CN107179525A - A kind of location fingerprint construction method of the Kriging regression based on Thiessen polygon - Google Patents

Abstract

The invention discloses an RSSI position fingerprint construction method based on Kriging interpolation of Thiessen polygons. The method constructs Thiessen polygons, and automatically constructs a triangular network according to discrete points, that is, constructs a Delaunay triangular network. Number the discrete points and the formed triangles, record which three discrete points each triangle is composed of, and then find out the numbers of all triangles adjacent to each discrete point, and record them. Sort the triangles adjacent to each discrete point clockwise or counterclockwise, so that the next step can be connected to generate a Thiessen polygon, calculate the circumcenter of each triangle, and record its coordinate position, according to the phase of each discrete point Adjacent triangles, connecting the circumcenters of these adjacent triangles, the Thiessen polygon is obtained. For the Thiessen polygon on the edge of the triangulation network, the vertical bisector can be intersected with the figure profile, and together with the figure profile form the Thiessen polygon. This method more accurately predicts the signal strength of the unsampled reference point.

Description

A Location Fingerprint Construction Method Based on Thiessen Polygon Kriging Interpolation

technical field

The invention relates to an RSSI position fingerprint construction method applied to indoor wireless positioning, and belongs to the technical field of wireless positioning.

Background technique

With the popularity of mobile terminals (especially smart phones), the demand for location-based services in crowded indoor areas such as large shopping malls, airports, and high-speed rail stations has increased dramatically. However, satellite navigation and positioning systems represented by GPS (Global Positioning System, Global Positioning System), BDS (BeiDou Navigation Satellite System, Beidou Satellite Navigation System), etc., can hardly work in indoor areas. A technical solution for satellite systems to provide positioning services for indoor areas. The construction of wireless cities, smart cities and other projects provides basic support for indoor positioning. For example, WiFi can also be used for positioning while meeting the needs of users to access the Internet. Due to the universality and ecological nature of ubiquitous wireless signals such as WiFi and Bluetooth, indoor positioning based on ubiquitous wireless signals has become a current research hotspot.

At present, the indoor positioning methods based on ubiquitous wireless signals mainly include location fingerprint matching and ranging rendezvous. However, the two methods have their own advantages and disadvantages. Among them, location fingerprint matching has high positioning accuracy, and it takes manpower and time to collect location fingerprint data, and the location fingerprint data needs to be maintained and updated.

The Chinese patent application CN104869536A entitled "Automatic Update Method and Device for Wireless Indoor Positioning Fingerprint Map" discloses the following technical solution, that is, using the position of the mobile device when it is stationary as a reference point to construct a mapping of fingerprint data between it and non-reference points relationship, and then based on this mapping relationship, a certain number of reference positions and the latest fingerprint data collected on it are used to generate non-reference point position fingerprint data when updating fingerprint data, but the invention CN104869536A needs to first determine the position of the mobile device when it is still, The positioning error has an adverse effect on the generation of location fingerprint data of non-reference points. In addition, the improvement of the mapping relationship that the invention CN104869536A relies on requires a long training time.

Contents of the invention

The purpose of the present invention is to address the deficiencies in the prior art above, to provide a RSSI position fingerprint construction method with high interpolation accuracy, the method utilizes the signal strength of the sampled reference point to predict the signal strength of the unsampled reference point, in the construction of WiFi indoor positioning In the process of fingerprint library, the signal acquisition intensity is greatly reduced, so that the fingerprint library can be quickly constructed.

The technical scheme that the present invention solves its technical problem is: a kind of RSSI position fingerprint construction method based on the kriging interpolation of Thiessen polygon, this method comprises the following steps:

Step 1: Build Thiessen Polygons

1) Automatically construct a triangular network according to discrete points, that is, construct a Delaunay triangular network. Number the discrete points and the resulting triangles, recording which three discrete points each triangle is made of.

2) Then find out the numbers of all triangles adjacent to each discrete point, and record them. This is as long as finding all the triangles with the same vertex in the constructed triangulation network.

3) Sort the triangles adjacent to each discrete point clockwise or counterclockwise, so that the next step can be connected to generate a Thiessen polygon. Let the discrete point be o. Find a triangle with o as the vertex, set it as A; take another vertex of triangle A except o, set it as a, then the other vertex can also be found, which is f; then the next triangle must be of is the side, that is triangle F; the other vertex of triangle F is e, then the next triangle has oe as the side; and so on, until returning to the side oa.

4) Calculate the circumcircle center of each triangle, and record its coordinate position.

5) According to the adjacent triangles of each discrete point, connect the circumcenters of these adjacent triangles to obtain a Thiessen polygon. For the Thiessen polygon on the edge of the triangulation network, the vertical bisector can be intersected with the figure profile, and together with the figure profile form the Thiessen polygon.

Step 2: RSSI Interpolation Estimation

Kriging interpolation is:

Where R(z ₀ ) is the RSSI value of the interpolation point z ₀ , λ _i is the weight of the sampling point z _i , and R(z _i ) is the RSSI value of the sampling point z _i

Assuming that the signal attribute value in the area satisfies the second-order stationary, for any point in the area:

Substitute formula (1) into formula (2) to get the constraints:

Minimize the variance of the unbiased estimate:

In formula (4), μ is the Lagrange coefficient, and solving the parameter set μ,λ ₁ ,λ ₂ ...λ _n that minimizes this cost function can satisfy its Estimated variance is minimized under constraints

make Differentiate for μ, λ _i respectively:

Find the system of kriging weight equations:

Its matrix representation:

Simplified expression:

C × ω = D

Then its weight is:

ω＝C ^-1 ×D

Transform covariance into variogram for spatial variables

Define the variogram:

in γ(z _i ,z _j )=-Cov(z _i ,z _j ) (9)

Substitute formula (9) into formula (6):

In practical applications, defined by the semivariance of formula (9), the value of the semivariance can be easily calculated by the following formula:

The present invention adopts the known (h, γ(h)), selects a suitable semi-variance model for fitting, and selects the interpolation result of the model corresponding to the smallest unbiased estimation variance as the final fingerprint database.

After using the above interpolation method to estimate the RSSI feature of each sampling point, the present invention first obtains the RSSI feature distribution from one of the signal sources, then obtains the RSSI feature distribution of other signal sources according to the same steps, and finally distributes these RSSI feature distributions The superposition is stored in the form of a feature vector with each sampling point as the unit, and the location fingerprint data at the current moment is obtained.

Beneficial effect:

1. The present invention uses the signal strength of the sampled reference point to predict the signal strength of the unsampled reference point, and greatly reduces the signal acquisition intensity in the process of building the fingerprint library in WiFi indoor positioning, so that the fingerprint library can be quickly built.

2. The present invention adopts the correlation of the signal strength of adjacent reference points, obtains the weight of the reference point to be measured by the semivariogram function between the sampling reference points, and predicts by several sampled reference points closest to the reference point to be predicted and the signal strength of the reference point to be predicted, and more accurately predict the signal strength of the unsampled reference point.

3. The present invention adopts the correct model and parameters to fit the correct result, which has a relatively large impact on the accuracy of the result, and selects a suitable semi-variance model to improve the accuracy of interpolation by calculating the minimum average unbiased estimated variance.

Description of drawings

Fig. 1 is the flowchart of the method of the present invention.

Fig. 2 is a distribution diagram of reference points in a positioning area in an example of the present invention.

detailed description

The present invention will be further described in detail below in conjunction with the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

In this embodiment, a method for constructing a fingerprint library in WiFi indoor positioning; as shown in Figure 1, includes: 1. collecting the signal strength time series of a reference point in the WiFi indoor positioning area; 2. using the Thiessen polygon algorithm to calculate 3. Collect the signal strength of other reference points according to the extracted signal characteristics; 4. Use the signal strength of the collected reference point to predict the signal strength of the unsampled reference point. Specifically, proceed as follows:

Step 1: Take the entire area covered by the circumscribed rectangle of the indoor area as the WiFi indoor positioning area, set any vertex of the circumscribed rectangle as the origin o, and the two sides adjacent to the origin are the x-axis and y-axis respectively, and establish a Cartesian coordinate system oxy ; In the specific process of establishing the coordinate system, the positioning area is located in the first quadrant of the coordinate system oxy.

Step 2: Divide the WiFi indoor positioning area evenly into d grids, and use the center point of each grid as a reference point to form a set of reference points, which is recorded as P={P ₁ ,P ₂ ,…,P _i , ..., P _d }, P _i represents the reference point in the i-th grid; 1≤i≤d; in this embodiment, as shown in Figure 2, the actual positioning environment is the author's laboratory, and the value of d Set at 100. The distance between adjacent reference points in each row is 1 meter, and the distance between two adjacent columns of reference points is also 1 meter.

Step 3: There are n routers set up in the WiFi indoor positioning area, recorded as AP={AP ₁ ,AP ₂ ,..AP _j ,...AP _n }, AP _j represents the jth router; 1≤j≤n ; In the present embodiment, the value of n is determined as 4. As shown in Figure 2, 4 APs are placed in the indoor area.

Step 4: Collect the signal strength of each AP at each vertex as shown in Figure 2, and use (x, y, Rss _A i _P1 , Rss _A i _P2 , Rss _A i _P3 , Rss _A i _P4 ): as the fingerprint data information of the current location , to establish a location fingerprint database.

Building Thiessen polygons involves:

1) Automatically construct a triangular network according to discrete points, that is, construct a Delaunay triangular network. Number the discrete points and the resulting triangles, recording which three discrete points each triangle is made of.

2) Then find out the numbers of all triangles adjacent to each discrete point, and record them. This is as long as finding all the triangles with the same vertex in the constructed triangulation network.

3) Sort the triangles adjacent to each discrete point clockwise or counterclockwise, so that the next step can be connected to generate a Thiessen polygon. Let the discrete point be o. Find a triangle with o as the vertex, set it as A; take another vertex of triangle A except o, set it as a, then the other vertex can also be found, which is f; then the next triangle must be of is the side, that is triangle F; the other vertex of triangle F is e, then the next triangle has oe as the side; and so on, until returning to the side oa.

4) Calculate the circumcircle center of each triangle, and record its coordinate position (x _j , y _j ).

5) According to the adjacent triangles of each discrete point, connect the circumcenters of these adjacent triangles to obtain a Thiessen polygon. For the Thiessen polygon on the edge of the triangulation network, the vertical bisector can be intersected with the figure profile, and together with the figure profile form the Thiessen polygon.

As shown in Figure 2, the points to be predicted use symbols. To represent, record the coordinates (x _j , y _j ) of the prediction point used;

Using the known coordinates and signal strength of sampling points, a set of data {(h ₀ ,γ(h ₀ )), (h ₁ ,γ(h ₁ )),...(h _m ,γ(h _m ))}, select the spherical model, exponential model, and Gaussian model for fitting respectively, and obtain the fitting functions γ _s (h), γ _e (h), and γ _g (h). Taking the spherical model as an example, substitute γ _s (h) Simplify Equation 9.

make Solve a system of linear equations in quaternions:

λ ₁ ＝(2*a*μ-3*μ+2*b*μ+2*c*μ+a^2*μ+b^2*μ+c^2*μ+a^2+b^ 2+c^2-2*a*b*c-2*a*b*μ-2*a*c*μ-2*b*c*μ-1)/(a^2-2*a* b-2*a*c+2*a+b^2-2*b*c+2*b+c^2+2*c-3)

λ ₂ ＝(a+ba*cb*c+c^2-1)/(a^2-2*a*b-2*a*c+2*a+b^2-2*b*c+ 2*b+c^2+2*c-3)

λ ₃ ＝(a+ca*bb*c+b^2-1)/(a^2-2*a*b-2*a*c+2*a+b^2-2*b*c+ 2*b+c^2+2*c-3)

μ＝(b+c-a*b-a*c+a^2-1)/(a^2-2*a*b-2*a*c+2*a+b^2-2*b*c+2 *b+c^2+2*c-3)

Substitute the obtained weights λ _i and μ into Taking the J mean value of the first n points (n=9), the spherical model J=2.8218, the exponential model J=0.3827, and the Gaussian model J=0.0317.

Select the weight λ _i obtained by the Gaussian model, and substitute Then the signal strength of the prediction point can be obtained.

After using the above interpolation method to estimate the RSSI feature of each sampling point, first obtain the RSSI feature distribution from one of the signal sources, then follow the same steps to get the RSSI feature distribution of other signal sources, and finally superimpose these RSSI feature distributions, Stored in the form of a feature vector with each sampling point as a unit, the location fingerprint data at the current moment can be obtained.

Claims (3)

1. a kind of RSSI location fingerprint construction methods of Kriging regression based on Thiessen polygon, it is characterised in that the side Method comprises the following steps：

Step 1：Build Thiessen polygon；

1) triangulation network is built according to discrete point automatically, that is, builds Delaunay triangulation network, discrete point and the triangle formed are compiled Number, recording each triangle is made up of which three discrete point；

2) and then the numberings of all triangles adjacent with each discrete point is found out, and recorded；

3) pair triangle adjacent with each discrete point by sorting clockwise or counterclockwise；

4) the circumscribed circle center of circle of each triangle is calculated, and records its coordinate position；

5) according to the adjacent triangle of each discrete point, the circumscribed circle center of circle of these adjacent triangles is connected, that is, obtains Tyson many Side shape, for the Thiessen polygon of triangle network edge, can make perpendicular bisector and intersect with mapborder, Tyson be constituted together with mapborder many Side shape；

Step 2：RSSI Interpolate estimations；

Kriging regression is：

<mrow> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

Wherein R (z₀) it is interpolation point z₀RSSI value, λ_iFor sampled point z_iWeights, R (z_i) it is sampled point z_iRSSI value；

Assuming that signal attribute value meets second-order stationary in region, to arbitrfary point in region：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>E</mi> <mo>&amp;lsqb;</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>D</mi> <mo>&amp;lsqb;</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

(1) formula substitution (2) formula is obtained into constraints is：

<mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

Make unbiased esti-mator variance minimum：

<mrow> <mi>min</mi> <mo>{</mo> <mi>E</mi> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> <mo>-</mo> <mi>&amp;mu;</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>

(4) μ is Lagrange coefficient in formula, solves the parameter set μ, λ for making this cost function minimum₁,λ₂...λ_n, then can meet ItsEstimate variance is minimum under constraints；

OrderRespectively to μ, λ_iDerivation is：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mrow> <mo>(</mo> <mi>J</mi> <mo>-</mo> <mi>&amp;mu;</mi> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>J</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mrow> <mo>(</mo> <mi>J</mi> <mo>-</mo> <mi>&amp;mu;</mi> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <mi>J</mi> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>)</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

Golden weights equation group in asking for gram：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mi>&amp;mu;</mi> <mo>=</mo> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2...</mn> <mi>n</mi> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

Its matrix is expressed as：

<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>n</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mrow> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>n</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mo>...</mo> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;lambda;</mi> <mi>n</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>&amp;mu;</mi> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>z</mi> <mn>1</mn> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>n</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

Simplified expression：

C × ω=D

So its weights is：

ω=C^-1×D

Covariance is converted into the variation function for seeking space variable

Define variation function：

<mrow> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>E</mi> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> </mrow> <mn>2</mn> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

Whereinγ(z_i,z_j)=- Cov (z_i,z_j)(9)

It is by (9) formula substitution (6) formula：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>&amp;mu;</mi> <mo>=</mo> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>...</mo> <mi>n</mi> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

In actual applications, defined by the semivariance of formula (9), the value for calculating semivariance by following formula (11) is：

<mrow> <mi>&amp;gamma;</mi> <mrow> <mo>(</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>N</mi> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msup> <mrow> <mo>&amp;lsqb;</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>+</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>R</mi> <mrow> <mo>(</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

2. a kind of RSSI location fingerprints structure side of Kriging regression based on Thiessen polygon according to claim 1 Method, it is characterised in that known to methods described utilization (h, γ (h)), select suitable semivariance model to be fitted, selection is most The interpolation result of model corresponding to small unbiased esti-mator variance is used as final fingerprint database.

3. a kind of RSSI location fingerprints structure side of Kriging regression based on Thiessen polygon according to claim 1 Method, it is characterised in that methods described is obtained first after the RSSI features of each sampled point are estimated using above interpolation method To the RSSI feature distributions from one of signal source, the RSSI features of other signal sources are then obtained according to same step These RSSI feature distributions, are finally superimposed by distribution, are stored according to the characteristic vector form in units of each sampled point, just To the location fingerprint data at current time.