CN101984364A - GPS weak signal capturing method based on sequential probability ratio - Google Patents

Abstract

The invention relates to a GPS weak signal capturing method based on a sequential probability ratio. The method comprises the steps of: (1) performing parallel code domain planar search on a sampled and quantized intermediate frequency digital signal which is output by the front end of a receiver, (2) calculating a threshold value corresponding to different unrelated accumulation times under a preset condition of false-alarm probability, (3) calculating a probability density function contained in an assumed signal, (4) calculating a probability (5) that the assumed signal is more than the threshold value, ending the search stage, if a signal is captured, or repeating the step (3), (4), (5) if no signal is captured, and if the unrelated integral accumulation times M reaches to 100 but still no signal is fund, that means no signal exists, ending the capturing stage as well. The method of the invention can efficiently shorten the capturing time of strong signals, reduce the whole capturing time and increase the capturing property.

Description

Based on the GPS feeble signal catching method of sequential probability than detection

Technical field

The present invention relates to GPS (Global Position System, GPS) signal data process field, be specifically related to a kind of GPS feeble signal catching method based on SPRT (Sequential Probability Ratio Test, sequential probability is than detecting).

Background technology

For common GPS receiver, can only receive signal greater than-160dBW left and right sides power.When the carrier that carries the GPS receiver during in indoor, urban canyons, forest and High Earth Orbit operation, gps signal is blocked and is decayed, the satellite-signal that receiver receives and faint, and receiver " be can't see " gps satellite, just can not carry out navigator fix.The GPS receiver acquisition is a process to PRN (Pseudo Random Noise) sign indicating number time-delay and carrier doppler estimation, and this information is used for the initialization tracking loop, is the basis that receiver can position.

Obtaining some achievements in research aspect the GPS receiver abroad aspect the feeble signal reception satellite navigation receiver.Japan NEC Corporation produces and can receive-the GPS receiver of 182dBW signal, and can accurately locate in buildings and between housing-group.U.S. Signav company produces the GPS receiver, but received signal is-signal of 185dBW to be exclusively used in the reception feeble signal, even in the parking lot, in the buildings and can both reliably working in the high building clump.Canada Galgary university and Denmark Aalborg university (Aalborg University) are present feeble signal GPS receiver algorithm and the most representative academic institution of hardware development, are in rank first in this field.In addition, famous university such as Stanford Univ USA, Cornell University, The Air Force Research Laboratory and research institution are all obtaining important achievement aspect the development of feeble signal GPS receiver.CCMDB algorithm and DBZP algorithm as Nesreen I.Zieda proposition.For the acquisition algorithm of GPS receiver under the weak signal conditions, in order to reach higher SNR, need the integral time of hundreds of ms, need to cross over the data bit transition edge, above method is to adopt coherent integration to add up-acquisition algorithm that non-coherent integration adds up and combines.

Coherent integration adds up-and the tired acquisition algorithm of non-coherent integration can effectively be caught weak gps signal, but the time complexity of this algorithm is higher, needs high performance hardware supported.In actual environment, general stronger and more weak gps satellite signal is and deposits, if every satellite-signal all adopt coherent integration add up-the non-coherent integration accumulation algorithm catches, and can increase mean acquisition time greatly.

Sequential probability is than a branch of detecting as mathematical statistics, and its title comes from the works of the same name that nineteen forty-seven A.Wald delivers, its research to as if so-called " sequential sampling plan ", and the sample that how the obtains deduction of going to take statistics with this sampling plan.Sequential sampling plan is meant when sampling, does not stipulate total sampling number (observation or experiment number) in advance, but takes out a small amount of sample earlier, and according to its result, decision stops sampling or continuation sampling, what are taken out again, goes down like this, till decision stops sampling.In the passive radar track initiation stage, a kind of track initiation method that is called sequential detection is also arranged, its principle is similar with sampling.Otherwise the sort of sampling plan of definite in advance sampling number is called the fixed sampling scheme.

This sequential probability is not fixed than the number of times that the maximum characteristics that detect detect, and is constantly to change according to the result who finishes detection.

Catch for the gps signal under the strong and weak signals coexistence situation, during the receiver cold start-up, do not have ephemeris information to use, before catching and do not know the number and separately the energy intensity of visible gps satellite in the sky.Under the general more weak situation of satellite-signal energy, be used for the location in order to capture the more weak gps satellite signal of energy, highly sensitive receiver have only by carrying out long coherent integration add up-the non-coherent integration accumulation algorithm carries out data processing, just can capture more weak gps satellite signal.The data processing time and the detection threshold of existing acquisition algorithm are all fixed, and all are that the most weak signal of energy is set in the satellite-signal that captures according to all needs.There is a very big waste in this algorithm on operand, that has also been handled strong signal as weak signal, strong signal has been carried out a lot of unnecessary calculating.

Summary of the invention

The objective of the invention is to: overcome the existing too high shortcoming of GPS feeble signal acquisition algorithm time complexity, provide a kind of based on the GPS feeble signal acquisition algorithm of sequential probability than detection, adapt to catching of varying strength signal, effectively shorten the capture time of strong signal, thereby reduce whole capture time, improve acquisition performance.

The objective of the invention is to be achieved through the following technical solutions: than the GPS feeble signal acquisition algorithm that detects, performing step is as follows based on sequential probability:

(1) is digital intermediate frequency signal after the sample quantization of N ms the is handled sign indicating number territory two-dimensional search that walk abreast to the data length of receiver front end output, obtains the envelope diagram of parallel yard territory two-dimensional search;

(2) the false-alarm probability P of setting _FaUnder the condition of=α, calculate the threshold value γ M of different noncoherent accumulation number of times M correspondences; Wherein α is predefined false-alarm probability value, and its representative value is 10 ^-6, the span of M is 1-100;

(3), calculate the probability density function of the signal envelope of hypothesis according to the envelope diagram of the parallel sign indicating number territory two-dimensional search that obtains in the step (1);

(4) according to the noncoherent accumulation number of times M that carries out now, the corresponding threshold value γ M that selects step (2) to obtain, the signal that calculation procedure (3) obtains supposing is greater than the probability of thresholding γ M

(5) testing result is adjudicated, if Then think to capture signal, finish the search phase; If

Think and do not capture signal, be the data of the N ms sign indicating number territory two-dimensional searches that walk abreast to next data length again, and it is the envelope diagram of Search Results is superimposed with the envelope diagram of Search Results before, note is made noncoherent accumulation number of times M and is added 1, repeating step (3), (4), (5), up to capturing signal, finish till the search phase; Also do not capture signal if non-coherent integration accumulative frequency M reaches 100, thinking does not have signal, finishes acquisition phase equally.

The false-alarm probability P that described step (2) is being set _FaUnder the condition of=α, the process that calculates the threshold value γ M of different noncoherent accumulation number of times M correspondences is:

Make that noise variance is 1, known noise envelope I ²+ Q ²Obeying degree of freedom is 2M's

(

Being called the obedience degree of freedom again is the center chi square distribution of 2M) be distributed as:

$p_0\left(x\right)\frac{1}{2^M\mathrm{\Γ}\left(M\right)}{x}^{M-1}\exp (-\frac{1}{2}x)---\left(1\right)$

Wherein Γ (M) is the Gamma function, and it is defined as Γ (M)=(M-1) Γ (M-1), and M is a positive integer in following formula, Γ (M)=(M-1)!

For the Acquisition Detection of the signal of GPS receiver, false-alarm probability P _FaWith the relation of detection threshold γ M, by p ₀(x) right tail probability provides:

$P_{\mathrm{fa}}=Q_{p_0}\left(\mathrm{\γ}\right)={\∫}_{{\mathrm{\γ}}_M}^{\∞}{p}_0\left(x\right)\mathrm{dx}---\left(2\right)$

According to (1) formula and (2) formula, known false-alarm probability P _Fa=α, degree of freedom 2M can calculate the corresponding threshold value γ M of different M values;

Calculate when noncoherent accumulation number of times M is 1 to 100 successively, make right tail Probability p ₀(x) the threshold value γ 1 that equals α arrives γ 100.

Described step (3) is according to the envelope diagram of the parallel sign indicating number territory two-dimensional search that obtains in the step (1), and the process of calculating the probability density function of the signal envelope of supposing is:

Except the search unit lattice of amplitude maximum, other cells all are considered as the processed result who obtains afterwards of noise; According to degree of freedom is 2M's The average that distributes satisfies

Then noise variance satisfies

Wherein M is the noncoherent accumulation number of times, σ ²Be noise variance; The amplitude of the detecting unit of amplitude maximum is made as the result that signal obtains after processed, and obeying parameter according to the envelope of signal plus noise again is the non-central of λ

Distribute, wherein non-central parameter λ equals the amplitude and the noise variance σ of the detecting unit of amplitude maximum ²Ratio, thereby the probability density function of the signal envelope that obtains supposing:

$p_1\left(x\right)=\frac{1}{2}{\left(\frac{x}{\mathrm{\λ}}\right)}^{\frac{M-1}{2}}\exp [-\frac{1}{2}(x+\mathrm{\λ})]I_{M-1}\left(\sqrt{\mathrm{\λx}}\right)---\left(3\right)$

Wherein

Revise Bei Saier (Bessel) function for the M-1 rank, it is defined as:

$I_{M-1}\left(\sqrt{\mathrm{\λx}}\right)=\underset{k=0}{\overset{\∞}{\mathrm{\Σ}}}\frac{{\left(\frac{1}{2}\sqrt{\mathrm{\λx}}\right)}^{2k+M-1}}{k!\mathrm{\Γ}(M-1+k+1)}---\left(4\right)$

The present invention's beneficial effect compared with prior art is mainly reflected in: catch gps signal under weak signal conditions, adopt coherent accumulation-noncoherent accumulation acquisition algorithm usually, but the complexity of this algorithm is higher, need the support of high-performance hardware.In actual environment, general stronger and more weak gps satellite signal is and deposits, if every satellite-signal all adopts coherent accumulation-noncoherent accumulation algorithm to catch, can increase mean acquisition time greatly.The present invention uses for reference sequential probability and constantly changes this thought of subsequent detection number of times than testing result before the basis that detects, be applied in the GPS feeble signal and catch the field, every processing one piece of data just carries out one-time detection, with adjudicating, if detect signal then finish the acquisition phase of this star with the corresponding thresholding of data length; If do not detect signal then handle down one piece of data, repeat said method, till detecting signal, this method of the present invention adds up with existing coherent integration-and Fei coherent integration accumulation algorithm compares, obviously shortened the strong signal capture time under the strong and weak signals concurrent conditions, thereby reduce whole capture time, improved acquisition performance, finally strengthened the real-time of highly sensitive receiver.

Description of drawings

Fig. 1 is of the present invention based on the GPS feeble signal catching method realization flow figure of sequential probability than detection;

Fig. 2 is of the present invention based on the GPS feeble signal catching method process synoptic diagram of sequential probability than detection;

Fig. 3 is receiver structure figure;

Fig. 4 catches schematic diagram for parallel sign indicating number of the present invention territory;

Parallel sign indicating number territory two-dimensional search envelope diagram when Fig. 5 is a signal energy of the present invention for-160dBW;

Parallel sign indicating number territory two-dimensional search envelope diagram when Fig. 6 is a signal energy of the present invention for-180dBW;

Fig. 7 is the signal plus noise envelope probability distribution synoptic diagram of signal energy of the present invention when more weak;

Fig. 8 is the signal plus noise envelope probability distribution synoptic diagram of signal energy of the present invention when strong.

Embodiment

As shown in Figure 1, of the present invention based on the GPS feeble signal catching method of sequential probability than detection, implementation step is as follows:

(1) the N ms to receiver front end output (when highly sensitive receiver is caught feeble signal, needs to handle sufficiently long one piece of data and just can capture signal; The length of this segment data was represented with the time, the representative value of this time span in this patent algorithm is 4ms, also can be adjusted into other values, here just represent with N ms) digital intermediate frequency signal after sample quantization the is handled sign indicating number territory two-dimensional search that walk abreast, obtain the envelope diagram of parallel yard territory two-dimensional search;

The present invention is a kind of high efficiency catching method that is applicable to highly sensitive receiver, and the position in receiver structure as shown in Figure 3.What catch that link receives is through the digital intermediate frequency signal after RF front end (RF:radio frequecy radio frequency) and the processing of ADC (ADC:analog to digital converter analog-digital converter) sample quantization; What catch link output is more accurate signal frequency and code phase information.The acquisition algorithm that receiver is commonly used has three kinds: serial acquisition algorithm, parallel frequency domain acquisition algorithm, parallel sign indicating number territory acquisition algorithm.The operation efficiency of wherein parallel sign indicating number territory acquisition algorithm is the highest, and the specific implementation method of the inventive method (1) is exactly to adopt the partial data disposal route of parallel sign indicating number territory catching method.

Concrete steps are as follows:

Fig. 4 catches schematic diagram for parallel sign indicating number territory, the I of (annotate: this part disposal route is a known technology) GPS intermediate-freuqncy signal r (k) and quadrature, the synthetic local carrier of Q two-way multiply each other and peel off carrier signal, obtain complex signal I+jQ, obtain Y (k) through FFT, the C/A sign indicating number that this locality is generated carries out getting complex conjugate after the FFT conversion and gets C (k), multiplies each other with Y (k) and is IFFT again and obtains the time domain correlation Peel off the C/A sign indicating number.To complex sequences

Delivery, yard envelope diagram of territory two-dimensional search at this moment just obtains walking abreast.

Illustrate the envelope diagram of parallel sign indicating number territory two-dimensional search.

When signal energy is very strong, for example receiver antenna out of doors, signal energy reaches-160dBW, at this moment 4ms (N gets representative value 4) data handle the two-dimensional search that obtains with parallel sign indicating number territory envelope diagram as shown in Figure 5, can significantly see the peak value of signal.

When signal energy was very weak, for example receiver antenna was indoor, and signal energy has only-180dBW, and at this moment 4ms (N gets representative value 4) data be can't see the peak value of signal with walking abreast yard envelope diagram of the two-dimensional search that the territory processing obtains as shown in Figure 6.

(2) the false-alarm probability P of setting _FaUnder the condition of=α, calculate the threshold value γ M of different noncoherent accumulation number of times M correspondences.Its calculation procedure is as follows:

The purpose of signal capture is to obtain signal frequency and code phase information more accurately, focuses on obtaining the information of signal, rather than guarantees the high accuracy that has of signal message.Therefore generally, false-alarm probability P _Fa=α gets α=0.9 and gets final product.

Make noise variance be 1 (because step (2) is to calculate the threshold value of comparing with testing result, and testing result has been carried out normalization in step (3), so corresponding thresholding is also wanted normalization, even noise variance is 1).Known noise envelope I ²+ Q ²Obeying degree of freedom is 2M's

Distribute (also can write and do the chi square distribution that freely mostly is 2M), degree of freedom is that the PDF (PDF:probability distribution function probability distribution function) of the chi square distribution of 2M is:

$p_0\left(x\right)\frac{1}{2^M\mathrm{\Γ}\left(M\right)}{x}^{M-1}\exp (-\frac{1}{2}x)---\left(1\right)$

Wherein Γ (M) is the Gamma function, and it is defined as Γ (M)=(M-1) Γ (M-1), and M is a positive integer in following formula, Γ (M)=(M-1)!

For the Acquisition Detection of the signal of GPS receiver, false-alarm probability P _FaWith the relation of detection threshold γ M, by p ₀(x) right tail probability provides:

$P_{\mathrm{fa}}=Q_{p_0}\left(\mathrm{\γ}\right)={\∫}_{{\mathrm{\γ}}_M}^{\∞}{p}_0\left(x\right)\mathrm{dx}---\left(2\right)$

According to (1) formula and (2) formula, known false-alarm probability P _Fa=α, degree of freedom 2M can calculate the corresponding threshold value γ M of different M values.(annotate: to formula (1) and the anti-concrete grammar of separating of formula (2) is known technology)

Calculate when noncoherent accumulation number of times M is 1 to 100 successively, make right tail probability equal the threshold value γ 1 to γ 100 of α;

(3), calculate the probability density function of the signal envelope of hypothesis according to the envelope diagram of the parallel sign indicating number territory two-dimensional search that obtains in the step (1).Its calculation procedure is as follows:

Except the search unit lattice of amplitude maximum, other cells all are considered as the processed result who obtains afterwards of noise; According to degree of freedom is 2M's

The average of distribution (being that degree of freedom is the chi square distribution of 2M) satisfies (wherein M is the noncoherent accumulation number of times, σ ²Be noise variance), then noise variance satisfies

The amplitude of the detecting unit of amplitude maximum is made as the result that signal obtains after processed, and obeying parameter according to the envelope of signal plus noise again is the non-central of λ

Distribute (being that degree of freedom is that the non-central parameter of 2M is the non-central chi square distribution of λ), wherein non-central parameter λ equals the amplitude and the noise variance σ of the detecting unit of amplitude maximum ²Ratio, thereby the probability density function of the signal plus noise envelope that obtains supposing:

$p_1\left(x\right)=\frac{1}{2}{\left(\frac{x}{\mathrm{\λ}}\right)}^{\frac{M-1}{2}}\exp [-\frac{1}{2}(x+\mathrm{\λ})]I_{M-1}\left(\sqrt{\mathrm{\λx}}\right)---\left(3\right)$

I wherein _r(u) revise Bei Saier (Bessel) function for the r rank, it is defined as:

$I_r\left(u\right)=\underset{k=0}{\overset{\∞}{\mathrm{\Σ}}}\frac{{\left(\frac{1}{2}u\right)}^{2k+r}}{k!\mathrm{\Γ}(r+k+1)}---\left(4\right)$

(4) calculate the probability of the signal of hypothesis greater than thresholding γ M

Its calculation procedure is as follows:

According to the noncoherent accumulation number of times M that carries out now, the corresponding threshold value γ M that selects step (2) to obtain; Calculation procedure

(3) obtain the signal supposed probability greater than thresholding γ M

Its calculation procedure is as follows:

The probability density function of known signal plus noise envelope is (3) formula, bring noncoherent accumulation number of times M, non-central parameter λ into (3) formula, the probability distribution graph that can draw the signal plus noise envelope, at straight line of transverse axis γ M place picture perpendicular to transverse axis, the calculating probability distribution plan accounts for the ratio of the total area at vertical line with the area on the right side, promptly calculates right tail probability

Illustrate the probability distribution graph and the right tail probability of signal plus noise envelope

When signal energy was more weak, the probability distribution graph of signal plus noise was the A line among Fig. 7, and the ratio that the black filling area accounts for the total area that A line and transverse axis surround is right tail probability

Obviously the right tail probability among Fig. 7 is less than 0.9

When signal energy was strong, the probability distribution graph of signal plus noise was the B line among Fig. 8, and the ratio that the black filling area accounts for the total area that B line and transverse axis surround is right tail probability

Obviously the right tail probability among Fig. 8 is greater than 0.9.

(5) testing result is adjudicated, if

Think to capture signal, finish the search phase; If

Think and do not capture signal, again to the following data of the N ms yard territory two-dimensional search that walk abreast, and it is the envelope diagram of Search Results is superimposed with the envelope diagram of Search Results before, note is made the noncoherent accumulation number of times and is added 1, repeating step (3), (4), (5), up to capturing signal, finish till the search phase.Also do not capture signal if the non-coherent integration accumulative frequency reaches 100, thinking does not have signal, finishes acquisition phase equally.

Generally, based on sequential probability operational process such as Fig. 2 than the GPS feeble signal catching method that detects.For example the signal of satellite 1 is more intense, only carries out 1 N ms data processing (being the M1=1 among Fig. 2), and the court verdict proof captures signal, just finishes the acquisition phase of satellite 1, altogether satellite 1 has been carried out the data processing of N ms.The signal energy of satellite 2 is more weak, carries out N ms data processing 1 time, and the judgement proof does not capture signal; Carry out N ms data processing again 1 time, adjudicate again, carried out the processing of M2 secondary data altogether and just captured signal, finish the acquisition phase of satellite 2, altogether satellite 2 has been carried out the data processing of M2*N ms.Satellite 32 is not present in the visual field of present receiving machine, just the signal of satellite 32 does not exist, carried out the data processing of the inferior N ms of M32 (M32=100) altogether, each judgement all proves and does not capture signal, the signal that just proves this satellite does not exist, finish the acquisition phase of satellite 32, altogether satellite 32 has been carried out the data processing of 100*N ms.

The emulation experiment that the present invention is effective is as follows:

Simulation object is the performance based on the SPRT acquisition algorithm of sequential probability ratio of conventional coherent accumulation-noncoherent accumulation algorithm and this patent invention in strong and weak signals when coexistence.

With the data that signal imitation produces, visible star one has 4, and signal to noise ratio (S/N ratio) is respectively-19dB ,-22dB ,-25dB ,-28dB.Suppose according to counting one by one and know day numbering of aerial visible star, catch the signal of these 4 satellites.The program runtime such as the table 1 of conventional relevant noncoherent accumulation algorithm and SPRT algorithm

The MATLAB working time of two kinds of algorithms of table 1

The algorithm title	Program runtime (s)
		Relevant noncoherent accumulation	61.35
SPRT	14.45

The gap of two kinds of method calculated amount is embodied in:

Conventional relevant noncoherent accumulation algorithm will guarantee to capture the above signal of signal to noise ratio (S/N ratio)-30dB, and the noncoherent accumulation number of times is at least 20.Having calculated each matrix size of 4*20=80 matrix (signal of 4 satellites, 20 matrixes of the calculated signals of every satellite) is 41*12000.Total calculated amount is

4*20*k*41*12000＝39360000k。

The SPRT algorithm is right-28dB signal incoherent accumulative frequency 10 ,-25dB signal incoherent accumulative frequency 6 ,-22dB signal and-19dB signal incoherent accumulative frequency is 1.Calculated (10+6+1+1)=18 matrix, each matrix size is 41*12000.Total calculated amount is

(10+6+1+1)*k*41*12000＝8856000k。

Under the sort signal energy condition, the calculated amount of SPRT algorithm has only the 39360000k/8856000k=22.5% of conventional relevant noncoherent accumulation algorithm computation amount.

If highly sensitive receiver (highly sensitive receiver refers to receive and handles energy and be lower than-signal of 180dBW) requires to detect the lower signal of signal to noise ratio (S/N ratio), the advantage that reduces of the calculated amount of SPRT algorithm is more obvious so; If when but carrying out the satellite-signal search, without any prior imformation, search for the signal of 32 satellites successively one time, what the calculated amount of SPRT algorithm reduced so is not clearly.This is because at acquisition phase, is can't distinguish not have signal and extremely faint signal; For the SPRT algorithm, search for a non-existent satellite-signal of basis, the content of calculating is identical with the relevant noncoherent accumulation algorithm of routine, all is to do noncoherent accumulation to arrive till the number of times upper limit of setting.So the SPRT algorithm is when this non-existent satellite-signal of search, performance and former algorithm are as broad as long.

Emulation experiment conclusion: the analysis and the emulation based on the SPRT acquisition algorithm of sequential probability ratio of the conventional coherent accumulation-noncoherent accumulation algorithm when strong and weak signals is coexisted and this patent invention, adopt sequential detection method as can be seen when carrying out the coexistence of strong and weak gps satellite signal and catch, the SPRT algorithm is better than relevant noncoherent accumulation algorithm greatly.Because it is higher to carry out the time complexity of coherent accumulation and noncoherent accumulation computing, and generally all there is stronger and more weak gps satellite signal in the actual environment, therefore the SPRT algorithm can reduce operation time, improve and reduce the time that gps satellite is caught, thereby improve the performance of high sensitivity GPS receiver acquisition algorithm.

The part that the present invention does not elaborate belongs to techniques well known.

Claims (3)

1. based on the GPS feeble signal catching method of sequential probability, it is characterized in that performing step is as follows than detection:

(1) is digital intermediate frequency signal after the sample quantization of N ms the is handled sign indicating number territory two-dimensional search that walk abreast to the data length of receiver front end output, obtains the envelope diagram of parallel yard territory two-dimensional search;

(2) the false-alarm probability P of setting _FaUnder the condition of=α, calculate the threshold value γ M of different noncoherent accumulation number of times M correspondences; Wherein α is predefined false-alarm probability value, and the span of M is 1-100;

(3), calculate the probability density function of the signal envelope of hypothesis according to the envelope diagram of the parallel sign indicating number territory two-dimensional search that obtains in the step (1);

(4) according to the noncoherent accumulation number of times M that carries out now, the corresponding threshold value γ M that selects step (2) to obtain, the signal that calculation procedure (3) obtains supposing is greater than the probability of thresholding γ M

(5) testing result is adjudicated, if

Then think to capture signal, finish the search phase; If Think and do not capture signal, be the data of the N ms sign indicating number territory two-dimensional searches that walk abreast to next data length again, and it is the envelope diagram of Search Results is superimposed with the envelope diagram of Search Results before, note is made noncoherent accumulation number of times M and is added 1, repeating step (3), (4), (5), up to capturing signal, finish till the search phase; Also do not capture signal if non-coherent integration accumulative frequency M reaches 100, thinking does not have signal, finishes acquisition phase equally.

2. according to claim 1 based on the GPS feeble signal acquisition algorithm of sequential probability than detection, it is characterized in that: the false-alarm probability P that described step (2) is being set _FaUnder the condition of=α, the process that calculates the threshold value γ M of different noncoherent accumulation number of times M correspondences is:

Make that noise variance is 1, known noise envelope I ²+ Q ²Obeying degree of freedom is 2M's

Be distributed as:

$p_0\left(x\right)\frac{1}{2^M\mathrm{\Γ}\left(M\right)}{x}^{M-1}\exp (-\frac{1}{2}x)---\left(1\right)$

Wherein Γ (M) is the Gamma function, and it is defined as Γ (M)=(M-1) Γ (M-1), and M is a positive integer in following formula, Γ (M)=(M-1)! ,

For the Acquisition Detection of the signal of GPS receiver, false-alarm probability P _FaWith the relation of detection threshold γ M, by p ₀(x) right tail probability provides:

$P_{\mathrm{fa}}=Q_{p_0}\left(\mathrm{\γ}\right)={\∫}_{{\mathrm{\γ}}_M}^{\∞}{p}_0\left(x\right)\mathrm{dx}---\left(2\right)$

According to (1) formula and (2) formula, known false-alarm probability P _Fa=α, degree of freedom 2M can calculate the corresponding threshold value γ M of different M values; Calculate when noncoherent accumulation number of times M is 1 to 100 successively, make right tail Probability p ₀(x) the threshold value γ 1 that equals α arrives γ 100.

3. according to claim 1 based on the GPS feeble signal acquisition algorithm of sequential probability than detection, it is characterized in that: described step (3) is according to the envelope diagram of the parallel sign indicating number territory two-dimensional search that obtains in the step (1), and the process of calculating the probability density function of the signal envelope of supposing is:

Except the search unit lattice of amplitude maximum, other cells all are considered as the processed result who obtains afterwards of noise; According to degree of freedom is 2M's

The average that distributes satisfies

Then noise variance satisfies

Wherein M is the noncoherent accumulation number of times, σ ²Be noise variance; The amplitude of the detecting unit of amplitude maximum is made as the result that signal obtains after processed, and obeying parameter according to the envelope of signal plus noise again is the non-central of λ

Distribute, wherein non-central parameter λ equals the amplitude and the noise variance σ of the detecting unit of amplitude maximum ²Ratio, thereby the probability density function of the signal envelope that obtains supposing:

$p_1\left(x\right)=\frac{1}{2}{\left(\frac{x}{\mathrm{\λ}}\right)}^{\frac{M-1}{2}}\exp [-\frac{1}{2}(x+\mathrm{\λ})]I_{M-1}\left(\sqrt{\mathrm{\λx}}\right)---\left(3\right)$

Wherein

Revise Bei Saier (Bessel) function for the M-1 rank, it is defined as:

$I_{M-1}\left(\sqrt{\mathrm{\λx}}\right)=\underset{k=0}{\overset{\∞}{\mathrm{\Σ}}}\frac{{\left(\frac{1}{2}\sqrt{\mathrm{\λx}}\right)}^{2k+M-1}}{k!\mathrm{\Γ}(M-1+k+1)}.---\left(4\right)$

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