CN101334462B - Integer ambiguity granularity changing determination method in single frequency receiving machine absolute positioning - Google Patents

Abstract

The invention discloses a determination method of variable granularity of integer ambiguity of a single-frequency receiver in the absolute positioning, belonging to the technical field of satellite navigation and positioning and relating to a method for carrying out the single-point precise positioning by the single-frequency receiver in a satellite navigation positioning system with the utilization of the satellite carrier phase. The determination method is based on the utilization of the single-point static positioning LAMBDA algorithm to calculate the float solution and the distribution variance of the integer ambiguity, firstly carries out the rough integral mapping of the float solution to complete the roughening of the integral domain of search space, then utilizes the rough integral granularity to change the search region and carries out the search of the integer ambiguity according to search conditions to obtain the integral domain of the integer ambiguity; then the rough integral granularity is continuously reduced, the process is repeated till the rough integral granularity is equal to 1, then the search of the integer ambiguity is completed, and the precise carrier phase integer ambiguity is obtained. The use of the invention can rapidly, conveniently and reliably realize the carrier phase high-precision positioning of the single-frequency receiver and can be applied in the low-cost and high-precision navigation positioning system.

Description

The change granularity of integer ambiguity is determined method in a kind of single frequency receiving absolute fix

Technical field

The invention belongs to satellite navigation and field of locating technology, relate to that single frequency receiving utilizes the satellite carrier phase place to carry out the pinpoint method of single-point in the satellite navigation and location system.

Background technology

In satellite navigation and location system, with respect to the high multifrequency receiver of cost, the bearing accuracy of single frequency receiving is lower, but cheap, and the commercial market has a high potential.The introducing of differential technique makes single frequency receiving also can realize the carrier phase location, but because differential technique requires to use two above single frequency receivings at least or open the network that differential signal is broadcasted, thereby strengthened the input of cost, and made that operation is very loaded down with trivial details.

No matter adopt the location technology of which kind of carrier phase, all to relate to this difficult point of resolving of integer ambiguity.Especially in the accurate location of single frequency receiving, how resolving integer ambiguity fast is key problem.In existing Carrier Phase Ambiguity Resolution algorithm, comparative maturity four classes are arranged: double frequency pseudorange method, THE AMBIGUITY FUNCTION METHOD USED, least square search procedure and blur level covariance method.Wherein, in actual engineering, obtained widespread use with the LAMBDA method in the blur level covariance method.The LAMBDA method is to be proposed by P.J.G Teunissen nineteen ninety-five, and purpose is definite problem of integer ambiguity during the carrier phase difference of solution single frequency receiving is located, and is the best algorithm of Carrier Phase Ambiguity Resolution in the carrier phase difference location of generally acknowledging at present.But the LAMBDA method needs equally the receiver more than two carry out integrated positioning, makes cost height and complex operation.

In order to reduce cost, to simplify the operation, require receiver can realize the single-point location.But up to now, relevant single frequency receiving is used for the pinpoint algorithm of single-point seldom, generally is that the LAMBDA method is transplanted in the single-point static immobilization model.But such transplanting algorithm carry out integer ambiguity to resolve efficient very low, be difficult to provide the result at short notice.Its reason is: in the single-point static immobilization, observe shorter epoch, the satellite transit scope is little, graphic change in spatial array is less, cause the parameter degree of correlation very big, make that the covariance matrix pathosis is serious in the Carrier Phase Ambiguity Resolution, cause the hunting zone super large, even, all can not search right value at short notice by Gaussian integer conversion and sequential search.

Summary of the invention

The change granularity that the invention provides integer ambiguity in a kind of single frequency receiving absolute fix is determined method, realizes resolving fast of integer ambiguity in the single frequency receiving absolute fix, thereby finally realizes the absolute accurate location fast of single frequency receiving.

The present invention has utilized the integer ambiguity floating-point of k (k 〉=4) satellite that the LAMBDA algorithm obtains to separate x _i(i=1,2 ..., k), the corresponding distribution variance σ that the integer ambiguity floating-point is separated _i(i=1,2 ..., k), and the covariance matrix Q of blur level _NThe computing method of each parameter are reference papers " The least-squares ambiguity d é cor relation adjustment:a method for fast GPS integer ambiguity estimation " P.J.G Teunissen work in detail, is published in periodical " Journal ofGeodesy " in nineteen ninety-five; Doctor's thesis " dynamically to high-precision fixed potential theory of dynamic GPS and applied research thereof ", Liu Lilong work,, Wuhan University in 2005.

Basic ideas of the present invention are to utilize the LAMBDA algorithm of single-point static immobilization, the floating-point that calculates integer ambiguity separate with distribution variance after, floating-point separated carry out the mapping of coarse integer, finish the integer field roughening of search volume, utilize coarse integer granularity to change the region of search again, by search condition integer ambiguity is searched for, obtained the integer field of integer ambiguity; Constantly reduce coarse integer granularity then, repeat above process, equal 1, finish search, thereby obtain accurate ambiguity of carrier phase integer ambiguity until coarse integer granularity.

Technical solution of the present invention is as follows:

The change granularity of integer ambiguity is determined method in a kind of single frequency receiving absolute fix, as shown in Figure 1, may further comprise the steps:

Step 1, phantom order frequency receiver have been followed the tracks of k or k above navigation satellite signal, utilize the LAMBDA algorithm of single-point static immobilization, and the floating-point that calculates integer ambiguity is separated x _i(i=1,2 ..., k) with distribution variance σ _i(i=1,2 ..., k), wherein k represents the number of Navsat, and k 〉=4.

Step 2, structure integer mapping are mapped as integer field { y with the region of search of integer ambiguity _i.

Construct a common integer mapping function f _I(x _i):

f _I(x _i)＝{y _i|x _i-3σ _i≤y _i≤x _i+3σ _i，y _i∈Z} (1)

Wherein: I={i-1, i-2 ..., 1}, x _iFor the integer ambiguity floating-point is separated σ _iFor the integer ambiguity floating-point is separated x _iDistribution variance, i=1,2 ..., k.

Step 3, by coarse integer granularity g, to the integer field { y of step 2 gained _iCarry out roughened:

Set initial coarse integer granularity g ₀=g=2 ^m, m ∈ Z and 2≤m≤10 are to the integer field { y of step 2 gained _iCarry out roughened, obtain:

${\left[y\right]}_{\mathrm{il}}=\{y_{\mathrm{il}}^1,y_{\mathrm{il}}^2,\·\·\·,y_{\mathrm{il}}^g\};i=\mathrm{1,2},\·\·\·,k;l=\mathrm{1,2},\·\·\·,L---\left(2\right)$

(2) in the formula, [y] _IlRepresent coarse integer; L represents integer field { y _iInteger number remove the integer behind g, round up and obtain;

Then, to [y] _IlCarry out following computing, obtain L blur level region of search:

(3) in the formula, Represent the numeral performance of coarse integer;

The expression get smaller or equal to

Maximum integer.

Step 4, structural environment search model.

The shape of blur level region of search and direction determined by its covariance matrix Q, searches for for the numeral of the coarse integer that utilizes the blur level region of search shows the integer that replaces wherein, and the estimator of setting integer ambiguity is:

${\hat{N}}_{i/I}={\hat{N}}_i-\underset{j=1}{\overset{i-1}{\mathrm{\Σ}}}{\mathrm{\σ}}_{{\hat{N}}_i{\hat{N}}_{j/J}}{\mathrm{\σ}}_{{\hat{N}}_{j/J}}^2({\hat{N}}_{j/J}-N_j)---\left(4\right)$

Wherein:

Representative

I={i-1, i-2 ..., 1},

Be meant after having determined preceding i-1 integer ambiguity value the estimated value of i integer ambiguity;

With

It is corresponding parameter between each blur level among the integer ambiguity covariance matrix Q;

Be that the integer ambiguity floating-point is separated x _idirectly round; N _jBe coarse integer [y] _jNumeral performance, promptly

J=1,2 ..., i-1; I=1,2 ..., k.

Like this, in the region of search that coarse integer constitutes, construct following conditional search model:

$\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{({\hat{N}}_{i/I}-N_i)}^2/{\mathrm{\σ}}_{{\hat{N}}_{i/I}}^2\≤{\mathrm{\χ}}^2---\left(5\right)$

Step 5, setting thresholding χ ², L blur level region of search of step 3 gained searched for.

Make thresholding

g ₀Be initial coarse integer granularity, g is current coarse integer granularity, g=g ₀/ 2.So just along with coarse integer granularity is more and more thinner, and the setting of thresholding is more and more looser, thereby guarantees can not miss the integer ambiguity right value.

According to the search model of step 4 structure, in conjunction with thresholding χ ², integer ambiguity is carried out following search:

$\left\{\begin{array}{c}{({\hat{N}}_1-N_1)}^2\≤{\mathrm{\σ}}_{{\hat{N}}_1}^2{\mathrm{\χ}}^2\\ {({\hat{N}}_{2/1}-N_2)}^2\≤{\mathrm{\σ}}_{{\hat{N}}_{2/1}}^2[{\mathrm{\χ}}^2-{({\hat{N}}_1-N_1)}^2/{\mathrm{\σ}}_{{\hat{N}}_1}^2]\\ .\\ .\\ .\\ {({\hat{N}}_{k/(k-1),\·\·\·,1}-N_k)}^2\≤{\mathrm{\σ}}_{{\hat{N}}_{k/(k-1),\·\·\·,1}}^2[{\mathrm{\χ}}^2-\underset{j=1}{\overset{k-1}{\mathrm{\Σ}}}{({\hat{N}}_{j/j-1,\·\·\·,1}-N_j)}^2/{\mathrm{\σ}}_{{\hat{N}}_{j/j-1,\·\·\·1}}^2\end{array}\right.---\left(6\right)$

Like this, extracting all integer ambiguities that satisfy search condition may value

Coarse integer [y] with correspondence _iScreen and be brought together.

Step 6, reduce coarse integer granularity g=g ₀/ 2, repeating step 3 up to granularity g=1, obtains final integer ambiguity value to step 6.

When coarse integer granularity g=1,, then utilize following decision condition if the Search Results of step 5 is still not unique:

$\underset{N}{\min }\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{({\hat{N}}_{i/I}-N_i)}^2/{\mathrm{\σ}}_{{\hat{N}}_{i/I}}^2---\left(7\right)$

Just can in alternative the separating of many groups, obtain the unique solution of integer ambiguity according to formula (7).

Compare with traditional solution single frequency receiving single-point location Carrier Phase Ambiguity Resolution algorithm (being the LAMBDA algorithm), the present invention can search the integer ambiguity right value apace, and the time complexity of search only is o (m).Because search speed is very fast, so loose to initial search volume area requirement, searching algorithm can convergence fast in comparatively wide region of search.And general Carrier Phase Ambiguity Resolution algorithm, the carrier track that carry out many epoch to be reducing the correlativity between parameter, thereby dwindles the region of search.

In sum, the change granularity optimization searching algorithm among the present invention can be carried out resolving fast of integer ambiguity following the tracks of under the carrier wave situation of less epoch, this be other single frequency receiving single-point location algorithms can not compare.Utilize the present invention, can be fast, convenient, realize single frequency receiving ground carrier phase hi-Fix reliably, can be applicable to cheaply to have better market prospect in the high precision navigation positioning system.

Description of drawings

Fig. 1 is a basic procedure synoptic diagram of the present invention.

Embodiment

In the technical solution of the present invention, can be according to the concrete number k (k 〉=4) and the initial coarse integer granularity g of Navsat ₀=g=2 ^mThe concrete different value of middle m (5≤m≤10) obtains different embodiments, and the change granularity of integer ambiguity determines that method is similar, does not repeat them here in its whole single frequency receiving absolute fix.

Claims (1)

1. the change granularity of integer ambiguity is determined method in the single frequency receiving absolute fix, may further comprise the steps:

Step 1, phantom order frequency receiver have been followed the tracks of k or k above navigation satellite signal, utilize the LAMBDA algorithm of single-point static immobilization, and the floating-point that calculates integer ambiguity is separated x _iWith distribution variance σ _i, wherein: i=1,2 ..., k, k represent the number of Navsat, and k 〉=4;

Step 2, structure integer mapping are mapped as integer field { y with the region of search of integer ambiguity _i}:

Construct a common integer mapping function f _I(x _i):

f _I(x _i)＝{y _i|x _i-3σ _i≤y _i≤x _i+3σ _i，y _i∈Z} (1)

Wherein: I={i-1, i-2 ..., 1}, x _iFor the integer ambiguity floating-point is separated σ _iFor the integer ambiguity floating-point is separated x _iDistribution variance, i=1,2 ..., k;

Step 3, by coarse integer granularity g, to the integer field { y of step 2 gained _iCarry out roughened:

Set initial coarse integer granularity g ₀=g=2 ^m, m ∈ Z and 2≤m≤10 are to the integer field { y of step 2 gained _iCarry out roughened, obtain:

(2) in the formula, [y] _IlRepresent coarse integer; L represents integer field { y _iInteger number remove the integer behind g, round up and obtain;

Then, to [y] _IlCarry out following computing, obtain L blur level region of search:

(3) in the formula,

Represent the numeral performance of coarse integer;

The expression get smaller or equal to Maximum integer;

Step 4, structural environment search model:

The estimator of setting integer ambiguity is:

Wherein,

Representative

I={i-1, i-2 ..., 1}, Be meant after having determined preceding i-1 blur level value the estimated value of i blur level;

With

It is corresponding parameter between each blur level among the blur level covariance matrix Q;

Be that the blur level floating-point is separated x _idirectly round; N _iBe integer ambiguity value to be tested in the coarse set of integers

Asterisk is defended in expression;

Like this, in the region of search that coarse integer constitutes, construct following conditional search model:

Step 5, setting thresholding χ ², L blur level region of search of step 3 gained searched for:

Make thresholding

g ₀Be initial coarse integer granularity, g is current coarse integer granularity, g=g ₀/ 2;

According to the search model of step 4 structure, in conjunction with thresholding χ ², integer ambiguity is carried out following search:

Like this, extracting all integer ambiguities that satisfy search condition may value Coarse integer [y] with correspondence _iScreen and be brought together;

Step 6, reduce coarse integer granularity g=g ₀/ 2, repeating step 3 up to granularity g=1, obtains final integer ambiguity value to step 6;

When coarse integer granularity g=1,, then utilize following decision condition if the Search Results of step 5 is still not unique:

Obtain the unique solution of integer ambiguity.

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