL, because it is insensitive and obtained widespread usage in PSK despreading receiver to carrier modulation data.Section's Stas ring phase detector algorithm commonly used is a two quadrant arc tangent phase demodulation algorithm:

$e_{\mathrm{pk}}={\tan }^{-1}(Q_{\mathrm{ps}}/I_{\mathrm{ps}})$

$={\tan }^{-1}\left(\frac{0.5A\·R\left[\mathrm{\ϵ}\left(k\right)\right]\·\sin c[\mathrm{\Δ}{f}_d\left(k\right)\·\mathrm{\πT}]\·\sin {\mathrm{\φ}}_k}{0.5A\·R\left[\mathrm{\ϵ}\left(k\right)\right]\·\sin c[\mathrm{\Δ}{f}_d\left(k\right)\·\mathrm{\πT}]\·\cos {\mathrm{\φ}}_k}\right)={\mathrm{\φ}}_k---\left(8\right)$

Two quadrant arc tangent phase detector tan ^-1(Q _Ps/ I _Ps) performance is linear, best performance in whole-90 °～90 ° scopes.

[5] loop filter of FLL FLL and phase-locked loop pll

Carrier track FLL (second order loop) adopts single order Jaffe-Rechtin wave filter, and carrier track phaselocked loop (third order PLL) adopts second order Jaffe-Rechtin wave filter.

To sum up, the carrier tracking loop line structure that three rank PLL phaselocked loops of the second-order F LL automatic frequency tracking ring of the frequency pulling of four phase phase demodulations+cross product frequency discrimination+two quadrant arc tangent phase demodulation constitute can satisfy the demand of general high dynamic task; Well-designed single order, second order Jaffe-Rechtin loop filter parameters can obtain higher carrier frequency/carrier phase tracking precision.

(2) high dynamically frequency spreading tracking loop

After FFT frequency domain parallel search was caught rough carrier frequency and pseudo-code phase, the spreading code of local regeneration spreading code and received signal was finished thick alignment, and error is within 1/2 chip.Subsequently, entrance code tracing process (corresponding with carrier track) realizes accurately aligning of spreading code phase place (delay).The closed loop of pseudo-code is followed the tracks of and is adopted delay phase-locked loop usually, utilize promptly that the local code generator produces that phase place is leading, delay signal and with the spread-spectrum signal quadrature mixing of the BPSK/QPSK modulation of input after relevant, relatively homophase I/ quadrature Q two branch road results come control code NCO and the generation local code signal consistent with the input code phase place to obtain the code phase error signal.

Pseudo-code phase of the present invention is followed the tracks of and has been adopted incoherent digital delay phase-locked loop (DDLL) algorithm structure, is made up of integration-remover, code phase discriminator, loop filter, sign indicating number NCO, regeneration code generator and shift register.Wherein the parameter of integration-remover, code phase discriminator and loop filter has determined the characteristic of code tracking loop.Narrow relevant in order to realize, reach the purpose of accurate tracking code phase, in loop design, produced the regeneration pseudo-code of instantaneous code, lead-lag 1/2 chip, lead-lag 1/4 chip, constituted relevant spacing respectively and be respectively 1 chip, 1/4 incoherent delay lock loop by shift register.In the code tracking loop, code phase discriminator compares the pre-detection integral result of homophase and quadrature branch, produces error signal, and by loop filter output code NCO frequency control word, control regeneration pseudo-code and reception pseudo-code are accurately alignd.Describe code tracking loop phase demodulation algorithm, code tracking loop path filter, the tracking of carrier wave auxiliary code ring below in detail.

[1] the sign indicating number ring Discr. phase demodulation algorithm of code tracking loop

The code phase digital correlation leading, instant, that lag behind that sign indicating number ring Discr. is input as carrier wave homophase I/ quadrature Q branch road accumulates the result.

Sign indicating number ring discriminator algorithm commonly used has three kinds: dot product power Discr. (I _Es-I _Ls) I _Ps+ (Q _Es-Q _Ls) Q _Ps, deduct after-power Discr. (I in advance _Es ²+ Q _Es ²)-(I _Ls ²+ Q _Ls ²), deduct hysteresis envelope Discr. in advance

Generally do not use and deduct hysteresis envelope Discr. in advance.

When the relevant generation of sign indicating number, loop carries out tracking mode, supposes relevant spacing d=2 δ, and the error signal that then deducts the output of retarded type coherent code phase detector in advance is

E(k)＝I _e(k)-I _l(k) (9)

＝0.5Asinc[Δf _d(k)·πT]·cos[Δf _d(k)·t _k+φ ₀]·{R[ε(k)-δ]-R[ε(k)+δ]}

As can be seen, error signal has dependence to carrier track from formula (9), when carrier wave not synchronously or when cycle slip occurring after following the tracks of, phase detector will produce non-quantitative, so generally not adopt phase dry type phase detector.Incoherent type code phase discriminator mainly contains and subtracts after-power phase detector and dot product phase detector in advance.The invention provides two kinds of different delay lock loop discriminator algorithm: normalized after-power Discr., the normalized dot product Discr. of subtracting in advance.

1. subtract the after-power Discr. in advance

$E_{\mathrm{el}}\left(k\right)=I_e^2\left(k\right)+Q_e^2\left(k\right)-I_l^2\left(k\right)-Q_l^2\left(k\right)$

$=0.25A^2\·{\sin c}^2[\mathrm{\Δ}{f}_d\left(k\right)\·\mathrm{\πT}]\·\left\{R^2\right[\mathrm{\ϵ}\left(k\right)-\mathrm{\δ}]-R^2[\mathrm{\ϵ}\left(k\right)+\mathrm{\δ}\left]\right\}$

$=0.25A^2{\sin c}^2[\mathrm{\Δ}{f}_d\left(k\right)\·\mathrm{\πT}]\·S_{\mathrm{el}}(\mathrm{\ϵ},\mathrm{\δ})---\left(10\right)$

In formula (10): I _Es(k), I _Ps(k) and I _Ls(k) be respectively the input in-phase signal with leading, instant, lag behind yard in relevant output; Q _Es(k), Q _Ps(k) and Q _Ls(k) be respectively input quadrature-phase and leading, instant, the sign indicating number that lags behind in relevant output, define and subtract after-power phase detector phase characteristic function S in advance _El(ε δ) is:

S _el(ε，δ)＝R ²[ε(k)-δ]-R ²[ε(k)+δ] (11)

When defining spreading code fully to punctual correlation and chip width T _cBeing 1 o'clock autocorrelation function can be expressed as:

$R\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{cc}0& (\mathrm{\&tau;}<-1)\\ 1+\mathrm{\&tau;}& (-1\&le;\mathrm{\&tau;}<0)\\ 1-\mathrm{\&tau;}& (0\&le;\mathrm{\&tau;}<1)\\ 0& (\mathrm{\&tau;}\&GreaterEqual;1)\end{array}\right.---\left(12\right)$

In formula (11) difference substitution formula (12), can be deducted the phase characteristic function of after-power phase detector in advance:

(i) when δ=1/2

$S_{\mathrm{el}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1-\mathrm{\&delta;})\\ -{(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (-1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ 4\mathrm{\&epsiv;}(1+\mathrm{\&delta;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1-\mathrm{\&delta;})\\ {(1-\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1+\mathrm{\&delta;})\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1+\mathrm{\&delta;})\end{array}\right.---\left(13\right)$

(ii) when δ=1/8 or δ=1/16

$S_{\mathrm{el}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1-\mathrm{\&delta;})\\ -{(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (-1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ -4\mathrm{\&delta;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-\mathrm{\&delta;})\\ 4\mathrm{\&epsiv;}(1-\mathrm{\&delta;})& (-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<+\mathrm{\&delta;})\\ 4\mathrm{\&delta;}(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1-\mathrm{\&delta;})\\ {(1-\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1+\mathrm{\&delta;})\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1+\mathrm{\&delta;})\end{array}\right.---\left(14\right)$

2. dot product Discr.

E _dp(k)＝[I _e(k)-I _l(k)]I _ps(k)+[Q _e(k)-Q _l(k)]Q _ps(k)

＝0.25A ²{R[ε(k)-δ]-R[ε(k)+δ]}·R[ε(k)]·sinc ²[Δf _d(k)·πT] (15)

＝0.25A ²sinc ²[Δf _d(k)·πT]·S _dp(ε，δ)

In formula (15): I _Es(k), I _Ps(k) and I _Ls(k) be respectively the input in-phase signal with leading, instant, lag behind yard in relevant output; Q _Es(k), Q _Ps(k) and Q _Ls(k) be respectively input quadrature digital signal and advanced code, instantaneous code, hysteresis sign indicating number in the output of digital correlation accumulation result behind phase place rotation result.Definition dot product phase detector phase characteristic function S _Dp(ε δ) is:

S _dp(ε，δ)＝{R[ε(k)-δ]-R[ε(k)+δ]}·R[ε(k)] (16)

(i) when δ=1/2

$S_{\mathrm{dp}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1)\\ -(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})(1+\mathrm{\&epsiv;})& (-1\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ 2\mathrm{\&epsiv;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<0)\\ 2\mathrm{\&epsiv;}(1-\mathrm{\&epsiv;})& (0\&le;\mathrm{\&epsiv;}<\mathrm{\&delta;})\\ (1-\mathrm{\&epsiv;}+\mathrm{\&delta;})(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1)\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1)\end{array}\right.---\left(17\right)$

(ii) when δ=1/8 or δ=1/16

$S_{\mathrm{dp}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1)\\ -(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})(1+\mathrm{\&epsiv;})& (-1\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ -2\mathrm{\&delta;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;-\mathrm{\&delta;})\\ 2\mathrm{\&epsiv;}(1+\mathrm{\&epsiv;})& (-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;0)\\ 2\mathrm{\&epsiv;}(1-\mathrm{\&epsiv;})& (0\&le;\mathrm{\&epsiv;}\&le;\mathrm{\&delta;})\\ 2\mathrm{\&delta;}(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;1-\mathrm{\&delta;})\\ (1-\mathrm{\&epsiv;}+\mathrm{\&delta;})(1-\mathrm{\&epsiv;})& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;1)\\ 0& (\mathrm{\&epsiv;}>1)\end{array}\right.---\left(18\right)$

[2] loop filter of code tracking loop

Because adopted the auxiliary of carrier wave ring in to code tracking, code tracking loop adopts second-order loop filter.Filtering algorithm of the present invention is selected second order Jaffe-Rechtin wave filter.

Dynamic and the thermal noise performance of following analysis code track loop.

1. loop dynamic performance

The dynamic measurement error of code tracking loop is by the exponent number and the bandwidth decision of loop filter, and for second order code tracking loop path filter, its dynamic measurement error is

${\mathrm{\&sigma;}}_e=\frac{d^{2}R/\mathrm{<figure-callout\; id="2"\; label="d\; t"\; filenames="HSA00000010858100052.png,HSA00000010858100061.png"\; state="\{\{state\}\}">d</figure-callout>}{t}^{}{}^2}{{\mathrm{\&omega;}}_n^2}---\left(19\right)$

In the formula (19): R is a unit with basic number of chips, loop natural frequency ω _n=1.89B _n, (B _nBe loop bandwidth).

Under normal conditions, the dynamic acceleration of carrier causes dynamic tracking error in the sign indicating number ring, but owing to exist fixing proportionate relationship between sign indicating number Doppler and the carrier doppler, when the carrier wave ring dynamically carries out accurate tracking to carrier, auxiliary by carrier wave, the most of dynamic error in can the blanking code ring, therefore, the physical presence dynamic error is very little in the sign indicating number ring, can not consider.

2. thermonoise trembles error (1 σ)

The thermal noise error that subtracts the after-power phase detector in advance is:

${\mathrm{\&sigma;}}_{\mathrm{nEL}}=\sqrt{\frac{B_{n}d}{2(C/N_0)}[1+\frac{2}{(2-d)(C/N_0)T}]}---\left(20\right)$

The thermal noise error of dot product phase detector is:

${\mathrm{\&sigma;}}_{\mathrm{nDP}}=\sqrt{\frac{B_{n}d}{2(C/N_0)}[1+\frac{1}{(C/N_0)T}]}---\left(21\right)$

In formula (20) and formula (21): B _nBe loop equivalent noise bandwidth (Hz) that d is a lead and lag sign indicating number related interval (chip), T is pre-detection integral time (s), C/N ₀For carrier to noise power ratio (is worked as C/N ₀When being unit representation with dB, it equals

[3] carrier wave auxiliary code ring is followed the tracks of the compensating for doppler dynamic error

Carrier tracking loop provides a carrier wave the auxiliary spread-spectrum code rate variation that causes owing to Doppler effect with true tracking in order to control code NCO output frequency when the accurate tracking carrier phase changes.Because the wavelength of Doppler effect on the signal and signal is inversely proportional to, so define the auxiliary scale factor of a carrier wave: $\mathrm{\&mu;}=\frac{f_{\mathrm{code}}}{f_{\mathrm{RF}}},$ f _CodeBe spread-spectrum code rate nominal value, f _RFBe radio-frequency carrier frequency nominal value.

The spreading code bit rate variable quantity (spreading code Doppler shift) that brings owing to dynamic motion is calculated by following formula:

${\hat{f}}_{d\_\mathrm{code}}(k+1)=\mathrm{\&mu;}\&CenterDot;{\hat{f}}_d(k+1)---\left(22\right)$

In the formula (22):

Be carrier wave

The carrier doppler frequency estimation of loop filter output;

Be spreading code Doppler shift estimated value.

Be scaled behind the frequency control word and the frequency offset control word P of code tracking loop ring _BiasAddition, the digital controlled oscillator NCO that feeds back to the pseudo-code delay lock loop together adjusts, and effectively reduces the influence of dynamic stress to the pseudo-code delay lock loop, thereby improves the performance of dynamic tracking and the tracking accuracy of code tracking loop.

The precision tracking of a kind of high dynamic signal of air fleet link of the present invention and measuring method, its advantage is: method of the present invention has solved the not good defective of traditional high dynamic receiver precision; Method disclosed by the invention can be widely used in satellite navigation receiver, range measurement system and the communication system based on suppressed carrier modulation direct sequence spread spectrum system.

Description of drawings

Figure 1 shows that the carrier tracking loop and the code tracking loop algorithm structure figure of the inventive method.

Figure 2 shows that carrier tracking loop algorithm structure figure among the present invention.

Figure 3 shows that FLL and PLL combined carriers following principle frame.

Figure 4 shows that cross product automatic frequency tracking ring schematic diagram.

Figure 5 shows that cross product frequency discriminator kam-frequency characteristic.

Figure 6 shows that the one-piece construction block diagram of code tracking loop.

Figure 7 shows that the structured flowchart of incoherent digital delay phase-locked loop (DDLL) algorithm.

The phase characteristic curve of Fig. 8 (a) expression subtracting in advance after-power phase detector.

The phase characteristic curve of Fig. 8 (b) expression dot product phase detector.

Figure 9 shows that the relation of sign indicating number ring thermal noise error and loop bandwidth; Wherein (a) is for subtracting the after-power Discr. in advance; (b) be the dot product Discr..

Embodiment

Below in conjunction with drawings and Examples, technical scheme of the present invention is described further.

Fig. 1 has provided the air fleet link asynchronous communication of the inventive method and the carrier track and the code tracking loop algorithm structure figure of measuring terminals.

Can eliminate by carrier wave is auxiliary the influence of pseudo-code tracing ring because the Doppler shift that carrier is dynamically introduced changes, the dynamic property of receiver depends primarily on carrier tracking technique.Usually have two kinds of tracking loops to adopt: a kind of is the phase-locked loop (PLL) (the costas ring promptly is wherein a kind of, but it is insensitive to the modulating data on the carrier wave) that is concerned with, and receiver need produce and the coherent carrier of incoming carrier with the frequency homophase; Another kind is incoherent frequency phase lock loop (FLL), receiver need produce with incoming carrier with frequently but do not require relevant carrier wave.Capturing carrier is realized with the normal costas of the employing ring of tracking reconstructed carrier phase coherence demodulation BPSK data.Coherent system has preferable performance to Gaussian noise, but relatively poor to the tolerance of communication link interference, the Doppler shift that dynamically introduced by carrier influences bigger.For the Doppler shift on a large scale of high dynamic carrier, the costas ring must have wide relatively bandwidth, this means that the snr threshold performance is that tracking power reduces.Coherent demodulation this moment is no longer suitable, and desirable scheme is to adopt non-coherent demodulation, i.e. automatic tracking frequencies of loop rather than phase place.Dynamically second order frequency locking tracking ring FLL has the dynamic property advantage of a few dB-Hz signal to noise ratio (S/N ratio) thresholdings than three rank phase-locked loop PLL for identical, but its tracking accuracy is low, and there is certain contradiction in the two, so the integration advantage of can learning from other's strong points to offset one's weaknesses in design.Introduce the design and analysis discussion of carrier tracking loop and code tracking loop algorithm below respectively.

(1) high dynamic carrier track loop

1, the principle of work of FLL and PLL combined carriers track loop

Adopted the dynamic carrier track strategy of suitable carrier in the carrier wave ring design of the present invention, promptly undertaken by the FFT frequency domain algorithm after pseudo-code phase catches, adopt four phase frequency discriminators further to draw and catch Doppler frequency, the initial tracking, Doppler frequency is dropped to several hertz from the hundreds of hertz, make it to enter the working range of cross product automatic frequency tracking ring; Adopt the strong FLL ring of dynamic capability to eliminate dynamic, steady track; The basic invention of adopting the little costas PLL of thermal noise error to improve carrier phase.Make tracking loop can satisfy the requirement of dynamic property and tracking accuracy simultaneously, the setting able to programme of loop parameter, and two kinds of tracking strategy switch in the mode of software with the carrier dynamic change, have guaranteed the dirigibility and the robustness of following the tracks of.The carrier tracking loop algorithm structure as shown in Figure 2.Because system works under high dynamic environment, carrier track adopts FLL and phaselocked loop to work simultaneously, follows the tracks of carrier wave.FLL estimates that in the basic enterprising line frequency of catching predicted frequency the output of adjusted in concert FLL NCO is carried out carrier wave and peeled off.Usually the employing integration is removed and is added frequency discriminating realization Frequency Estimation, and the time that the range of linearity of Frequency Estimation is removed by integration determines, and the saltus step of data bit can not take place in integration checkout time section.In the embodiment of the invention: carrier wave NCO is biased to the frequency word of the intermediate frequency correspondence of digital medium-frequency signal:

Pseudo-code and carrier wave just enter tracking phase after finishing and tentatively catching.Because this moment, the resolution of Doppler frequency prediction only was 500Hz, residual Doppler frequency composition is also bigger, therefore at first adopts the frequency pulling module with estimating carrier frequencies residual delta f _kDrop to below the 10Hz, then according to carrier phase θ _kAdjudicate, if θ _kGreater than 10 °, carrier track then adopts the cross product frequency discriminator to carry out frequency-tracking; If θ _kLess than 10 °, then adopt pure PLL to carry out Phase Tracking.Outlet selector among Fig. 3 is exactly according to Δ f _kAnd θ _kDifferent situations, selecting is that output by the frequency pulling algorithm feeds back to carrier wave NCO, still feeds back to carrier wave NCO (as shown in Figure 3) by output of FLL loop or the output of PLL loop

2, integration-remover and frequency, phase place decision algorithm

The effect of integration-remover is as follows:

1. low-pass filter: integration-remover is equivalent to a low-pass filter, after the filtering mixing with the frequency composition;

2. input signal is carried out low-pass filtering, eliminate dynamically and the influence of radio noise;

3. input signal is accumulated, improve the signal to noise ratio (S/N ratio) of signal, increase receiver sensitivity.The sampling rate of receiver radio frequency front end is 62.11MHz, and when pre-detection was 0.2ms integral time, 12422 data integrations are added up can make the noise acoustic ratio improve nearly 42dB;

4. down-sampled rate: the sampling rate of the input intermediate-freuqncy signal of answering machine is 62.11MHz, and the integration remover whenever adds up 12422 and exports once result, and promptly data sampling rate is reduced to 5kHz, the length in an about pseudo-code cycle.Because before bit synchronization, if surpass the length in a pseudo-code cycle integral time, may cross over the saltus step of data bit so in section integral time, the I that obtains in this case, Q two-way integration are removed result's mistake.So selecting the integration checkout time is 0.2ms.

If sample frequency is $f_s=\frac{1}{T_s},$ T _sBe sampling interval, the received signal down coversion after if sampling obtain:

s(i)＝A _i·PN _I(i·T _s-τ)·cos[(ω _I+ω _d)i+φ]+A _i·PN _Q(i·T _s-τ)·sin[(ω _I+ω _d)i+φ] (1)

In the formula (1): ω _I=2 π f _IT _sBe the received signal IF-FRE; ω _d=2 π f _dT _sBe Doppler frequency; φ is a phase of received signal; PN _I(iT _s); PN _Q(iT _s) be respectively homophase pseudo-code and quadrature pseudo-code; τ is the received signal time-delay.

If the in-phase signal and the orthogonal signal of receiving cable carrier wave NCO output are respectively:

$\left\{\begin{array}{c}{I}_R\left(i\right)=A_R\&CenterDot;\cos [({\mathrm{\&omega;}}_I+{\widehat{\mathrm{\&omega;}}}_d)i+\widehat{\mathrm{\&phi;}}]\\ Q_R\left(i\right)=-A_R\&CenterDot;\sin [({\mathrm{\&omega;}}_I+{\widehat{\mathrm{\&omega;}}}_d)i+\widehat{\mathrm{\&phi;}}]\end{array}\right.---\left(2\right)$

In the formula (2): A _RAmplitude for NCO output cosine and sine signal; ${\widehat{\mathrm{\&omega;}}}_d=2\mathrm{\&pi;}{\hat{f}}_d{T}_s$ ( Be Doppler frequency f in to received signal _dEstimation); Be the estimation of phase to received signal.

I, Q branch road integration-remover in related interval end output result are:

$\left\{\begin{array}{c}{I}_{\mathrm{ps}}\left(k\right)\&ap;A\&CenterDot;R\left[\mathrm{\&epsiv;}\left(k\right)\right]\&CenterDot;\sin c[\mathrm{\&Delta;}{\mathrm{\&omega;}}_d\left(k\right)\&CenterDot;N/2]\cos {\mathrm{\&theta;}}_k+n_I\left(k\right)\\ Q_{\mathrm{ps}}\left(k\right)\&ap;A\&CenterDot;R\left[\mathrm{\&epsiv;}\left(k\right)\right]\&CenterDot;\sin c[\mathrm{\&Delta;}{\mathrm{\&omega;}}_d\left(k\right)\&CenterDot;N/2]\sin {\mathrm{\&theta;}}_k+n_Q\left(k\right)\end{array}\right.---\left(3\right)$

In the formula (3): A is a signal amplitude; Δ ω _d(k) estimate residual error for Doppler shift, $\mathrm{\&Delta;}{\mathrm{\&omega;}}_d\left(k\right)={\mathrm{\&omega;}}_d\left(k\right)-{\widehat{\mathrm{\&omega;}}}_d\left(k\right);$ ε (k) is code phase (time-delay) estimated bias (truly delays time and estimate to delay time poor), ε (k)=Δ τ; R () is two desirable level autocorrelation functions of pseudo-random code, is the function of time; N is that the integration of integration remover is counted; θ _kBe carrier phase error, θ _k=kN Δ w _d(k)-Δ w _d(k) N/2+ Δ φ; n _I(k), n _Q(k) be random noise.Formula (3) is very important, is the foundation of carrying out frequency tracking error estimation, cross product frequency discrimination and arc tangent phase demodulation algorithm.

The frequency judgement adopts expression formula as follows:

$\mathrm{\&Delta;}{f}_k=\frac{1}{T_{\mathrm{ID}}}[I(k-1)Q\left(k\right)-I\left(k\right)Q(k-1)]---\left(4\right)$

In the formula (4), T _IDBe the integration checkout time.

In with four phase frequency discriminator frequency pulling processes, adopt Δ f _kJudge that whether current frequency is less than 10Hz.If current frequency Δ f _kLess than 10Hz, then change the FLL tracking loop over to and carry out frequency-tracking; Otherwise, continue the frequency pulling process.

When following the tracks of beginning, need frequency be drawn to below the 10Hz from the hundreds of hertz with the frequency pulling module, then according to carrier phase θ _kAdjudicate.If θ _kGreater than 10 °, receiver carries out frequency-tracking with the cross product frequency discriminator; If θ _kLess than 10 °, then adopt pure PLL ring to carry out Phase Tracking.

Phase place judgement expression formula is:

${\mathrm{\&eta;}}_k=\left|\frac{Q_s\left(k\right)}{I_s\left(k\right)}\right|=\left|\frac{\sin {\mathrm{\&theta;}}_k}{\cos {\mathrm{\&theta;}}_s}\right|=\left|\mathrm{tg}{\mathrm{\&theta;}}_k\right|---\left(5\right)$

Work as θ in the following formula _kWhen very little, tg θ _kWith θ _kBe directly proportional.If θ _kIn the time of＜10 °, change phaselocked loop over to and follow the tracks of, θ _kBring following formula into for=10 °, obtain phase place decision threshold η _k=0.176.

3, four phase frequency discriminators are realized frequency pulling

Behind the acquiring pseudo code, the carrier doppler frequency swing is directed into a Doppler frequency search unit scope, i.e. 500Hz, and this moment, estimated frequency error was still very big, might exceed the linear following range of cross product frequency discriminator.Therefore, at first utilize the frequency pulling module that frequency pulling is arrived in the following range of cross product frequency discriminator.

The present invention adopts four phase frequency discriminators to carry out the frequency pulling algorithm: four phase frequency discriminator computing method are simple, and operand is little, but need repeatedly traction just can finish frequency pulling below 10Hz.In the frequency pulling process, adopt Δ f _kWhether judge current frequency less than 10Hz, if current frequency Δ f _kLess than 10Hz, then change the FLL tracking loop over to and carry out the high-frequency tracking; Otherwise, continue the frequency pulling process.

4, cross product frequency discrimination automatic frequency tracking (CP-AFC) locking ring (FLL)

When four phase frequency discriminators will bigger frequency error be drawn within certain scope, just can realize accurate frequency-tracking with the cross product frequency discriminator.FLL produces suitable frequency with the restituted signal carrier wave by carrier wave NCO, and is insensitive to 180 ° of counter-rotatings of in-phase signal phase place, therefore when the signal initial acquisition, realizes frequency lock than realizing that phase locking is easy.The present invention adopts cross product automatic frequency tracking algorithm (CP-AFC) to realize the FLL frequency discriminator.With respect to other algorithm, this algorithm performance when low signal-to-noise ratio is approaching best.

When frequency error during, adopt the cross product frequency discriminator to realize accurate frequency-tracking less than 10Hz.Cross product automatic frequency tracking ring schematic diagram 4.Wherein, T is the integration interval time of integration-remover.

Cross product frequency discriminator output e _FkFor:

e _fk＝I(k-1)Q(k)-I(k)Q(k-1)

＝0.25A ²D(k)D(k-1)R[ε(k)][ε(k-1)] (6)

·sinc[Δf _d(k)·πT]·sinc[Δf _d(k-1)·πT]·sin(φ _k-φ _k-1)

In the formula (6): T is the integration checkout time.Owing to catch when finishing, will receive pseudo-code and local pseudo-code is alignd substantially, establishing the time interval is the unit interval, modulating data invariant position in the measurement process continuously is so have D (k) D (k-1)=1, R[ε (k)] and ≈ 1, R[ε (k-1)] ≈ 1, φ _k=Δ f _d(k) t+ φ ₀, φ _k-φ _K-1=[Δ f _d(k)-Δ f _d(k-1)] T=Δ f _dT; When frequency pulling is finished, Doppler shift evaluated error Δ f _d＜10 °/Hz, phase error | Δ f _d(k) π T|＜＜during pi/2, sinc ²[Δ f _d(k) π T] → 1, sin (φ _k-φ _K-1) → φ _k-φ _K-1So the phase change (frequency) in controlled quentity controlled variable and unit interval is directly proportional, control the purpose that carrier wave NCO reaches frequency-tracking through wave filter with this.

The cross product frequency discriminator is output as

e _fk＝θ _k-θ _k-1＝2πΔf _d(k)·T (7)

Cross product frequency discriminator kam-frequency characteristic as shown in Figure 5.

As can be seen, in error hour, e _FkWith Doppler shift angular frequency evaluated error Δ f _dBe directly proportional.Owing to exist and code phase error ε (k) and Doppler shift evaluated error Δ f _dRelevant item, the gain of frequency discriminator has been subjected to influence to a certain degree.For carrier phase tracking, second-order F LL encircles and can follow the tracks of phase place and the frequency change rate that all even uniform acceleration produces with zero steady-state error, follows the tracks of the derivative of the frequency change rate of carrier acceleration generation with steady-state error.

5, Phase Tracking locking ring (PLL)

Inphase quadrature phaselocked loop (Costas ring) is a kind of of PLL, because it is insensitive and obtained widespread usage in PSK despreading receiver to carrier modulation data.Section's Stas ring phase detector algorithm commonly used is a two quadrant arc tangent phase demodulation algorithm:

$e_{\mathrm{pk}}={\tan }^{-1}(Q_{\mathrm{ps}}/I_{\mathrm{ps}})$

$={\tan }^{-1}\left(\frac{0.5A\&CenterDot;R\left[\mathrm{\&epsiv;}\left(k\right)\right]\&CenterDot;\sin c[\mathrm{\&Delta;}{f}_d\left(k\right)\&CenterDot;\mathrm{\&pi;T}]\&CenterDot;\sin {\mathrm{\&phi;}}_k}{0.5A\&CenterDot;R\left[\mathrm{\&epsiv;}\left(k\right)\right]\&CenterDot;\sin c[\mathrm{\&Delta;}{f}_d\left(k\right)\&CenterDot;\mathrm{\&pi;T}]\&CenterDot;\cos {\mathrm{\&phi;}}_k}\right)={\mathrm{\&phi;}}_k---\left(8\right)$

Two quadrant arc tangent phase detector tan ^-1(Q _Ps/ I _Ps) performance is linear, best performance in whole-90 °～90 ° scopes.The phase detector output signal is relevant with sign indicating number delay time error and Doppler shift evaluated error.Because receiver adopts independently code tracking loop and carrier tracking loop, the carrier wave ring closes at that the sign indicating number ring is relevant take place after, so code phase has been aligned in the scope of allowing, and is little to the carrier track influence.The Doppler shift evaluated error is in the doppler searching unit scope, might be bigger, this moment section Stas ring phase demodulation function amplitude fading, phase characteristic is affected, directly catching or follow the tracks of phase place is the comparison difficulty.When receiver is drawn to estimated frequency error in the acceptable scope by four phase frequency discriminators, the cross product frequency discriminator makes carrier tracking loop reach stable tracking mode, employing section Stas ring carrier phase tracking pattern.Section's Stas ring is the same as the dynamic sensitivity with general PLL, but can produce the observed quantity of the most accurate pseudorange rate of change.For given signal power, section's Stas ring also provides the data demodulates lower than FLL bit error rate.

6, the loop filter of FLL FLL and phase-locked loop pll

The selection of loop filter will be considered two kinds of factors: filter order and noise bandwidth, the selection of these two parameters are directly determining the dynamic response of loop to input signal.Single order track loop (loop filter is 0 rank) can be followed the tracks of the phase step input, and does not have steady state phase error, but when the tracking frequencies step is imported, just has steady state phase error; Desirable second order track loop (loop filter is 1 rank) can be followed the tracks of phase step and frequency step signal, and not have steady-state error, but when tracking frequencies oblique ascension signal is imported, just be had the steady track error; Three rank track loop (loop filter is 2 rank) can correctly be followed the tracks of phase step, frequency step and frequency oblique ascension signal, and do not have steady-state error.FLL is with respect to phaselocked loop, and is better to dynamic stress.For tackle same dynamically, the exponent number of FLL can be than the exponent number of phaselocked loop low single order.So carrier track FLL (second order loop) adopts single order Jaffe-Rechtin wave filter, carrier track phaselocked loop (third order PLL) adopts second order Jaffe-Rechtin wave filter.

Sum up the tracking error of carrier tracking loop FLL and PLL at last, be mainly derived from:

1. signal Doppler dynamic stress: the acceleration of relative motion (second derivative of Doppler shift amount) causes;

2. the thermonoise of loop trembles error: dynamically relevant with loop bandwidth with the signal carrier-to-noise ratio;

3. the random drift of frequency marking: relevant with the Allan variance of local frequency marking, general influence factor very I to ignore.

In sum, the carrier tracking loop line structure (Fig. 6) that constitutes of three rank PLL phaselocked loops of the second-order F LL automatic frequency tracking ring of the frequency pulling of four phase phase demodulations+cross product frequency discrimination+two quadrant arc tangent phase demodulation can satisfy the demand of general high dynamic task; Well-designed single order, second order Jaffe-Rechtin loop filter parameters can obtain higher carrier frequency/carrier phase tracking precision.

(2) high dynamically frequency spreading tracking loop

1, the design concept of frequency spreading tracking loop algorithm

After FFT frequency domain parallel search was caught rough carrier frequency and pseudo-code phase, the spreading code of local regeneration spreading code and received signal was finished thick alignment, and error is within 1/2 chip.Subsequently, entrance code tracing process (corresponding with carrier track) realizes accurately aligning of spreading code phase place (delay).Therefore, code tracking loop and carrier track ring structure, algorithm and design have homoorganicity.

The closed loop of pseudo-code is followed the tracks of and is adopted delay phase-locked loop usually, utilize promptly that the local code generator produces that phase place is leading, delay signal and with the spread-spectrum signal quadrature mixing of the BPSK/QPSK modulation of input after relevant, relatively homophase I/ quadrature Q two branch road results come control code NCO and the generation local code signal consistent with the input code phase place to obtain the code phase error signal.The present invention adopts in advance-lags behind incoherent track loop, and it does not need coherent carrier in the process of following the tracks of, and the carrier track state is not had dependence, and combination property is superior.The one-piece construction block diagram of code tracking loop as shown in Figure 6.

Pseudo-code phase of the present invention is followed the tracks of and has been adopted incoherent digital delay phase-locked loop (DDLL) algorithm structure (as shown in Figure 7), is made up of integration-remover, code phase discriminator, loop filter, sign indicating number NCO, regeneration code generator and shift register etc.Wherein the parameter of integration-remover, code phase discriminator and loop filter has determined the characteristic of code tracking loop.Narrow relevant in order to realize, reach the purpose of accurate tracking code phase, in loop design, produced the regeneration pseudo-code of instantaneous code, lead-lag 1/2 chip, lead-lag 1/4 chip, constituted relevant spacing respectively and be respectively 1 chip, 1/4 incoherent delay lock loop by shift register.In the code tracking loop, code phase discriminator compares the pre-detection integral result of homophase and quadrature branch, produces error signal, and by loop filter output code NCO frequency control word, control regeneration pseudo-code and reception pseudo-code are accurately alignd.

In the embodiment of the invention: the integration in the code tracking loop-remover adopts the structure identical with carrier tracking loop, and the pre-detection time also is 0.2ms, and promptly every 0.2ms integration adds up 12422 times.Integration-remover is discussed in the carrier tracking loop algorithm, and code tracking loop phase demodulation algorithm, code tracking loop path filter, the tracking of carrier wave auxiliary code ring are discussed below.

2, the sign indicating number ring Discr. phase demodulation algorithm of code tracking loop

Code phase discriminator produces the correlated error amount according to the correlation of homophase and quadrature branch, the performance of the type decided delay lock loop of delay lock loop, and what can produce the correlated error amount can be coherent code phase detector or non-coherent code phase detector.The code phase digital correlation leading, instant, that lag behind that sign indicating number ring Discr. is input as carrier wave homophase I/ quadrature Q branch road accumulates the result.

Sign indicating number ring discriminator algorithm commonly used has three kinds: dot product power Discr. (I _Es-I _Ls) I _Ps+ (Q _Es-Q _Ls) Q _Ps, deduct after-power Discr. (I in advance _Es ²+ Q _Es ²)-(I _Ls ²+ Q _Ls ²), deduct hysteresis envelope Discr. in advance

In essence, deduct after-power in advance and deduct two kinds of Discr.s of hysteresis envelope in advance identical DLL Discr. error performance is arranged, and it is bigger to deduct hysteresis envelope operand in advance, does not generally use and deducts hysteresis envelope Discr. in advance.

When the relevant generation of sign indicating number, loop carries out tracking mode, supposes relevant spacing d=2 δ, and the error signal that then subtracts the output of retarded type coherent code phase detector in advance is

E(k)＝I _e(k)-I _l(k) (9)

＝0.5Asinc[Δf _d(k)·πT]·cos[Δf _d(k)·t _k+φ ₀]·{R[ε(k)-δ]-R[ε(k)+δ]}

As can be seen, error signal has dependence to carrier track from formula (9), when carrier wave not synchronously or when cycle slip occurring after following the tracks of, phase detector will produce non-quantitative, so generally not adopt phase dry type phase detector.Incoherent type code phase discriminator mainly contains and subtracts after-power phase detector and dot product phase detector in advance.The invention provides two kinds of different delay lock loop discriminator algorithm: the normalized after-power Discr. that subtracts in advance; Normalized dot product Discr..

(1) subtracts the after-power phase detector in advance

$E_{\mathrm{el}}\left(k\right)=I_e^2\left(k\right)+Q_e^2\left(k\right)-I_l^2\left(k\right)-Q_l^2\left(k\right)$

$=0.25A^2\&CenterDot;{\sin c}^2[\mathrm{\&Delta;}{f}_d\left(k\right)\&CenterDot;\mathrm{\&pi;T}]\&CenterDot;\left\{R^2\right[\mathrm{\&epsiv;}\left(k\right)-\mathrm{\&delta;}]-R^2[\mathrm{\&epsiv;}\left(k\right)+\mathrm{\&delta;}\left]\right\}$

$=0.25A^2{\sin c}^2[\mathrm{\&Delta;}{f}_d\left(k\right)\&CenterDot;\mathrm{\&pi;T}]\&CenterDot;S_{\mathrm{el}}(\mathrm{\&epsiv;},\mathrm{\&delta;})---\left(10\right)$

In formula (10): I _Es(k), I _Ps(k) and I _Ls(k) be respectively the input in-phase signal with leading, instant, lag behind yard in relevant output; Q _Es(k), Q _Ps(k) and Q _Ls(k) be respectively input quadrature-phase and leading, instant, the sign indicating number that lags behind in relevant output, define and subtract after-power phase detector phase characteristic function S in advance _El(ε δ) is:

S _el(ε，δ)＝R ²[ε(k)-δ]-R ²[ε(k)+δ] (11)

When defining spreading code fully to punctual correlation and chip width T _cBeing 1 o'clock autocorrelation function can be expressed as:

$R\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{cc}0& (\mathrm{\&tau;}<-1)\\ 1+\mathrm{\&tau;}& (-1\&le;\mathrm{\&tau;}<0)\\ 1-\mathrm{\&tau;}& (0\&le;\mathrm{\&tau;}<1)\\ 0& (\mathrm{\&tau;}\&GreaterEqual;1)\end{array}\right.---\left(12\right)$

In formula (11) difference substitution formula (12), can be subtracted the phase characteristic function of after-power phase detector in advance:

1. when δ=1/2

$S_{\mathrm{el}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1-\mathrm{\&delta;})\\ -{(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (-1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ 4\mathrm{\&epsiv;}(1+\mathrm{\&delta;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1-\mathrm{\&delta;})\\ {(1-\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1+\mathrm{\&delta;})\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1+\mathrm{\&delta;})\end{array}\right.---\left(13\right)$

2. when δ=1/8 or δ=1/16

$S_{\mathrm{el}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1-\mathrm{\&delta;})\\ -{(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (-1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ -4\mathrm{\&delta;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-\mathrm{\&delta;})\\ 4\mathrm{\&epsiv;}(1-\mathrm{\&delta;})& (-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<+\mathrm{\&delta;})\\ 4\mathrm{\&delta;}(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1-\mathrm{\&delta;})\\ {(1-\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1+\mathrm{\&delta;})\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1+\mathrm{\&delta;})\end{array}\right.---\left(14\right)$

(2) dot product phase detector

E _dp(k)＝[I _e(k)-I _l(k)]I _ps(k)+[Q _e(k)-Q _l(k)]Q _ps(k)

＝0.25A ²{R[ε(k)-δ]-R[ε(k)+δ]}·R[ε(k)]·sinc ²[Δf _d(k)·πT] (15)

＝0.25A ²sinc ²[Δf _d(k)·πT]·S _dp(ε，δ)

In formula (15): I _Es(k), I _Ps(k) and I _Ls(k) be respectively the input in-phase signal with leading, instant, lag behind yard in relevant output; Q _Es(k), Q _Ps(k) and Q _Ls(k) be respectively input quadrature digital signal and advanced code, instantaneous code, hysteresis sign indicating number in the output of digital correlation accumulation result behind phase place rotation result.Definition dot product phase detector phase characteristic function S _Dp(ε δ) is:

S _dp(ε，δ)＝{R[ε(k)-δ]-R[ε(k)+δ]}·R[ε(k)] (16)

1. when δ=1/2

$S_{\mathrm{dp}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1)\\ -(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})(1+\mathrm{\&epsiv;})& (-1\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ 2\mathrm{\&epsiv;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<0)\\ 2\mathrm{\&epsiv;}(1-\mathrm{\&epsiv;})& (0\&le;\mathrm{\&epsiv;}<\mathrm{\&delta;})\\ (1-\mathrm{\&epsiv;}+\mathrm{\&delta;})(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1)\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1)\end{array}\right.---\left(17\right)$

2. when δ=1/8 or δ=1/16

$S_{\mathrm{dp}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1)\\ -(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})(1+\mathrm{\&epsiv;})& (-1\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ -2\mathrm{\&delta;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;-\mathrm{\&delta;})\\ 2\mathrm{\&epsiv;}(1+\mathrm{\&epsiv;})& (-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;0)\\ 2\mathrm{\&epsiv;}(1-\mathrm{\&epsiv;})& (0\&le;\mathrm{\&epsiv;}\&le;\mathrm{\&delta;})\\ 2\mathrm{\&delta;}(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;1-\mathrm{\&delta;})\\ (1-\mathrm{\&epsiv;}+\mathrm{\&delta;})(1-\mathrm{\&epsiv;})& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;1)\\ 0& (\mathrm{\&epsiv;}>1)\end{array}\right.---\left(18\right)$

In an embodiment: use I _Ps ²+ Q _Ps ²(instantaneous code phase place constantly power) is respectively to subtracting the after-power phase detector in advance and the dot product phase detector carries out normalized, it has eliminated the influence that signal amplitude and carrier track bring by normalization, suppress noise effectively and reduced the impulse disturbances influence, constant phase detector phase demodulation gain is provided, has avoided after the digital correlation accumulation, increasing an AGC controller again.

The phase characteristic curve of Fig. 8 (a) expression subtracting in advance after-power phase detector, as can be seen from the figure, in subtracting the after-power phase detector in advance, along with reducing of related interval, the range of linearity of phase characteristic curve diminishes, the gain of phase detector (the phase characteristic curve is at the slope at place at zero point) becomes big, and it shows that subtracting the after-power phase detector in advance has narrow relevant advantage.The phase characteristic curve of Fig. 8 (b) expression dot product phase detector, as can be seen from the figure, in the dot product phase detector, along with reducing of related interval, the range of linearity of phase characteristic curve diminishes, but the phase characteristic curve of phase detector does not take place obviously to improve.

Studies show that narrow correlation tracking can improve the tracking accuracy of pseudo-code tracing ring.The normalized after-power phase detector that subtracts in advance has the advantage that is suitable for narrow relevant spacing, the big and discriminator sensitivity of its gain is than higher, but gain is less when code phase is big, is applicable to that therefore narrow correlation tracking and the lead-lag code interval minimum interval situation more than 0.05 chip is followed the tracks of and be applicable to the high sensitivity in code tracking loop tracking later stage.The pseudo-code delay lock loop that is 1/4,1/8 chip to relevant spacing adopts the normalized after-power dot product phase detector that subtracts in advance.Consider to deduct in advance the after-power Discr. when identical d value, thermonoise vibration error is greater than dot product power Discr., and dot product power Discr. is applicable to the situation (simultaneously dot product power Discr. operand less) of lead-lag sign indicating number minimum interval more than 0.1 chip.Therefore comprehensive comparative analysis is thought: dot product phase detector operand is compared lessly with subtracting the after-power phase detector in advance, relatively is suitable as at the phase demodulation algorithm of code tracking during the initial stage; When high precision code tracking subsequently, employing subtracts the after-power phase detector in advance and carries out narrow relevant phase demodulation algorithm.Studies show that the influence of adopting narrow correlation technique can alleviate multipath effect effectively.

NovAtel company is to the C/A code tracking of GPS the time, adopted spacing from 1 chip to the variable correlator bank of 0.05 chip, and adopt the normalized after-power phase detector that subtracts in advance when narrow related interval, C/A code tracking noiseproof feature is better than 10cm (1 σ), has reached the tracking accuracy of P sign indicating number.

3, design of the loop filter of code tracking loop and error analysis

When system works under high dynamic environment, will there be dynamic tracking error in code tracking loop.Because Doppler's composition of sign indicating number clock frequency becomes the fixed proportion relation with the carrier doppler frequency, therefore designing carrier tracking loop, that code tracking loop is carried out carrier wave is auxiliary, can the blanking code tracking loop dynamically most of, the dynamic tracking error of code tracking loop can be ignored in design.Because adopted the auxiliary of carrier wave ring in to code tracking, code tracking loop adopts second-order loop filter.Filtering algorithm of the present invention is selected second order Jaffe-Rechtin wave filter.

Dynamic and the thermal noise performance of following analysis code track loop.

1. loop dynamic performance

The dynamic measurement error of code tracking loop is by the exponent number and the bandwidth decision of loop filter, and for second order code tracking loop path filter, its dynamic measurement error is

${\mathrm{\&sigma;}}_e=\frac{d^{2}R/\mathrm{<figure-callout\; id="2"\; label="d\; t"\; filenames="HSA00000010858100052.png,HSA00000010858100061.png"\; state="\{\{state\}\}">d</figure-callout>}{t}^{}{}^2}{{\mathrm{\&omega;}}_n^2}---\left(19\right)$

In the formula (19): R is a unit with basic number of chips, loop natural frequency ω _n=1.89B _n, (B _nBe loop bandwidth).

Under normal conditions, the dynamic acceleration of carrier causes dynamic tracking error in the sign indicating number ring, but owing to exist fixing proportionate relationship between sign indicating number Doppler and the carrier doppler, when the carrier wave ring dynamically carries out accurate tracking to carrier, auxiliary by carrier wave, the most of dynamic error in can the blanking code ring, therefore, the physical presence dynamic error is very little in the sign indicating number ring, can not consider.

2. thermonoise trembles error (1 σ)

The thermal noise error that subtracts the after-power phase detector in advance is:

${\mathrm{\&sigma;}}_{\mathrm{nEL}}=\sqrt{\frac{B_{n}d}{2(C/N_0)}[1+\frac{2}{(2-d)(C/N_0)T}]}---\left(20\right)$

The thermal noise error of dot product phase detector is:

${\mathrm{\&sigma;}}_{\mathrm{nDP}}=\sqrt{\frac{B_{n}d}{2(C/N_0)}[1+\frac{1}{(C/N_0)T}]}---\left(21\right)$

In formula (20) and formula (21): B _nBe loop equivalent noise bandwidth (Hz) that d is a lead and lag sign indicating number related interval (chip), T is pre-detection integral time (s), C/N ₀For carrier to noise power ratio (is worked as C/N ₀When being unit representation with dB, it equals

According to formula (20) and formula (21) and Fig. 9 as can be known: code tracking loop design parameter (lead and lag sign indicating number related interval d, pre-detection T integral time, loop bandwidth B _n) give regularly carrier-to-noise ratio C/N ₀Big more, sign indicating number ring thermonoise variance is more little, tracking accuracy is high more.Under the prerequisite that satisfies sign indicating number gyration attitude tracking performance, B _nThe smaller the better recommendation is between 1/20Hz～1/10Hz.From the theoretical analysis of this section as can be known, (carrier-to-noise ratio C/N under the large-signal dynamic condition ₀Wide variation) and under Doppler's dynamic condition (relative motion changes violent), to loop bandwidth B _nRequirement be contradiction, narrow loop bandwidth helps eliminating the former influence (suppress thermonoise vibration error), wide loop bandwidth helps eliminating latter's influence (inhibition tracking error), measured result has also reflected this rule.

4, carrier wave auxiliary code ring is followed the tracks of the compensating for doppler dynamic error

Carrier tracking loop provides a carrier wave the auxiliary spread-spectrum code rate variation that causes owing to Doppler effect with true tracking in order to control code NCO output frequency when the accurate tracking carrier phase changes.Because the wavelength of Doppler effect on the signal and signal is inversely proportional to, so define the auxiliary scale factor of a carrier wave: $\mathrm{\&mu;}=\frac{f_{\mathrm{code}}}{f_{\mathrm{RF}}},$ f _CodeBe spread-spectrum code rate nominal value, f _RFBe radio-frequency carrier frequency nominal value.

The spreading code bit rate variable quantity (spreading code Doppler shift) that brings owing to dynamic motion is calculated by following formula:

${\hat{f}}_{d\_\mathrm{code}}(k+1)=\mathrm{\&mu;}\&CenterDot;{\hat{f}}_d(k+1)---\left(22\right)$

In the formula (22):

Carrier doppler frequency estimation for the output of carrier loop wave filter;

Be spreading code Doppler shift estimated value.

Be scaled behind the frequency control word and the frequency offset control word P of code tracking loop ring _BiasAddition, the digital controlled oscillator NCO that feeds back to the pseudo-code delay lock loop together adjusts, and effectively reduces the influence of dynamic stress to the pseudo-code delay lock loop, thereby improves the performance of dynamic tracking and the tracking accuracy of code tracking loop.

Obtaining high-precision carrier doppler frequency displacement estimated value has great importance, can be used in carrier wave ring that precision tests the speed, continuous carrier phase observation, integrated Doppler measurement, carrier wave auxiliary code ring followed the tracks of acquisition precision distance measurement, design arrowband and the signal dynamics that the sign indicating number ring wave filter suppresses carrier-to-noise ratio variation on a large scale, a tracking accuracy that improves carrier wave ring and sign indicating number ring, reduction losing lock probability, improve loop signal to noise ratio and receiver sensitivity, or the like.Particularly can be used for secondary encryption frame hopping directly catch, be used to happen suddenly spread spectrum system and spread spectrum range finding/non-spread spectrum number and pass the extrapolation forecast of the carrier doppler and the code phase of multipling channel system, or the like, for some gordian technique of air fleet link provides solution.

Claims (1)

1. the precision tracking of a high dynamic signal of air fleet link and measuring method, it is to realize on the digital signal processor DSP of circuit board and FPGA; It is characterized in that: this method is specific as follows:

(1) high dynamic carrier track loop

This high dynamic carrier track loop unit, adopt the dynamic carrier track strategy of suitable carrier, promptly undertaken by the FFT frequency domain algorithm after pseudo-code phase catches, adopt four phase frequency discriminators further to draw and catch Doppler frequency, the initial tracking, Doppler frequency is dropped to several hertz from the hundreds of hertz, make it to enter the working range of cross product automatic frequency tracking ring; Adopt the strong FLL ring of dynamic capability to eliminate dynamic, steady track; Adopt the little costas PLL of thermal noise error to improve carrier phase; Specific as follows:

[1] integration-remover and frequency, phase place decision algorithm

If sample frequency is T _sBe sampling interval, the received signal down coversion after if sampling obtain:

S(i)＝A _i·PN _I(i·T _s-τ)·cos[(ω _I+ω _d)i+φ]+A _i·PN _Q(i·T _s-τ)·sin[(ω _I+ω _d)i+φ](1)

In the formula (1): ω _I=2 π f _IT _sBe the received signal IF-FRE; ω _d=2 π f _dT _sBe Doppler frequency; φ is a phase of received signal; PN _I(iT _s); PN _Q(iT _s) be respectively homophase pseudo-code and quadrature pseudo-code; τ is the received signal time-delay;

If the in-phase signal and the orthogonal signal of receiving cable carrier wave NCO output are respectively:

$\left\{\begin{array}{c}{I}_R\left(i\right)=A_R\&CenterDot;\cos [({\mathrm{\&omega;}}_I+\widehat{{\mathrm{\&omega;}}_d})i+\widehat{\mathrm{\&phi;}}]\\ Q_R\left(i\right)=-A_R\&CenterDot;\sin [({\mathrm{\&omega;}}_I+{\widehat{\mathrm{\&omega;}}}_d)i+\widehat{\mathrm{\&phi;}}]\end{array}\right.---\left(2\right)$

In the formula (2): A _RAmplitude for NCO output cosine and sine signal;

Wherein,

Be Doppler frequency f in to received signal _dEstimation; Be the estimation of phase to received signal;

I, Q branch road integration-remover in related interval end output result are:

$\left\{\begin{array}{c}{I}_{\mathrm{ps}}\left(k\right)\&ap;A\&CenterDot;R\left[\mathrm{\&epsiv;}\left(k\right)\right]\&CenterDot;\sin c[\mathrm{\&Delta;}{\mathrm{\&omega;}}_d\left(k\right)\&CenterDot;N/2]\cos {\mathrm{\&theta;}}_k+n_I\left(k\right)\\ Q_{\mathrm{ps}}\left(k\right)\&ap;A\&CenterDot;R\left[\mathrm{\&epsiv;}\left(k\right)\right]\&CenterDot;\sin c[\mathrm{\&Delta;}{\mathrm{\&omega;}}_d\left(k\right)\&CenterDot;N/2]\sin {\mathrm{\&theta;}}_k+n_Q\left(k\right)\end{array}\right.---\left(3\right)$

In the formula (3): A is a signal amplitude; Δ ω _d(k) estimate residual error for Doppler shift,

ε (k) is the code phase estimated bias---truly delay time and estimate to delay time poor, ε (k)=Δ τ; R () is two desirable level autocorrelation functions of pseudo-random code, is the function of time; N is that the integration of integration remover is counted; θ _kBe carrier phase error, θ _k=kN Δ w _d(k)-Δ w _d(k) N/2+ Δ φ; n _I(k), n _Q(k) be random noise;

The frequency judgement adopts expression formula as follows:

$\mathrm{\&Delta;}{f}_k=\frac{1}{T_{\mathrm{ID}}}[I(k-1)Q\left(k\right)-I\left(k\right)Q(k-1)]---\left(4\right)$

In the formula (4), T _IDBe the integration checkout time;

In with four phase frequency discriminator frequency pulling processes, adopt Δ f _kJudge that whether current frequency is less than 10Hz; If current frequency Δ f _kLess than 10Hz, then change the FLL tracking loop over to and carry out frequency-tracking; Otherwise, continue the frequency pulling process;

When following the tracks of beginning, need frequency be drawn to below the 10Hz from the hundreds of hertz with the frequency pulling module, then according to carrier phase θ _kAdjudicate; If θ _kGreater than 10 °, receiver carries out frequency-tracking with the cross product frequency discriminator; If θ _kLess than 10 °, then adopt pure PLL ring to carry out Phase Tracking;

Phase place judgement expression formula is:

${\mathrm{\&eta;}}_k=\left|\frac{Q_s\left(k\right)}{I_s\left(k\right)}\right|=\left|\frac{\sin {\mathrm{\&theta;}}_k}{\cos {\mathrm{\&theta;}}_k}\right|=\left|\mathrm{tg}{\mathrm{\&theta;}}_k\right|---\left(5\right)$

Work as θ in the following formula _kWhen very little, tg θ _kWith θ _kBe directly proportional; If θ _kIn the time of＜10 °, change phaselocked loop over to and follow the tracks of, θ _kBring following formula into for=10 °, obtain phase place decision threshold η _k=0.176;

[2] four phase frequency discriminators are realized frequency pulling

Behind the acquiring pseudo code, the carrier doppler frequency swing is directed into a Doppler frequency search unit scope, i.e. 500Hz, this moment, estimated frequency error was still very big, therefore, at first utilize the frequency pulling module with frequency pulling in the following range of cross product frequency discriminator; Adopt four phase frequency discriminators to carry out the frequency pulling algorithm, need after the repeatedly traction frequency pulling below 10Hz; In the frequency pulling process, adopt Δ f _kWhether judge current frequency less than 10Hz, if current frequency Δ f _kLess than 10Hz, then change the FLL tracking loop over to and carry out the high-frequency tracking; Otherwise, continue the frequency pulling process;

[3] cross product frequency discrimination automatic frequency tracking locking ring;

When frequency error during, adopt the cross product frequency discriminator to realize accurate frequency-tracking less than 10Hz; Wherein, T is the integration interval time of integration-remover;

Cross product frequency discriminator output e _FkFor:

e _fk＝I(k-1)Q(k)-I(k)Q(k-1)

＝0.25A ²D(k)D(k-1)R[ε(k)][ε(k-1)] (6)

·sin?c[Δf _d(k)·πT]·sinc[Δf _d(k-1)·πT]·sin(φ _k-φ _k-1)

In the formula (6): T is the integration checkout time; Owing to catch when finishing, will receive pseudo-code and local pseudo-code is alignd substantially, establishing the time interval is the unit interval, modulating data invariant position in the measurement process continuously is so have D (k) D (k-1)=1, R[ε (k)] and ≈ 1, R[ε (k-1)] ≈ 1, φ _k=Δ f _d(k) t+ φ ₀, φ _k-φ _K-1=[Δ f _d(k)-Δ f _d(k-1)] T=Δ f _dT; When frequency pulling is finished, Doppler shift evaluated error Δ f _d＜10 °/Hz, phase error | Δ f _d(k) π T|＜＜during pi/2, sin c ²[Δ f _d(k) π T] → 1, sin (φ _k-φ _K-1) → φ _k-φ _K-1So phase change in controlled quentity controlled variable and unit interval; Be directly proportional, control the purpose that carrier wave NCO reaches frequency-tracking through wave filter with this;

The cross product frequency discriminator is output as

e _fk＝φ _k-φ _k-1＝2πΔf _d(k)·T (7)

[4] Phase Tracking locking ring;

The inphase quadrature phaselocked loop, promptly section's Stas ring is a kind of of Phase Tracking locking ring, section's Stas ring phase detector algorithm commonly used is a two quadrant arc tangent phase demodulation algorithm:

$e_{\mathrm{pk}}={\tan }^{-1}(Q_{\mathrm{ps}}/I_{\mathrm{ps}})$

$={\tan }^{-1}\left(\frac{0.5A\&CenterDot;R\left[\mathrm{\&epsiv;}\left(k\right)\right]\&CenterDot;\sin c[\mathrm{\&Delta;}{f}_d\left(k\right)\&CenterDot;\mathrm{\&pi;T}]\&CenterDot;\sin {\mathrm{\&phi;}}_k}{0.5A\&CenterDot;R\left[\mathrm{\&epsiv;}\left(k\right)\right]\&CenterDot;\sin c[\mathrm{\&Delta;}{f}_d\left(k\right)\&CenterDot;\mathrm{\&pi;T}]\&CenterDot;\cos {\mathrm{\&phi;}}_k}\right)={\mathrm{\&phi;}}_k---\left(8\right)$

Two quadrant arc tangent phase detector tan ^-1(Q _Ps/ I _Ps) performance is linear, best performance in whole-90 °～90 ° scopes;

[5] loop filter of FLL FLL and phase-locked loop pll

The carrier track FLL adopts single order Jaffe-Rechtin wave filter, and the carrier track phaselocked loop adopts second order Jaffe-Rechtin wave filter;

To sum up, the carrier tracking loop line structure that three rank PLL phaselocked loops of the second-order F LL automatic frequency tracking ring ten two quadrant arc tangent phase demodulations of the frequency pulling of four phase phase demodulations+cross product frequency discrimination constitute can satisfy the demand of general high dynamic task; Well-designed single order, second order Jaffe-Rechtin loop filter parameters can obtain higher carrier frequency/carrier phase tracking precision;

(2) high dynamically frequency spreading tracking loop

After FFT frequency domain parallel search was caught rough carrier frequency and pseudo-code phase, the spreading code of local regeneration spreading code and received signal was finished thick alignment, and error is within 1/2 chip; Subsequently, the entrance code tracing process, realization spreading code phase place is accurately aimed at; The closed loop of pseudo-code is followed the tracks of and is adopted delay phase-locked loop usually, utilize promptly that the local code generator produces that phase place is leading, delay signal and with the spread-spectrum signal quadrature mixing of the BPSK/QPSK modulation of input after relevant, relatively homophase I/ quadrature Q two branch road results come control code NCO and the generation local code signal consistent with the input code phase place to obtain the code phase error signal;

Described pseudo-code phase is followed the tracks of and adopted incoherent digital delay phase-locked loop is the DDLL algorithm structure, is made up of integration-remover, code phase discriminator, loop filter, sign indicating number NCO, regeneration code generator and shift register; Wherein the parameter of integration-remover, code phase discriminator and loop filter has determined the characteristic of code tracking loop; Narrow relevant in order to realize, reach the purpose of accurate tracking code phase, in loop design, produced the regeneration pseudo-code of instantaneous code, lead-lag 1/2 chip, lead-lag 1/4 chip, constituted relevant spacing respectively and be respectively 1 chip, 1/4 incoherent delay lock loop by shift register; In the code tracking loop, code phase discriminator compares the pre-detection integral result of homophase and quadrature branch, produces error signal, and by loop filter output code NCO frequency control word, control regeneration pseudo-code and reception pseudo-code are accurately alignd; Describe code tracking loop phase demodulation algorithm, code tracking loop path filter, the tracking of carrier wave auxiliary code ring below in detail:

[1] the sign indicating number ring Discr. phase demodulation algorithm of code tracking loop

The code phase digital correlation leading, instant, that lag behind that sign indicating number ring Discr. is input as carrier wave homophase I/ quadrature Q branch road accumulates the result;

Sign indicating number ring discriminator algorithm commonly used has three kinds: dot product power Discr. (I _Es-I _Ls) I _Ps+ (Q _Es-Q _Ls) Q _Ps, deduct after-power Discr. (I in advance _Es ²+ Q _Es ²)-(I _Ls ²+ Q _Ls ²), deduct hysteresis envelope Discr. in advance

Generally do not use and deduct hysteresis envelope Discr. in advance;

When the relevant generation of sign indicating number, loop carries out tracking mode, supposes relevant spacing d=2 δ, and the error signal that then deducts the output of retarded type coherent code phase detector in advance is

E(k)＝I _e(k)-I _l(k)

(9)

＝0.5A?sinc[Δf _d(k)·πT]·cos[Δf _d(k)·t _k+φ ₀]·{R[ε(k)-δ]-R[ε(k)+δ]}

As can be seen, error signal has dependence to carrier track from formula (9), when carrier wave not synchronously or when cycle slip occurring after following the tracks of, phase detector will produce non-quantitative, so generally not adopt phase dry type phase detector; Incoherent type code phase discriminator mainly contains and subtracts after-power phase detector and dot product phase detector in advance; The invention provides two kinds of different delay lock loop discriminator algorithm: normalized after-power Discr., the normalized dot product Discr. of subtracting in advance;

1. subtract the after-power Discr. in advance

$E_{\mathrm{el}}\left(k\right)=I_e^2\left(k\right)+Q_e^2\left(k\right)-I_l^2\left(k\right)-Q_l^2\left(k\right)$

$=0.25A^2\&CenterDot;{\sin c}^2[\mathrm{\&Delta;}{f}_d\left(k\right)\&CenterDot;\mathrm{\&pi;T}]\&CenterDot;\left\{R^2\right[\mathrm{\&epsiv;}\left(k\right)-\mathrm{\&delta;}]-R^2[\mathrm{\&epsiv;}\left(k\right)+\mathrm{\&delta;}\left]\right\}---\left(10\right)$

$=0.25A^2\sin c^2[\mathrm{\&Delta;}{f}_d\left(k\right)\&CenterDot;\mathrm{\&pi;T}]\&CenterDot;S_{\mathrm{el}}(\mathrm{\&epsiv;},\mathrm{\&delta;})$

In formula (10): I _Es(k), I _Ps(k) and I _Ls(k) be respectively the input in-phase signal with leading, instant, lag behind yard in relevant output; Q _Es(k), Q _Ps(k) and Q _Ls(k) be respectively input quadrature-phase and leading, instant, the sign indicating number that lags behind in relevant output, define and subtract after-power phase detector phase characteristic function S in advance _El(ε δ) is:

S _el(ε，δ)＝R ²[ε(k)-δ]-R ²[ε(k)+δ] (11)

When defining spreading code fully to punctual correlation and chip width T _cBeing 1 o'clock autocorrelation function can be expressed as:

$R\left(\mathrm{\&tau;}\right)=\left\{\begin{array}{cc}0& (\mathrm{\&tau;}<-1)\\ 1+\mathrm{\&tau;}& (-1\&le;\mathrm{\&tau;}<0)\\ 1-\mathrm{\&tau;}& (0\&le;\mathrm{\&tau;}<1)\\ 0& (\mathrm{\&tau;}\&GreaterEqual;1)\end{array}\right.---\left(12\right)$

In formula (11) difference substitution formula (12), can be deducted the phase characteristic function of after-power phase detector in advance:

(i) when δ=1/2

$S_{\mathrm{el}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1-\mathrm{\&delta;})\\ -{(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (-1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ 4\mathrm{\&epsiv;}(1+\mathrm{\&delta;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1-\mathrm{\&delta;})\\ {(1-\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1+\mathrm{\&delta;})\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1+\mathrm{\&delta;})\end{array}\right.---\left(13\right)$

(ii) when δ=1/8 or δ=1/16

$S_{\mathrm{el}}(\mathrm{\&epsiv;},\mathrm{\&delta;})\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1-\mathrm{\&delta;})\\ -{(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (-1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ -4\mathrm{\&delta;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<-\mathrm{\&delta;})\\ 4\mathrm{\&epsiv;}(1-\mathrm{\&delta;})& (-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<+\mathrm{\&delta;})\\ 4\mathrm{\&delta;}(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1-\mathrm{\&delta;})\\ {(1-\mathrm{\&epsiv;}+\mathrm{\&delta;})}^2& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1+\mathrm{\&delta;})\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1+\mathrm{\&delta;})\end{array}\right.---\left(14\right)$

2. dot product Discr.

E _dp(k)＝[I _e(k)-I _l(k)]I _ps(k)+[Q _e(k)-Q _l(k)]Q _ps(k)

＝0.25A ²{R[ε(k)-δ]-R[ε(k)+δ]}·R[ε(k)]·sinc ²[Δf _d(k)·πT] (15)

＝0.25A ²?sinc ²[Δf _d(k)·πT]·S _dp(ε，δ)

In formula (15): I _Es(k), I _Ps(k) and I _Ls(k) be respectively the input in-phase signal with leading, instant, lag behind yard in relevant output; Q _Es(k), Q _Ps(k) and Q _Ls(k) be respectively input quadrature digital signal and advanced code, instantaneous code, hysteresis sign indicating number in the output of digital correlation accumulation result behind phase place rotation result; Definition dot product phase detector phase characteristic function S _Dp(ε δ) is:

S _dp(ε，δ)＝{R[ε(k)-δ]-R[ε(k)+δ]}·R[ε(k)] (16)

(i) when δ=1/2

$S_{\mathrm{dp}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1)\\ -(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})(1+\mathrm{\&epsiv;})& (-1\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ 2\mathrm{\&epsiv;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<0)\\ 2\mathrm{\&epsiv;}(1-\mathrm{\&epsiv;})& (0\&le;\mathrm{\&epsiv;}<\mathrm{\&delta;})\\ (1-\mathrm{\&epsiv;}+\mathrm{\&delta;})(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}<1)\\ 0& (\mathrm{\&epsiv;}\&GreaterEqual;1)\end{array}\right.---\left(17\right)$

(ii) when δ=1/8 or δ=1/16

$S_{\mathrm{dp}}(\mathrm{\&epsiv;},\mathrm{\&delta;})=\left\{\begin{array}{cc}0& (\mathrm{\&epsiv;}<-1)\\ -(1+\mathrm{\&epsiv;}+\mathrm{\&delta;})(1+\mathrm{\&epsiv;})& (-1\&le;\mathrm{\&epsiv;}<-1+\mathrm{\&delta;})\\ -2\mathrm{\&delta;}(1+\mathrm{\&epsiv;})& (-1+\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;-\mathrm{\&delta;})\\ 2\mathrm{\&epsiv;}(1+\mathrm{\&epsiv;})& (-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;0)\\ 2\mathrm{\&epsiv;}(1-\mathrm{\&epsiv;})& (0\&le;\mathrm{\&epsiv;}\&le;\mathrm{\&delta;})\\ 2\mathrm{\&delta;}(1-\mathrm{\&epsiv;})& (\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;1-\mathrm{\&delta;})\\ (1-\mathrm{\&epsiv;}+\mathrm{\&delta;})(1-\mathrm{\&epsiv;})& (1-\mathrm{\&delta;}\&le;\mathrm{\&epsiv;}\&le;1)\\ 0& (\mathrm{\&epsiv;}>1)\end{array}\right.---\left(18\right)$

[2] loop filter of code tracking loop

Because adopted the auxiliary of carrier wave ring in to code tracking, code tracking loop adopts second-order loop filter; Filtering algorithm of the present invention is selected second order Jaffe-Rechtin wave filter;

Dynamic and the thermal noise performance of following analysis code track loop:

1. loop dynamic performance

The dynamic measurement error of code tracking loop is by the exponent number and the bandwidth decision of loop filter, and for second order code tracking loop path filter, its dynamic measurement error is

${\mathrm{\&sigma;}}_e=\frac{d^{2}R/{\mathrm{dt}}^2}{{\mathrm{\&omega;}}_n^2}---\left(19\right)$

In the formula (19): R is a unit with basic number of chips, loop natural frequency ω _n=1.89B _n, wherein, B _nBe loop bandwidth;

Under normal conditions, the dynamic acceleration of carrier causes dynamic tracking error in the sign indicating number ring, but owing to exist fixing proportionate relationship between sign indicating number Doppler and the carrier doppler, when the carrier wave ring dynamically carries out accurate tracking to carrier, auxiliary by carrier wave, the most of dynamic error in can the blanking code ring, therefore, the physical presence dynamic error is very little in the sign indicating number ring, can not consider;

2. thermonoise trembles error

The thermal noise error that subtracts the after-power phase detector in advance is:

${\mathrm{\&sigma;}}_{\mathrm{nEL}}=\sqrt{\frac{B_{n}d}{2(C/N_0)}[1+\frac{2}{(2-d)(C/N_0)T}]}---\left(20\right)$

The thermal noise error of dot product phase detector is:

${\mathrm{\&sigma;}}_{\mathrm{nDP}}=\sqrt{\frac{B_{n}d}{2(C/N_0)}[1+\frac{1}{(C/N_0)T}]}---\left(21\right)$

In formula (20) and formula (21): B _nBe the loop equivalent noise bandwidth, d is a lead and lag sign indicating number related interval, and T is pre-detection integral time, C/N ₀Be carrier to noise power ratio, wherein, work as C/N ₀When being unit representation with dB, it equals

[3] carrier wave auxiliary code ring is followed the tracks of the compensating for doppler dynamic error

Carrier tracking loop provides a carrier wave the auxiliary spread-spectrum code rate variation that causes owing to Doppler effect with true tracking in order to control code NCO output frequency when the accurate tracking carrier phase changes; Because the wavelength of Doppler effect on the signal and signal is inversely proportional to, so define the auxiliary scale factor of a carrier wave: f _CodeBe spread-spectrum code rate nominal value, f _RFBe radio-frequency carrier frequency nominal value;

Spreading code bit rate variable quantity---spreading code Doppler shift owing to dynamic motion brings, calculated by following formula:

${\hat{f}}_{d\_\mathrm{code}}(k+1)=\mathrm{\&mu;}\&CenterDot;{\hat{f}}_d(k+1)---\left(22\right)$

In the formula (22): Carrier doppler frequency estimation for the output of carrier loop wave filter;

Be spreading code Doppler shift estimated value;

Be scaled behind the frequency control word and the frequency offset control word P of code tracking loop ring _BiasAddition, the digital controlled oscillator NCO that feeds back to the pseudo-code delay lock loop together adjusts, and effectively reduces the influence of dynamic stress to the pseudo-code delay lock loop, thereby improves the performance of dynamic tracking and the tracking accuracy of code tracking loop.

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