CN101561484B - Method for acquiring pseudo code of GNSS signal - Google Patents

Abstract

The invention discloses a method for acquiring a pseudo code of a GNSS signal, which is mainly suitable for acquiring the code of a conventional ranging code signal in a GNSS receiver. The method comprehensive uses a Winograd Fourier transform algorithm, a prime factor algorithm PFA and a Cooley-Tukey FFT algorithm to perform discrete Fourier transform DFT and inverse discrete Fourier transform IDFT, thereby simplifying time domain-related algorithms by using a DFT and IDFT group calculation and completing the related acquisition of the pseudo code of the GNSS signal. The method of the invention belongs to a code parallel frequency domain acquisition method which has fast acquisition and is advantageous over the conventional time-domain acquisition method in software and hardware resource consumption; and meanwhile, due to the characteristic of the combination of the WFTA, PFA and Cooley-Tukey FFT algorithms, the method can perform the DFT and IDFT calculation of all sampling points ofthe sequence of the pseudo code and retains the related characteristics of the sequence of the pseudo code, thereby achieving an acquisition performance better than that of a classic double sampling- based fast Fourier transform FFT acquisition method.

Description

A kind of GNSS signal method for acquiring pseudo code

Technical field

The invention belongs to the satellite navigation field, be specifically related to a kind of GNSS signal method for acquiring pseudo code.

Background technology

Global navigation satellite positioning system (Global Navigation Satellite System, guide number SS) become one of the fastest information industry of global evolution, characteristics with global, round-the-clock, continuity and real-time can provide the location to the user, test the speed and service such as time service.Because GNSS is bringing into play crucial effects aspect military, civilian, be designed, build and use so more be under the jurisdiction of the subsystem of GNSS system.

Wherein, adopt the navigation message of two generations of the modern satellite navigation system of spread spectrum ranging code such as GPS, the Big Dipper, Galileo etc. pseudo-random code and carrier wave to be carried out twice modulation, form emission earthward continuously behind the radiowave with data mode.The user then intercepts and captures the satellite-signal in the visual field and then tries to achieve navigator fix information by receiver, and the communication infrastructure of system is spread spectrum communication, and this is the concise and to the point principle of work of modern satellite navigation system.

The top priority of GNSS receiver is the GNSS signal of catching and following the tracks of from satellite.The design of GNSS signal capture strategy is one of core content of receiver development with realization.Adopt the GNSS signal received power of spread spectrum ranging code little, so must be at first when receiving carry out the pseudo-code despreading of being correlated with to signal.Simultaneously, because the uncertainty of Doppler shift must be carried out two-dimensional search with fixing interval when therefore catching on code phase and frequency.Can be divided into again the two process of searching for respectively: the search strategy of pseudo-code serial carrier wave serial, parallel search strategy, the search strategy of the parallel carrier wave serial of pseudo-code, the parallel search strategy of the parallel carrier wave of pseudo-code of pseudo-code serial carrier wave.Capture time corresponding to various search strategies has nothing in common with each other, complete walk abreast fastest, and the speed of full serial is the slowest.

Traditional acquiring pseudo code mode adopts correlator or matched filter to finish related operation in time domain, and these two kinds of methods are used for the serial search of pseudo-code more; If realize the parallel search of pseudo-code with it, though can accelerate acquisition speed, need a plurality of correlators or matched filter concurrent operation, will expend a large amount of software and hardware resources.Method for acquiring pseudo code based on FFT utilizes the circumference correlation theorem, the frequency spectrum that converts the time domain correlation computations of received signal and local regeneration pseudo-code to the frequency domain calculating of multiplying each other, realize the pseudo-code parallel capture, also reduced software and hardware resources when significantly reducing capture time.At present the FFT method for acquiring pseudo code of open source information adopts modes such as zero padding method, linear interpolation, Sinc interpolation that sampled point is carried out secondary treating more, to obtain the sampled point of 2 integral number power, conveniently realizes the FFT computing.But after these modes of process were handled, the correlativity of pseudo-code sequence among the GNSS that weakened had weakened correlation peak, is unfavorable for catching of GNSS signal.

Summary of the invention

The present invention proposes a kind of GNSS signal acquisition methods.Be applicable to that mainly the sign indicating number of common ranging code signal is caught in the GNSS receiver.This method integrated use Winograd fourier transform algorithm (Winograd Fourier transformalgorithm, be called for short WFTA), using prime factor algorithm (prime factor FFT algorithm, be called for short PFA) and the Cooley-Tukey fft algorithm remove to carry out discrete Fourier transformation (Discrete Fourier Transform, be called for short DFT) and inverse discrete Fourier transform (Inverse Discrete Fourier Transform, be called for short IDFT) computing, thereby utilize DFT and IDFT grouped calculation to simplify time-domain related calculation, finish the pseudo-code correlation capturing of GNSS signal.The inventive method belongs to the parallel frequency domain catching method of pseudo-code, and acquisition speed is fast, and software and hardware resources consumption is better than traditional time domain catching method again; Simultaneously, because characteristics in conjunction with WFTA, PFA and Cooley-Tukey fft algorithm, can carry out DFT and IDFT computing to all sampled points of pseudo-code sequence, the correlation properties that better keep pseudo-code sequence, so its acquisition performance is better than typical Fast Fourier Transform (FFT) based on double sampling (Fast Fourier Transform is called for short FFT) catching method.

A kind of GNSS signal method for acquiring pseudo code of the present invention, this method may further comprise the steps:

Step 1: the baseband signal that has the carrier wave residual error enters first sampling thief, carries out sampling processing;

Step 2: first sampling thief is exported all sampled points and is entered a DFT transducer, and a DFT transducer is finished all DFT conversion of counting;

Step 3: output numerical value pointwise in multiplier of DFT transducer output numerical value and conjugate output circuit is multiplied each other;

Step 4: multiplier operation result input IDFT transducer, the IDFT transducer is finished all IDFT conversion of counting;

Step 5:IDFT transformation results input square transducer, square transducer carries out the pointwise square operation;

Step 6: the square value of each point input judgement comparer, judgement comparer are searched for wherein maximal value and are compared with detection threshold.If greater than thresholding, acquisition success then; Otherwise, catch failure, change search rate, return step 1, proceed acquiring pseudo code.

By WFTA, PFA and Cooley-Tukey fft algorithm combinatorial operation are realized when carrying out DFT and IDFT conversion in described step 2, the step 4.

Conjugate output circuit in the described step 3 can may further comprise the steps when producing conjugate:

Step a: the local code generator produces pseudo-code sequence;

Step b: second sampling thief carries out sampling processing to pseudo-code sequence;

Step c: second sampling thief is exported all sampled points and is entered the 2nd DFT transducer, and the 2nd DFT transducer is finished all DFT conversion of counting;

Steps d: the 2nd DFT transducer output valve carries out exporting after the complex conjugate conversion in getting conjugate circuit.

The complex conjugate transformation results of the conjugate output circuit in the described step 3 output is stored in the storer of local receiver after also but calculated off-line finishes, and calls through local receiver and to output in the multiplier.

DFT conversion among the described step c also is by WFTA, and PFA and Cooley-Tukey fft algorithm combinatorial operation are realized.

The invention has the advantages that:

(1) GNSS signal acquiring pseudo code is handled at frequency domain, utilize DFT and IDFT grouped calculation to simplify time-domain related calculation, increased substantially the relevant counting yield of multiple branch circuit in the GNSS receiver, help catching fast and recapturing of signal, be very suitable for feeble signal environment, interference environment and than the signal capture under the high dynamic environment;

(2) in conjunction with the characteristics of WFTA, PFA and Cooley-Tukey fft algorithm, all sampled points of pseudo-code sequence are carried out DFT and IDFT computing, better keep the correlation properties of pseudo-code sequence, improve acquisition performance.

Description of drawings

Fig. 1 is a kind of GNSS signal method for acquiring pseudo code schematic flow sheet of the present invention;

Fig. 2 is the schematic flow sheet that conjugate produces in a kind of GNSS signal method for acquiring pseudo code of the present invention;

Fig. 3 is 5000 DFT STRUCTURE DECOMPOSITION synoptic diagram in a kind of method for acquiring pseudo code embodiment of the present invention;

Fig. 4 is 5000 DFT calculation process synoptic diagram in a kind of method for acquiring pseudo code embodiment of the present invention;

Fig. 5 is C/A phase acquisition figure as a result in a kind of method for acquiring pseudo code embodiment of the present invention;

Fig. 6 catches figure as a result for gps signal two dimension in a kind of method for acquiring pseudo code embodiment of the present invention;

Fig. 7 carries out the relevant peaks comparison diagram that gps signal C/A sign indicating number is caught for five kinds of methods in a kind of method for acquiring pseudo code embodiment of the present invention.

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention is applicable to that mainly the GNSS receiver carries out acquiring pseudo code to the common ranging code signal of GNSS.Base band pseudo-code signal after the inventive method is at first handled the GNSS receiver is sampled, go to carry out DFT and IDFT computing at all sampled point integrated use Winograd fourier transform algorithms, using prime factor algorithm and Cooley-Tukey fft algorithm then, thereby utilize DFT and IDFT grouped calculation to simplify time-domain related calculation, finish the pseudo-code correlation capturing of GNSS signal.

As shown in Figure 1, this method may further comprise the steps:

Step 1: the baseband signal that has the carrier wave residual error enters first sampling thief, carries out sampling processing;

The GNSS signal forms digital medium-frequency signal and enters Capture Circle after the receiver radio frequency front-end processing, obtain existing the pseudo-code sequence of carrier wave residual error and noise after search rate in the Capture Circle and the digital medium-frequency signal mixing, the output valve s (n) that obtains sampling after first sampling thief is sampled to this pseudo-code sequence, output valve when s (n) is n sampled point; If the pseudo-code cycle is T _c, sample frequency is f _s, then the total sampling number N in each pseudo-code cycle is T _cf _s

Step 2: first sampling thief is exported all sampled points and is entered a DFT transducer, and a DFT transducer is finished all DFT conversion of counting.

The sampling number N of first sampling thief output is uncertain to be 2 integral number power, if FFT methods such as fired basis 2, base 4 need carry out sampling processing 2 times to sampled point, this can weaken the correlativity of former pseudo-code sequence.So in conjunction with the characteristics of WFTA, PFA and Cooley-Tukey fft algorithm, all sampled points of pseudo-code sequence are carried out DFT and IDFT computing among the present invention.

By digital signal processing rudimentary knowledge as can be known, k ∈ [0, N-1] the N point DFT to sampled point sequence s (n) is defined as follows:

$S\left(k\right)=\underset{n=0}{\overset{N-1}{\mathrm{\Σ}}}s\left(n\right)W_N^{\mathrm{nk}}---\left(1\right)$

Here k ∈ [0, N-1], wherein N is a positive integer, W _NFor containing the natural index of variable N, $W_N=e^{\frac{-j2\mathrm{\π}}{N}},$ $W_N^{\mathrm{nk}}={\left(W_N\right)}^{\mathrm{nk}}=e^{\frac{-j2\mathrm{\πnk}}{N}}.$

One dimension N point DFT can convert N to ₁* N ₂Two-dimentional DFT, N wherein ₁, N ₂Be positive integer.

Make N=N ₁N ₂, the index of Cooley-Tukey fft algorithm is mapped as:

The index mapping of n:

n＝N ₂n ₁+n ₂， $\left\{\begin{array}{c}0\≤n_1\≤N_1-1\\ 0{\≤n}_2\≤N_2-1\end{array}\right.---\left(2\right)$

The index mapping of k:

k＝k ₁+N ₁k ₂， $\left\{\begin{array}{c}0\≤k_1\≤N_1-1\\ 0\≤k_2\≤N_2-1\end{array}\right.---\left(3\right)$

N, n in the formula (2) ₁, n ₂For the time Domain Index, the n correspondence is carried out the time Domain Index of N point DFT, n ₁Correspondence is carried out N ₁The time Domain Index of point DFT, n ₂Correspondence is carried out N ₂The time Domain Index of point DFT; K, k in the formula (3) ₁, k ₂Be the frequency domain index, the k correspondence is carried out the frequency domain index of N point DFT, k ₁Correspondence is carried out N ₁The frequency domain index of point DFT, k ₂Correspondence is carried out N ₂The frequency domain index of point DFT.

N=N ₁N ₂The Cooley-Tukey FFT of point DFT is undertaken by following steps:

A. calculate the index conversion of list entries according to formula (2);

B. calculate N ₂Individual length is N ₁The DFT of point;

C. in the output of first conversion stage, use twiddle factor

Wherein $W_N^{n_2{k}_1}={\left(W_N\right)}^{n_2{k}_1};$

D. calculate N ₁Individual length is N ₂The DFT of point;

E. calculate the index conversion of output sequence according to (3).

The N after if N decomposes ₁, N ₂Two factors are relatively prime, then can use the PFA algorithm and carry out N point DFT computing.

The index mapping of n:

n＝(N ₂n ₁+N ₁n ₂)modN $\left\{\begin{array}{c}0\≤n_1\≤N_1-1\\ 0{\≤n}_2\≤N_2-1\end{array}\right.---\left(\text{4}\right)$

The index mapping of k:

$k=(N_2{<N_2^{-1}>}_{N_1}{k}_1+N_1{<N_1^{-1}>}_{N_2}{k}_2)\mathrm{mod}N$ $\left\{\begin{array}{c}0\&le;k_1\&le;N_1-1\\ 0\&le;k_2\&le;N_2-1\end{array}\right.---\left(5\right)$

Here, ${<N_2^{-1}>}_{N_1}=N_2^{\mathrm{\&phi;}\left(N_1\right)-1}\mathrm{mod}{N}_1,$ Promptly

To N ₁Delivery; Mod is a modulo operation, and φ is an Euler's function, φ (q)=S (p)=(p, q)=1, p≤q|p ∈ Z ⁺, φ (1)=1, i.e. φ (q) expression is for a positive integer q, less than q and and the number of the relatively prime positive integer of q.

N, n in the formula (4) ₁, n ₂For the time Domain Index, the n correspondence is carried out the time Domain Index of N point DFT, n ₁Correspondence is carried out N ₁The time Domain Index of point DFT, n ₂Correspondence is carried out N ₂The time Domain Index of point DFT; K, k in the formula (5) ₁, k ₂Be the frequency domain index, the k correspondence is carried out the frequency domain index of N point DFT, k ₁Correspondence is carried out N ₁The frequency domain index of point DFT, k ₂Correspondence is carried out N ₂The frequency domain index of point DFT.

Carry out N=N with the PFA algorithm ₁N ₂The DFT computing of point can be undertaken by following steps:

A. calculate the index conversion of list entries according to formula (4);

B. calculate N ₂Individual length is N ₁The DFT of point;

C. calculate N ₁Individual length is N ₂The DFT of point;

D. calculate the index conversion of output sequence according to (5).

The WFTA algorithm can be expressed as matrix form:

X＝ODIx (6)

Wherein, x is an input vector, and D is a diagonal matrix, and I and O are the matrixes that only contains plus and minus calculation, and X is the Fourier transform output valve of x.Winograd's N=2 has derived, the WFTA computing formula of 3,4,5,7,8,9,16 these 8 numbers, and by these formula, we can use minimum taking advantage of and add number of times and directly calculate corresponding DFT value of counting.

Therefore when calculating N point DFT, can earlier N be decomposed step by step, i.e. N=N ₁N ₂, N ₁=N ₃N ₄..., N _b=N _tN _T+1Wherein 2,3,4,5,7,8,9,16 DFT can calculate with the WFTA formula, wherein N ₁, N ₂, N ₃, N ₄N _b, N _t, N _T+1And b, t are positive integer; If relatively prime between the factor, then can use PFA and calculate; If not relatively prime between the factor, then use the Cooley-Tukey fft algorithm and calculate.

Step 3: output numerical value pointwise in multiplier of DFT transducer output numerical value and conjugate output circuit is multiplied each other.

Can carry out according to following steps when as shown in Figure 2, the conjugate output circuit produces conjugate here:

(1) the local code generator produces pseudo-code sequence;

(2) second sampling thiefs carry out sampling processing to pseudo-code sequence;

(3) second sampling thiefs are exported all sampled points and are entered the 2nd DFT transducer, and the 2nd DFT transducer is finished all DFT conversion of counting;

(4) the 2nd DFT transducer output valves carry out exporting after the complex conjugate conversion in getting conjugate circuit.

Because pseudo-code sequence and sample frequency are determined, the complex conjugate transformation results of the output of the conjugate output circuit is here also determined.So be stored in the storer of local receiver after also complex conjugate transformed value calculated off-line can being finished, and call through local receiver and to output in the multiplier.

Step 4: multiplier operation result input IDFT transducer, finish the IDFT conversion that all are counted;

Here the computing method of IDFT are identical with DFT computing method realization thinking in the step 2, also need integrated use WFTA, PFA, Cooley-Tukey fft algorithm.

According to the rudimentary knowledge of digital signal processing, the corresponding frequency domain of time domain convolution multiplies each other.Therefore can finish the related operation of time domain at frequency domain, promptly can by DFT and IDFT in groups computing finish the circular correlation of two signals.

Mathematical model is as follows: sampling thief output sequence s (n) with the related function of the sample sequence y (n) of local pseudo-code is:

$R_{\mathrm{sy}}\left(m\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}[s\left(n\right)\&times;y(n-m)]=\mathrm{IDFT}[S\left(k\right)\&times;\stackrel{\&OverBar;}{Y\left(k\right)}]---\left(7\right)$

In the formula (7), m, n are integer and 0≤m≤N-1,0≤n≤N-1, n-m sampled value in the local pseudo-code sample sequence of y (n-m) expression, S (k)=DFT[s (n)], Y (k)=DFT[y (n)], the complex conjugate of Y (k) expression Y (k).

Therefore, the IDFT processing through step 4 just can draw the correlation peak corresponding to each chip.

Step 5: IDFT transformation results input square transducer, carry out the pointwise square operation;

Step 6: the square value of each point input judgement comparer, judgement comparer are searched for wherein maximal value and are compared with detection threshold.If greater than thresholding, acquisition success then; Otherwise, catch failure, change search rate, return step 1, proceed acquiring pseudo code.

During acquisition success, the chip of peak-peak correspondence is the catch code phase place.

So that the thick catch code of L1 signal of GPS (Coarse/Acquisition sign indicating number,, be called for short the C/A sign indicating number) is captured as example, specific implementation method of the present invention is described below the embodiment 1.

Because the cycle of C/A sign indicating number is 1ms, make the sample frequency f of GPS receiver _sBe 5MHz, then in the C/A sign indicating number cycle of each GPS 5000 sampled points arranged.If the correlation integral cycle is 1 C/A sign indicating number cycle, then need to carry out DFT and IDFT in the inventive method step at 5000, the decomposition texture of 5000 DFT/IDFT is as shown in Figure 3.

Wherein, ground floor can be decomposed into 125 * 40 (N ₁=125, N ₂=40),, adopt Cooley-TukeyFFT to carry out 5000 DFT computing as formula (8).At first calculate the index conversion of list entries according to formula (2); Calculate 40 length again and be 125 DFT; Then in the output of first conversion stage, use twiddle factor

Calculate 125 length then and be 40 DFT; Last index conversion of calculating output sequence according to (3) formula.

$X(k_1,k_2)=\underset{n_2=0}{\overset{39}{\mathrm{\&Sigma;}}}\underset{n_1=0}{\overset{124}{\mathrm{\&Sigma;}}}\left(x(n_1,n_2)W_{125}^{n_1{k}_1}\right)W_{5000}^{n_2{k}_1}{W}_{40}^{n_2{k}_2}---\left(8\right)$

In the formula (8), twiddle factor $W_{125}^{n_1{k}_1}=e^{\frac{-j2\mathrm{\&pi;}{n}_1{k}_1}{125}},$ Twiddle factor $W_{5000}^{n_2{k}_1}=e^{\frac{-j2\mathrm{\&pi;}{n}_2{k}_1}{5000}},$ Twiddle factor $W_{40}^{n_2{k}_2}=e^{\frac{-j2\mathrm{\&pi;}{n}_2{k}_2}{40}}.$

So show as Fig. 3,125 DFT and 40 DFT of the second layer can be continued to be decomposed into 5 * 5 * 5 and 5 * 8.And then 125 DFT calculates by the Cooley-Tukey fft algorithm, and 5 DFT wherein finish according to the WFTA algorithm; Because 5,8 liang of numbers are relatively prime, so 40 DFT is by the PFA algorithm computation, as shown in Equation (9).Wherein 5 points, 8 DFT also can be according to the WFTA algorithm computation.

$X(k_1,k_2)=\underset{n_2=0}{\overset{7}{\mathrm{\&Sigma;}}}\underset{n_1=0}{\overset{4}{\mathrm{\&Sigma;}}}\left(x(n_1,n_2)W_5^{n_1{k}_1}\right)W_8^{n_2{k}_2}---\left(9\right)$

In the formula (9), twiddle factor $W_5^{n_1{k}_1}=e^{\frac{-j2\mathrm{\&pi;}{n}_1{k}_1}{5}},$ Twiddle factor $W_8^{n_2{k}_2}=e^{\frac{-j2\mathrm{\&pi;}{n}_2{k}_2}{8}}.$

To sum up, Fig. 4 has provided the calculation process of 5000 DFT.Receiver carries out the C/A sign indicating number when catching, and sampling thief is at first sampled to the baseband signal that has the carrier wave residual error, has 5000 sampled points in each 1ms signal; These 5000 sampled points enter the DFT transducer, finish the DFT computing according to Fig. 4 flow process; 5000 numerical value of DFT transducer output, 5000 numerical value pointwises in multiplier of yoke value output circuit output together multiply each other; Multiplied result is imported the IDFT transducer, finishes 5000 IDFT conversion according to Fig. 4 flow process; IDFT transformation results input square transducer, square transducer carries out the pointwise square operation; If the maximal value in each square value is greater than detection threshold, C/A sign indicating number acquisition success then; Otherwise the change search rate is handled the intermediate frequency signal mixing, repeats above step, proceeds the C/A sign indicating number and catches.Carry out according to this step, can conveniently finish the catching of L1 signal C/A sign indicating number of GPS.

GNSS signal acquiring pseudo code is handled at frequency domain, utilizes DFT and IDFT grouped calculation to simplify time-domain related calculation, has increased substantially the relevant counting yield of multiple branch circuit, helps catching fast and recapturing of signal.The present invention is in conjunction with the characteristics of WFTA, PFA and Cooley-Tukey fft algorithm, all sampled points to pseudo-code sequence carry out DFT and IDFT computing, with modes such as employing zero padding method, linear interpolation, Sinc interpolation sampled point being carried out secondary treating realizes comparing based on the catching method of FFT, better keep the correlation properties of pseudo-code sequence, improve acquisition performance.

Computer simulation program produces the L1 signal of GPS, is transformed to by RF on the intermediate frequency of 1.25MHz, and the sample frequency of receiving end is set to 5MHz, so in the C/A sign indicating number cycle of each GPS 5000 sampled points is arranged.It is 504 sampled points that the chip time-delay is set, and Doppler frequency deviation is 1907Hz, and the signal to noise ratio (S/N ratio) that arrives the intermediate-freuqncy signal of receiver is-15dB.

When application the inventive method was caught, accompanying drawing 5 was depicted as the correlated results in a C/A sign indicating number cycle, was that correlation peak appears in 504 sample point in the chip time-delay as seen.The inventive method completes successfully yard territory to accompanying drawing 6 and the frequency field two dimension is caught synoptic diagram in order to use.

We use zero padding method, linear interpolation method and sinc interpolation method double sampling to 4096 point respectively to 5000 sampled points in the 1ms, and respectively these 3 groups of new sequences are carried out finishing acquiring pseudo code based on the related operation of FFT.Average packet method and the inventive method of also using in this area are simultaneously carried out acquiring pseudo code.Accompanying drawing 7 has been described to use above-mentioned 5 kinds of methods and has been carried out the situation that sign indicating number is caught the relevant peaks that obtains.As can be seen from Figure 7,5 kinds of methods can both reach maximum relevant peaks at default coordinate.But the correlation peak maximum of the inventive method is of value to catching of signal most.

Claims (2)

1. GNSS signal method for acquiring pseudo code, this method may further comprise the steps:

Step 1: the baseband signal that has the carrier wave residual error enters first sampling thief, carries out sampling processing;

It is characterized in that,

Step 2: first sampling thief is exported all sampled points and is entered a DFT transducer, and a DFT transducer is finished all DFT conversion of counting;

Computing method integrated use WFTA, the PFA of DFT, Cooley-Tukey fft algorithm:

N point DFT to sampled point sequence s (n) is defined as follows:

$S\left(k\right)=\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}s\left(n\right)W_N^{\mathrm{nk}}---\left(1\right)$

Here k ∈ [0, N-1], wherein s (n) is the sampling output valve, and N is total hits, and N is a positive integer, W _NFor containing the natural index of variable N,

One dimension N point DFT converts N to ₁* N ₂Two-dimentional DFT, N wherein ₁, N ₂Be positive integer;

Make N=N ₁N ₂, the index of Cooley-Tukey fft algorithm is mapped as:

The index mapping of n:

n＝N ₂n ₁+n ₂， $\left\{\begin{array}{c}0\&le;n_1\&le;N_1-1\\ 0\&le;n_2\&le;N_2-1\end{array}\right.---\left(2\right)$

The index mapping of k:

k＝k ₁+N ₁k ₂， $\left\{\begin{array}{c}0\&le;k_1\&le;N_1-1\\ 0\&le;k_2\&le;N_2-1\end{array}\right.---\left(3\right)$

N, n in the formula (2) ₁, n ₂For the time Domain Index, the n correspondence is carried out the time Domain Index of N point DFT, n ₁Correspondence is carried out N ₁The time Domain Index of point DFT, n ₂Correspondence is carried out N ₂The time Domain Index of point DFT;

K, k in the formula (3) ₁, k ₂Be the frequency domain index, the k correspondence is carried out the frequency domain index of N point DFT, k ₁Correspondence is carried out N ₁The frequency domain index of point DFT, k ₂Correspondence is carried out N ₂The frequency domain index of point DFT;

N=N ₁N ₂The Cooley-Tukey FFT of point DFT is undertaken by following steps:

A. calculate the index conversion of list entries according to formula (2);

B. calculate N ₂Individual length is N ₁The DFT of point;

C. in the output of first conversion stage, use twiddle factor Wherein

D. calculate N ₁Individual length is N ₂The DFT of point;

E. calculate the index conversion of output sequence according to formula (3);

The N after if N decomposes ₁, N ₂Two factors are relatively prime, then use the PFA algorithm and carry out N point DFT computing;

The index mapping of n:

n＝(N ₂n ₁+N ₁n ₂)mod?N $\left\{\begin{array}{c}0\&le;n_1\&le;N_1-1\\ 0\&le;n_2\&le;N_2-1\end{array}\right.---\left(4\right)$

The index mapping of k:

$k=(N_2{\&lang;N_2^{-1}\&rang;}_{N_1}{k}_1+N_1{\&lang;N_1^{-1}\&rang;}_{N_2}{k}_2)\mathrm{mod}N\left\{\begin{array}{c}0\&le;k_1\&le;N_1-1\\ 0\&le;k_2\&le;N_2-1\end{array}\right.---\left(5\right)$

Here,

Promptly

To N ₁Delivery; Mod is a modulo operation, and φ is an Euler's function, φ (q)=S (p)=(p, q)=1, p≤q|p ∈ Z+}, φ (1)=1, i.e. φ (q) expression is for a positive integer q, less than q and and the number of the relatively prime positive integer of q;

N, n in the formula (4) ₁, n ₂For the time Domain Index, the n correspondence is carried out the time Domain Index of N point DFT, n ₁Correspondence is carried out N ₁The time Domain Index of point DFT, n ₂Correspondence is carried out N ₂The time Domain Index of point DFT;

K, k in the formula (5) ₁, k ₂Be the frequency domain index, the k correspondence is carried out the frequency domain index of N point DFT, k ₁Correspondence is carried out N ₁The frequency domain index of point DFT, k ₂Correspondence is carried out N ₂The frequency domain index of point DFT;

Carry out N=N with the PFA algorithm ₁N ₂The DFT computing of point is undertaken by following steps:

A. calculate the index conversion of list entries according to formula (4);

B. calculate N ₂Individual length is N ₁The DFT of point;

C. calculate N ₁Individual length is N ₂The DFT of point;

D. calculate the index conversion of output sequence according to formula (5);

The WFTA algorithm table is shown as matrix form:

X＝ODIx (6)

Wherein, x is an input vector, and D is a diagonal matrix, and I and O are the matrixes that only contains plus and minus calculation, and X is the Fourier transform output valve of x;

When calculating N point DFT, earlier N is decomposed step by step, i.e. N=N ₁N ₂, N ₁=N ₃N ₄... N _b=N _tN _T+1, wherein 2,3,4,5,7,8,9,16 DFT calculates with the WFTA formula, wherein N ₁, N ₂, N ₃, N ₄N _b, N _T+1And b, t are positive integer; If relatively prime between the factor, then use PFA and calculate; If not relatively prime between the factor, then use the Cooley-Tukey fft algorithm and calculate;

Step 3: output numerical value pointwise in multiplier of DFT transducer output numerical value and conjugate output circuit is multiplied each other; When producing conjugate, the conjugate output circuit carries out according to following steps:

(1) the local code generator produces pseudo-code sequence;

(2) second sampling thiefs carry out sampling processing to pseudo-code sequence;

(3) second sampling thiefs are exported all sampled points and are entered the 2nd DFT transducer, and the 2nd DFT transducer is finished all DFT conversion of counting; Wherein said DFT conversion also is integrated use WFTA, PFA, Cooley-TukeyFFT algorithm;

(4) the 2nd DFT transducer output valves carry out exporting after the complex conjugate conversion in getting conjugate circuit;

Step 4: multiplier operation result input IDFT transducer, finish the IDFT conversion that all are counted;

The method of calculating DFT in the computing method of IDFT and the step 2 is similar, also is integrated use WFTA, PFA, Cooley-Tukey fft algorithm;

IDFT through step 4 handles, and draws the correlation peak corresponding to each chip;

Step 5: IDFT transformation results input square transducer, carry out the pointwise square operation;

Step 6: the square value of each point input judgement comparer, judgement comparer are searched for wherein maximal value and are compared with detection threshold; If greater than thresholding, acquisition success then; Otherwise, catch failure, change search rate, return step 1, proceed acquiring pseudo code.

2. a kind of GNSS signal method for acquiring pseudo code according to claim 1, it is characterized in that: the complex conjugate transformation results for the conjugate output circuit in step 3 output also has a kind of disposal route: be stored in after calculated off-line finishes in the storer of local receiver, and call through local receiver and to output in the multiplier.

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