CN105430740A - Indoor wireless positioning method based on a WiFi signal intensity simulation and position fingerprint algorithm - Google Patents

Abstract

The invention relates to an indoor wireless positioning method based on a WiFi signal intensity simulation and position fingerprint algorithm. Indoor environment modeling is realized by firstly utilizing a ray tracking algorithm, and multi-path spreading locus is calculated; RanPlan iBuildNET software is then utilized to simulate field intensity superposition values of all rays of each reception point in a zone, a signal intensity distribution information graph is drafted, and a finger database is established; and matching positioning is carried out through the position finger algorithm. According to the method, the ray tracking algorithm and the position algorithm are combined organically, and positioning is realized through signal intensity equal height graph simulation. As shown in experiment results, on the conditions that the positioning function is realized and positioning precision reaches system performance requirements, operation steps of the position finger positioning algorithm are optimized to a certain degree, positioning time and manpower cost under the serious environment are not only saved, but also personal safety is further guaranteed.

Description

Based on the indoor wireless positioning method of WiFi signal Strength Simulation and location fingerprint algorithm

Technical field

The present invention relates to a kind of indoor wireless location algorithm based on WiFi signal Strength Simulation and location fingerprint algorithm, by ray tracing algorithm and location fingerprint algorithm are organically combined, design a kind of location fingerprint indoor wireless location algorithm can exempting off-line training step, belong to the association area that the indoor wireless location algorithm based on WiFi signal intensity is studied.

Background technology

For the LBS (user location services) of heavy dependence user exact position, based on the localization method great potential of WiFi signal intensity.The method can utilize the existing network facilities, and existing equipment adds corresponding software function, can be applied to indoor, can be applied to outdoor occasion again, and little by geographical environment restriction, without the need to increasing hardware, lower deployment cost is low, low in energy consumption.So far, the localization method based on WiFi signal intensity is mainly divided into two large classes: location fingerprint positioning mode, based on the method for wireless signal propagation model (or location, three limits).Many colleges and universities and research institution have carried out comparatively deeply this field and have studied widely, and the fruitful achievement of some of them comprises: the systems such as RADAR, Horus, Mole, EPE, SkyhookWireless.These system major parts all reach certain positioning precision, but respective range of application receives certain restriction: as RADAR, Horus system, and its algorithm too complicated (as Mole, EPE system), can not meet the needs of quick position.Therefore, current LBS field needs one both to average out in computation complexity and positioning precision two, can meet again the novel localization method of various location occasion.

Indoor Position Techniques Based on Location Fingerprint is the important technology in indoor wireless positioning field, it has that precision is high, strong robustness and the feature such as easy to operate, and do not need extra hardware facility, cheap, the existing WiFi router disposed can be utilized to position, be extensively subject to the welcome of numerous researcher and user.The realization of location fingerprint location algorithm is generally divided into two stages: off-line training step and on-line testing stage.The main purpose of off-line training step is image data, set up location fingerprint database, its detailed process is: first determine reference point RP in area to be targeted, then on each RP, measure the RSS signal from each AP, namely all accessible AP signal strength informations are gathered, and by the signal characteristic of RSS signal stored in fingerprint base.Physical location due to RP is known, and the location fingerprint database set up like this is be mutually related in physical space and signal space.The on-line testing stage, user also claims test point (TP in site undetermined, TestPoint) place uses the same method and measures from the RSS signal of each AP, then this information is uploaded in location-server, the RSS information received is mated with the location fingerprint information in fingerprint base according to certain search matching algorithm by location-server, obtain the position of user and this positioning result is passed to user, thus completing whole position fixing process.

But blemish in an otherwise perfect thing is, the method needs the Received signal strength characteristic information gathering each reference point in area to be targeted in advance, so not only can at substantial manpower and materials, and when in the face of accident (such as fire or earthquake), due to bad environments, be pressed for time, cannot set up fast and cannot set up location fingerprint storehouse even at all, thus whole navigation system is paralysed, cannot normally work.

Ray casting is a kind of prediction algorithm of comparative maturity, and it passes through the velocity of wave of given launch point and acceptance point position and medium, solves the ray tracing from launch point to acceptance point and tendency (time that signal is propagated) thereof.Since the end of the eighties, along with Kirch2hoff integration pre-stack depth migration obtains a series of success in solution engineering construction system problem, ray-tracing procedure as one of its algorithm basis have also been obtained very large promotion and development, has occurred the New Algorithm being different from conventional method in a large number.The refraction of these algorithms mainly based on Snell is theoretical, Huygens principle and Fermat theoretical, analysis is carried out to ray and obtains earthquake wave trajectory.Existing method can be divided into the local ray tracing law theory being extrapolated for basis with pointwise, and with global analysis, check overall ray casting into starting point.

Summary of the invention

In order to exempt heavy off-line training step task, WiFi signal Strength Simulation and location fingerprint algorithm have been carried out organic combination by the present invention, under the condition of known building structure, the modeling of indoor propagation environment is carried out by ray tracing algorithm, predictive simulation goes out the distribution map of each acceptance point signal strength intensity (WLAN signal) indoor, emulation intensity level is imported fingerprint base as AP characteristic information label and completes foundation, thus binding site fingerprinting localization algorithm positions.

Main purpose of the present invention is the burdensome task replacing off-line training step with off-lined signal Strength Simulation, when not in advance target approach region realize indoor wireless location.For achieving the above object, the technical solution used in the present invention is: first utilize ray tracing algorithm to indoor environment modeling, by carrying out propagation path tracking to every bar ray, calculates its multipath transmisstion track; Then use RanPlaniBuildNET software emulation to go out the field intensity superposition value of all rays of each acceptance point in region, thus draw out the distributed intelligence of signal strength signal intensity, set up fingerprint base; Coupling location is carried out finally by location fingerprint algorithm.

The technical solution adopted in the present invention comprises the following steps:

Step 1, utilizes ray tracing algorithm to indoor environment modeling.

The present invention selects the bikini equation of plane $\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0,$ Whole region is made up of two horizontal planes and several vertical planes, in order to determine the coefficient of horizontal plane and vertical plane, chooses arbitrarily 3 point (x respectively in each plane ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x ₃, y ₃, z ₃), bring the coordinate of each point into plane bikini equation, composition 3 × 3 determinants, make it solve x, y, z coefficient separately, are finally expressed as the general equation Ax+By+Cz+D=0 (A of plane ²+ B ²+ C ²≠ 0), calculation procedure is as follows:

First planar get arbitrarily 3 points, its coordinate is substituting to plane bikini equation $\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0,$ Then by determinant decomposition computation $\⇒\left\{\begin{array}{c}(x-x_1)\[(y_2-y_1)(z_3-z_1)-(z_2-z_1)(y_3-y_1)\]\\ -(y-y_1)\[(x_2-x_1)(z_3-z_1)-(z_2-z_1)(x_3-x_1)\]\\ +(z-z_1)\[(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\]\end{array}\right\},$ Equation coefficient A, B, C, D show the most at last $\⇒Ax+By+Cz+D=0\⇒\left\{\begin{array}{c}A=(y_2-y_1)(z_3-z_1)-(z_2-z_1)(y_3-y_1)\\ B=(z_2-z_1)(x_3-x_1)-(x_2-x_1)(z_3-z_1)\\ C=(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\\ D=x_1\[(z_2-z_1)(y_3-y_1)-(y_2-y_1)(z_3-z_1)\]\\ +y_1\[(x_2-x_1)(z_3-z_1)-(z_2-z_1)(x_3-x_1)\]\\ -z_1\[(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\]\end{array}\right.$

One by one the concrete equation of all horizontal planes and vertical plane and the domain of definition are showed by the method, form Indoor environment solid geometric pattern.

Step 2, by carrying out propagation path tracking to every bar ray, calculates its multipath transmisstion track.

Geometric optical theory shows, indoor environment radio wave propagation mode is mainly divided into direct projection, reflection and diffraction, and wherein diffraction has again several situations such as smooth surface diffraction, summit diffraction and wedge diffraction.

The propagation path of this several circulation way has and respective solves rule.Wherein, direct projection is exactly the visual pathways of point-to-point transmission, connects at 2; Reflection is exactly electric wave in propagation distance, runs into the stop of a smooth surface, changes the direction of propagation, and the angle of reflection of reflected wave requires equal with the incidence angle of incident wave.In this article, the reflection of mainly building walls is reflected.

According to geometric theory of diffraction (GTD), diffraction be exactly electric wave in communication process, when running into the summit of barrier, wedge, convex surface, a ray will produce without the different ray in several directions.This scene is called diffraction phenomenon.Mainly be divided into smooth surface diffraction, summit diffraction and wedge diffraction.

It is pointed out that in these three kinds of diffraction, the energy attenuation of smooth surface diffraction and summit diffraction is quickly, very little on the impact of final result of calculation, does not generally consider in research.Therefore in this article, we only consider wedge diffraction.

Document proposes a kind of multipath propagation paths computational methods based on ray trace inverse algorithms.For this experimental situation, because body of wall is thick and heavy, transmission loss is very large, and signal strength signal intensity amplitude attenuation is serious, so we ignore transmission propagate the impact brought, and only considers the multipath transmisstion sight of direct projection, reflection, diffraction.In this article, consider the attenuation degree in radio signal propagation process, we only consider that direct projection, primary event and secondary reflection, a diffraction and second time diffraction, primary event and a diffraction combine this several multipath transmisstion state.Wherein diffraction only considers wedge diffraction.

When carrying out propagation forecast with ray tracking method, the field intensity of acceptance point is exactly all rays through acceptance point superposition sum.May be direct path, reflection path, diffraction path in every bar ray path, also may be the mixed path of direct projection, reflection, diffraction.After route searching completes, we just can carry out the calculating of field intensity according to all propagation paths of gained.According to the difference in path, calculating is divided into direct projection field intensity, reflection field intensity and diffraction field intensity three parts by us.

Be the total field intensity expression formula of received field point below:

E _total＝∑E _x

$E_x={\mathrm{xG}}_{tx}{G}_{rx}{L}_x\left(n\right)\underset{y}{\Π}\stackrel{\‾}{R}\left({\mathrm{\θ}}_{yx}\right)\underset{z}{\Π}\stackrel{\‾}{D}\left({\mathrm{\φ}}_{zx}\right)E_0$

E in above formula _xfor xth bar ray is at the electric field intensity of acceptance point; E ₀for launching electric field vector; L _x(n) be xth bar ray arrive acceptance point through the decay of path n at free space; for the reflection coefficient of xth article ray y secondary reflection, incidence angle is θ _yx; for the diffraction coefficient of xth article ray the z time diffraction, incidence angle is φ _zx; G _txand G _rxthe gain of transmitting antenna and reception antenna respectively.

Step 3, uses RanPlaniBuildNET software emulation to go out the field intensity superposition value of all rays of each acceptance point in region.

The basic thought carrying out signal strength signal intensity emulation is: ray sends from the signal source point of fixed position, and launch the ray of certain number to free space all directions with fixing angle step, follow the tracks of the propagation path of every bar ray, and calculate ray run into barrier produce reflection, diffraction, transmission ray propagates path, according to a upper joint, the present invention only consider direct projection, once with secondary reflection, once with the propagation condition such as second time diffraction and a primary event diffraction.According to Fresnel equation and geometrical diffraction theory/consistency diffraction theory etc., determine reflection, diffraction and transmission loss, determine every bar ray its can be passed through field intensity size a little, the field intensity that last coherent superposition many rays produce at pilot place to be measured.Launch some rays with a discrete angular increment to space all directions from transmitting terminal, follow the trail of each bar ray, each ray is relatively independent, calculating based on each acceptance point, instead of based on ray.Therefore the amount of calculation of this algorithm is proportional to reflection, diffraction counts and receive and count, and is inversely proportional to the increment of divergent-ray angle.The method also has shortcoming, determines as angle step is bad, and too large angle step easily makes some acceptance points because not receiving reflection, diffracted signal and being left in the basket, and too little angle component turn increases amount of calculation.

According to the inverse algorithms of above-mentioned ray tracing algorithm, the field intensity of continuous space any point can be calculated, and need in practical application to carry out analog computation by computer, realize the algorithm of ray trace in software based on spatial discretization principle, specifically can be completed by following 5 steps.

1. add up interior of building geographic information data

2. three-dimensional path search

3. can the calculating of sighting distance (LOS, LineofSight) ray field intensity

4. non-can the calculating of sighting distance (NLOS) ray field intensity

5. the field intensity of each bar ray generation of superposition

Use RanPlaniBuildNET software to calculate the field intensity of continuous space any point, field intensity resolution is set to 5 meters.

Step 4, carries out coupling location by location fingerprint algorithm.

The present invention uses weighting k-nearest neighbor (WKNN, WeightedKNearestNeighbour) weighting k-nearest neighbor to add weight factor at coupling positioning stage, is used for weighing the percentage contribution that different Neighbor Points positions test point.Generally, the physical location of Neighbor Points and test point is nearer, and it is larger to the percentage contribution of location, and weight factor is also larger.

Try to achieve the distance D of different reference point and test point, relatively and choose the reference point that wherein K minimum value is corresponding, then the coordinate of test point can be calculated by following formula.

$(x,y)=\underset{i=1}{\overset{K}{\Σ}}{w}_i(x_i,y_i)$

Wherein, w _irepresent the weight factor of i-th reference point in position fixing process.Work as w _iget identical value, i.e. w _iduring=1/k, all Neighbor Points are identical for the contribution of location, and weighting k-nearest neighbor is k-nearest neighbor.Intuitively it seems, w _ivalue depend on the Euclidean distance of RSS between reference point and test point, i.e. D value.Have the reference point of minimum D value, its percentage contribution for location is maximum, and weight factor is maximum.And there is the reference point of maximum D value, its percentage contribution for location is minimum, and weight factor is minimum.Therefore, w _icomputing formula as follows:

$w_i=\frac{1/D_i^2}{\underset{i=1}{\overset{K}{\Σ}}1/D_i^2}$

Logical decision filter is used to carry out filtering to signal strength signal intensity original sample value:

The signal strength values about this focus that the signal strength values about this focus that near label of distance focus the stores reference label far away than distance focus stores is large, if there is the phenomenon contrary with the above results, automatically this part sampled result is rejected, positioned by sampled result next time;

And amplitude limiting processing is carried out to the raw signal strength received, amplitude is limited in-80dB.

Accompanying drawing explanation

Fig. 1, single reflection path schematic diagram.

Fig. 2, secondary reflection path schematic diagram.

Fig. 3, a diffraction propagation path profile.

Fig. 4, second time diffraction propagation path figure.

Fig. 5, a diffraction single-hop propagation path profile.

Fig. 6, the reflection of curved surface.

Fig. 7, the reflection of two planes.

Fig. 8, ray-traced travel model.

Fig. 9, position error is added up.

Figure 10, deviation accumulation probability distribution CDF scheme.

Embodiment

Step 1, utilizes ray tracing algorithm to indoor environment modeling.

The expression-form of plane equation has following four kinds usually:

Point French: A (x-x ₀)+B (y-y ₀)+C (z-z ₀)=0, wherein m ₀(x ₀, y ₀, z ₀)

General equation: Ax+By+Cz+D=0 (A ²+ B ²+ C ²≠ 0)

Intercept form equation: $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1(abc\≠0)$

Bikini: $\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0$

The present invention selects the bikini equation of plane $\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0,$ Whole region is made up of two horizontal planes and several vertical planes, in order to determine the coefficient of horizontal plane and vertical plane, chooses arbitrarily 3 point (x respectively in each plane ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x ₃, y ₃, z ₃), bring the coordinate of each point into plane bikini equation, composition 3 × 3 determinants, make it solve x, y, z coefficient separately, are finally expressed as the general equation Ax+By+Cz+D=0 (A of plane ²+ B ²+ C ²≠ 0), calculation procedure is as follows:

First planar get arbitrarily 3 points, its coordinate is substituting to plane bikini equation $\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0,$ Then by determinant decomposition computation $\⇒\left\{\begin{array}{c}(x-x_1)\[(y_2-y_1)(z_3-z_1)-(z_2-z_1)(y_3-y_1)\]\\ -(y-y_1)\[(x_2-x_1)(z_3-z_1)-(z_2-z_1)(x_3-x_1)\]\\ +(z-z_1)\[(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\]\end{array}\right\},$ Equation coefficient A, B, C, D show the most at last $\⇒Ax+By+Cz+D=0\⇒\left\{\begin{array}{c}A=(y_2-y_1)(z_3-z_1)-(z_2-z_1)(y_3-y_1)\\ B=(z_2-z_1)(x_3-x_1)-(x_2-x_1)(z_3-z_1)\\ C=(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\\ D=x_1\[(z_2-z_1)(y_3-y_1)-(y_2-y_1)(z_3-z_1)\]\\ +y_1\[(x_2-x_1)(z_3-z_1)-(z_2-z_1)(x_3-x_1)\]\\ -z_1\[(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\]\end{array}\right.$

One by one the concrete equation of all horizontal planes and vertical plane and the domain of definition are showed by the method, form Indoor environment solid geometric pattern.

The material map that architectural drawing marks is carried out equivalent process in a self contained data base, once there is the material do not had in database, be equivalent to immediate other materials according to test experience or body of wall geological information, such as, thick KT plate decoration be equivalent to veneer etc.Such operation can be avoided occurring mistake to a certain extent in modeling process, causes fingerprint base error.

Step 2, by carrying out propagation path tracking to every bar ray, calculates its multipath transmisstion track.

Step 2.1, set up divergent-ray equation:

The present invention using omni-directional antenna as signal source.Omni-directional antenna, namely in the horizontal direction figure shows as 360 ° of homogeneous radiations, namely said without concrete transmit direction, in the vertical direction figure shows as the wave beam of one fixed width, generally lobe width is less, and gain is larger.

After signal source is opened, the to all the winds ray of the some numbers of uniform emission, the emission angle interval of often pair of adjacent ray is certain, is passed to each point that can cover in whole region through direct projection, reflection, transmission and diffraction.Ray equation can be regarded as the linear equation in space, the divergent-ray position of starting point residing for signal source, terminal be this ray in indoor after direct projection, reflection, transmission and diffraction propagation, the position (if do not receive the signal strength values of certain emission source in certain position, this place being described not in its coverage) of signal strength signal intensity minimum value can be received.

The equation of space line has following several usually:

General equation: space line L can regard two plane π as ₁and π ₂intersection.Following equation group is called the general equation of space line:

$\left\{\begin{array}{c}{A}_{1}x+B_{1}y+C_{1}z+D_1=0\\ A_{2}x+B_{2}y+C_{2}z+D_2=0\end{array}\right.$

Symmetrical expression equation a: if non-vanishing vector is parallel to a known straight line, this vector is just referred to as the direction vector of this straight line.Obviously, any vector on straight line is all parallel to the direction vector of straight line.

Cross space a bit can do and a known straight line can only be parallel to as straight line, therefore, as the M of on straight line L ₀(x ₀, y ₀, z ₀) and its direction vector after given, the position of space line L has just been decided completely.

If M (x, y, z) is any point on straight line L, then and

Therefore conversely, as fruit dot M not on the linel, then with not parallel, thus above formula is false.Therefore, above equation group is exactly the equation of straight line L.This equation is claimed to be the symmetrical expression equation of straight line.

Parametric equation: the either direction vector of straight line coordinate m, n, p are called one group of direction number of this straight line, and its direction cosines are called the direction cosines of this straight line.

As established $\frac{x-x_0}{m}=\frac{y-y_0}{n}=\frac{z-z_0}{p}=t,$ Then $\left\{\begin{array}{c}x=x_0+mt\\ y=y_0+nt\\ z=z_0+pt\end{array}\right.,$ This equation group is called the parametric equation of straight line.

Used herein is the parametric equation of straight line $\frac{x-x_0}{m}=\frac{y-y_0}{n}=\frac{z-z_0}{p}=t,\left\{\begin{array}{c}x=x_0+mt\\ y=y_0+nt\\ z=z_0+pt\end{array}\right.$

As the equation of ray, point (x ₀, y ₀, z ₀) be emission source position coordinate, the direction vector of ray for the emission angle of ray.

Step 2.2, multipath transmisstion approach calculates

(1). direct path calculates

The principle of direct path search is by source point T _xwith field point R _xconnect, if do not have barrier between line, then direct path exists; Otherwise, there is not direct path.The validation verification of direct path is as follows:

Judge to connect source point T _xwith field point R _xin the straight line obtained and scene, whether all metopes have intersection point, if there is intersection point, obtain the coordinate of intersection point P; Otherwise, prove T _xwith R _xbetween do not have barrier to block, show that direct path exists.If more than judge to there is intersection point P, also need the validity proving this intersection point further: verify whether this intersecting point coordinate is positioned at source point T _xwith field point R _xbetween, if so, then prove to there is barrier between source point and field point, direct path does not exist, otherwise this intersection point is positioned at outside source point and the field point line segment that is two-end-point, then do not have barrier between them, be visible, then there is direct path.

(2). reflection path calculates

Single reflection path:

Known source point T _xwith field point R _x, based on image theory, single reflection path step is:

Make source point T _xabout face S ₁mirror point T _x ¹; Connect T _x ¹, R _xhand over planar S ₁in a F ₁; Judge pip F ₁validity (whether meeting following three conditions); F ₁be positioned at mirror point T _x ¹with field point R _xbetween; F ₁be positioned at planar S ₁interior (on four edges, otherwise can not can there is wedge diffraction); Source point T _xto pip F ₁, pip F ₁to field point R _xbetween all clear block.If pip checking effectively, then T _x---F ₁---R _xit is an effective single reflection path; Visible planar all between traversal source point and field point, according to ray emission angle, repeats above institute in steps, finds all single reflection paths.

Secondary reflection path: known source point T _xwith field point R _x, based on image theory, secondary reflection path step is:

Make source point T _xabout face S ₁mirror point T _x ¹, remake mirror point T _x ¹about face S ₂mirror point T _x ²; Connect T _x ¹, F ₂hand over planar S ₁in a F ₁; Connect T _x ², R _xhand over planar S ₂in a F ₂; Judge pip F ₁, F ₂validity (whether meeting following three conditions); Primary event point F ₁be positioned at mirror point T _x ¹with secondary counter exit point F ₂between, secondary counter exit point F ₂be positioned at mirror point T _x ²with field point R _xbetween; Primary event point F ₁be positioned at planar S ₁in, secondary counter exit point F ₂be positioned at planar S ₂interior (on four edges, otherwise can not can there is wedge diffraction); Source point T _xto primary event point F ₁, primary event point F ₁to secondary counter exit point F ₂, secondary counter exit point F ₂to field point R _xbetween all clear block.If pip checking effectively, then T _x---F ₁---F ₂---R _xit is an effective secondary reflection path; Visible planar all between traversal source point and field point, according to ray emission angle, repeats above institute in steps, finds all secondary reflection paths.

(3). diffraction path computing

In this indoor environment, the height of dual-mode antenna is mostly lower than barriers such as surrounding wall, cupboard, door and windows, and the amount of radiation that electric wave arrives acceptance point through barrier top diffraction seldom and to arrive intensity very little.Therefore, ignore the diffraction effect of top of building herein, and only consider the diffraction of vertical wedge.

A diffraction path:

Known source point T _xwith field point R _xas a diffraction propagation path, based on consistency diffraction theory, one time diffraction path step is:

According to Keller edge diffraction law, ∠ T _xb ₁a ₁=∠ R _xb ₁c ₁, therefore the plane of incidence and diffraction face 1 are deployed in a plane, and as one time, diffraction launches shown in schematic diagram, if known source point coordinate T _x(x _t, y _t, z _t) and field point coordinates R _x(x _r, y _r, z _r), and vertical wedge A ₁c ₁on coordinate is known, then Diffraction Point B ₁coordinate solution formula be:

$\[x_{B_1},y_{B_1},z_r+(z_t-z_r)\frac{\sqrt{{(x_{B_1}-x_r)}^2+{(y_{B_1}-y_r)}^2}}{\sqrt{{(x_t-x_{B_1})}^2+{(y_t-y_{B_1})}^2}+\sqrt{{(x_{B_1}-x_r)}^2+{(y_{B_1}-y_r)}^2}}\]$

Judge Diffraction Point B ₁validity (whether following two conditions meet simultaneously): B ₁at line segment A ₁c ₁on; Source point T _xto Diffraction Point B ₁, Diffraction Point B ₁to field point R _xbetween all clear block.If Diffraction Point checking effectively, then T _x---B ₁---R _xit is an effective diffraction path; Traversal source point and visual vertical wedges all between the point of field, according to ray emission angle, repeat above institute in steps, find all diffraction paths.

Second time diffraction path:

Known source point T _xwith field point R _xas second time diffraction propagation path, second time diffraction path step is:

According to Keller edge diffraction law, ∠ T _xb ₁a ₁=∠ B ₂b ₁c ₁, ∠ B ₁b ₂a ₂=∠ R _xb ₂c ₂, therefore the plane of incidence, diffraction face 1 and diffraction face 2 are deployed in a plane, as second time diffraction launches shown in schematic diagram, if known source point coordinate T _x(x _t, y _t, z _t) and field point coordinates R _x(x _r, y _r, z _r), and each vertical wedge A ₁c ₁, A ₂c ₂on with coordinate is known, then Diffraction Point B ₁and B ₂coordinate solution formula be:

B ₁：

$\[x_{B_1},y_{B_1},z_r+(z_t-z_r)\frac{\sqrt{{(x_{B_1}-x_r)}^2+{(y_{B_1}-y_r)}^2}}{\sqrt{{(x_t-x_{B_1})}^2+{(y_t-y_{B_1})}^2}+\sqrt{{(x_{B_1}-x_r)}^2+{(y_{B_1}-y_r)}^2}}\]$

B ₂：

$\left[\begin{array}{c}{x}_{B_2},y_{B_2},z_r+(z_t-z_r)\frac{\sqrt{{(x_{B_1}-x_{B_2})}^2+{(y_{B_1}-y_{B_2})}^2}+\sqrt{{(x_{B_2}-x_r)}^2+{(y_{B_2}-y_r)}^2}}{\sqrt{{(x_t-x_{B_1})}^2+{(y_t-y_{B_1})}^2}+\sqrt{{(x_{B_1}-x_{B_2})}^2+{(y_{B_1}-y_{B_2})}^2}}\\ +\sqrt{{(x_{B_2}-x_r)}^2+{(y_{B_2}-y_r)}^2}\end{array}\right]$

Judge Diffraction Point B ₁and B ₂validity (whether following two conditions meet simultaneously): B ₁at line segment A ₁c ₁on, B ₂at line segment A ₂c ₂on; Source point T _xto Diffraction Point B ₁, Diffraction Point B ₁to Diffraction Point B ₂, Diffraction Point B ₂to field point R _xbetween all clear block.If two Diffraction Point checkings are all effective, then T _x---B ₁---B ₂---R _xit is an effective second time diffraction path; Traversal source point and visual vertical wedges all between the point of field, according to ray emission angle, repeat above institute in steps, find all second time diffraction paths.

(4). the search of reflection diffraction mixed path

The track-while-scan relative complex of reflection diffraction mixed path, herein to reflect the situation that a diffraction shown in diffraction mixed path schematic diagram 4-6 adds primary event, introduce the searching method of reflection diffraction mixed path, concrete steps are:

Make field point R _xabout the mirror point R of reflecting surface S _x1; According to Keller edge diffraction law, ∠ R _x1b ₁a ₁=∠ T _xb ₁c ₁, therefore the plane of incidence and diffraction face are deployed in a plane, as a diffraction primary event launches shown in schematic diagram, if known source point coordinate T _x(x _t, y _t, z _t) and R _xmirror point coordinate R _x1(x _r1, y _r1, z _r1), and vertical wedge A ₁c ₁on coordinate known, then A ₁c ₁upper Diffraction Point B ₁coordinate solution formula be:

$\[x_{B_1},y_{B_1},(z_{r1}-z_t)\frac{\sqrt{{(x_{B_1}-x_t)}^2+{(y_{B_1}-y_t)}^2}}{\sqrt{{(x_{B_1}-x_t)}^2+{(y_{B_1}-y_t)}^2}+\sqrt{{(x_{r1}-x_{B_1})}^2+{(y_{r1}-y_{B_1})}^2}}\]$

Judge Diffraction Point B ₁validity (whether simultaneously meeting following two conditions): B ₁at line segment A ₁c ₁on; R _x1---B ₁between (not comprising reflecting surface S), B ₁---T _xbetween all block without building.If Diffraction Point B ₁checking effectively, connects B ₁, R _x1hand over planar S in a R1; Judge pip R1 validity (whether simultaneously meeting following three conditions): R1 is positioned at R _x1with B ₁between; R1 is positioned at planar S effective coverage (on four edges, otherwise wedge diffraction can not can occur); R _x---block without building between R1.If R1 also verifies effectively, then T _x---B ₁---R1---R _xbe that an effective diffraction adds single reflection path; Traversal source point and all visual vertical wedges and visible planar between the point of field, according to ray emission angle, repeat above institute in steps, find an all diffraction to add single reflection path.

Step 3, uses RanPlaniBuildNET software emulation to go out the field intensity superposition value of all rays of each acceptance point in region.

4. test point signal strength superposition calculation

When carrying out propagation forecast with ray tracking method, the field intensity of acceptance point is exactly all rays through acceptance point superposition sum.May be direct path, reflection path, diffraction path in every bar ray path, also may be the mixed path of direct projection, reflection, diffraction.After route searching completes, we just can carry out the calculating of field intensity according to all propagation paths of gained.According to the difference in path, calculating is divided into direct projection field intensity, reflection field intensity and diffraction field intensity three parts by us.

Be the total field intensity expression formula (4-13) of received field point below:

E _total＝∑E _x

$E_x={\mathrm{xG}}_{tx}{G}_{rx}{L}_x\left(n\right)\underset{y}{\Π}\stackrel{\‾}{R}\left({\mathrm{\θ}}_{yx}\right)\underset{z}{\Π}\stackrel{\‾}{D}\left({\mathrm{\φ}}_{zx}\right)E_0$

E in above formula _xfor xth bar ray is at the electric field intensity of acceptance point; E ₀for launching electric field vector; L _x(n) be xth bar ray arrive acceptance point through the decay of path n at free space; for the reflection coefficient of xth article ray y secondary reflection, incidence angle is θ _yx; for the diffraction coefficient of xth article ray the z time diffraction, incidence angle is φ _zx; G _txand G _rxthe gain of transmitting antenna and reception antenna respectively.

(1). direct projection ray field intensity calculates

As second chapter mistake, free space direct projection ray field intensity is as follows:

In theory, wireless signal is when clear and noiseless spatial, and receiving terminal received power can represent by following mathematical expression:

$P_r\left(d\right)=\frac{P_t{G}_t{G}_r{\mathrm{\λ}}^2}{{\left(4\mathrm{\π}\right)}^2{d}^2\mathrm{\γ}}$

Wherein P _tbase station's transmission power, P _rd () is receiving terminal received power, G _ttransmitting terminal antenna gain, G _rbe receiving terminal antenna gain, γ is propagated loss index, and the material with Environment Obstacles thing changes and changes.λ is the wavelength of transmission wave, and d is the distance between receiving terminal and transmitting terminal.

Under free space, namely do not have barrier for infinitely-great vacuum environment around antenna, be in desirable propagation conditions, now propagation loss formula is:

PL(d) _[dB]＝20·lg(f)+20·lg(d)+32.4

Wherein f is the transmission frequency of transmission wave.

(2). indirect ray field intensity calculates

Reflection due to curved surface is present in studied environment in a large number, and therefore the situation of camber reflection is here mainly discussed.Arbitrary surface z=f (x, y), source point is positioned at S (x ₁, y ₁, z ₁), incident ray, via 1 R (x, y, z) on curved surface, reflects Receiving yaxd point F (x ₂, y ₂, z ₂), reflection total optical path s is:

$s=s_1+s_2=\sqrt{{(x-x_1)}^2+{(y-y_1)}^2+{(z-z_1)}^2}+\sqrt{{(x-x_2)}^2+{(y-y_2)}^2+{(z-z_2)}^2}$

According to Fermat's theorem, can be obtained the position R (x, y, z) of pip by above formula, if reflecting surface is plane, above formula has analytic solutions.

If during z=0, S be (0,0, z), the coordinate of pip can be obtained:

$(x,y,z)=(\frac{x_1{s}_2+x_2{s}_1}{s_1+s_2},\frac{y_1{s}_2+y_2{s}_1}{s_1+s_2},0)$

The pip of above formula is the mirror point of source point and the line of field point and the intersection point of reflecting surface.According to reflection law, just this result can be obtained.If reflection is made up of two or more plane, also can by this problem of this analytical method solving.

The reflection case that two planes form, source point S (x ₁, y ₁) corresponding to the mirror point F (x in face 1 ₂, y ₂) pip in face 1 can be obtained.

In addition, the ray reflecting through face 1 and reflect through face 2, can correspond to the mirror point S in face 1 by source point ₁mirror point S on face 2 ₂obtain the pip on face 2.According to geometrical relationship, known R ₂s ₂the intersection point in F and face 2, and R ₁then R ₂s ₁with the intersection point in face 1.

For the calculating of field point F, need first to calculate the field E at pip R place ⁱ(R), so calculate through face 1 reflect after electromagnetic field E ^r(R), then must show up the last field E at a F place ^r(F):

E ^r(F)＝E ⁱ(s)As(s ₁)RAs(s ₂)exp[jk(s ₁+s ₂)]

E ⁱs initial electric field that () is incident electromagnetic wave, As (s ₁) be diffusion coefficient electromagnetic between source point and pip, As (s ₂) for pip show up a little between electromagnetic diffusion coefficient; R is reflection coefficient matrix:

$R=\left[\begin{array}{cc}{R}_{\mathrm{\α}\mathrm{\α}}& R_{\mathrm{\α}\mathrm{\β}}\\ R_{\mathrm{\β}\mathrm{\α}}& R_{\mathrm{\β}\mathrm{\β}}\end{array}\right]$

$R_{\mathrm{\α}\mathrm{\α}}=R_{\⊥}=\frac{{\mathrm{cos\θ}}_i-\sqrt{{\mathrm{\ϵ}}_2/{\mathrm{\ϵ}}_1-{\sin }^2{\mathrm{\θ}}_i}}{{\mathrm{cos\θ}}_i+\sqrt{{\mathrm{\ϵ}}_2/{\mathrm{\ϵ}}_1-{\sin }^2{\mathrm{\θ}}_i}}$

$R_{\mathrm{\β}\mathrm{\β}}=R_{\left|\right|}=\frac{{\mathrm{\ϵ}}_2/{\mathrm{\ϵ}}_1{\mathrm{cos\θ}}_i-\sqrt{{\mathrm{\ϵ}}_2/{\mathrm{\ϵ}}_1-{\sin }^2{\mathrm{\θ}}_i}}{{\mathrm{\ϵ}}_2/{\mathrm{\ϵ}}_1{\mathrm{cos\θ}}_i+\sqrt{{\mathrm{\ϵ}}_2/{\mathrm{\ϵ}}_1-{\sin }^2{\mathrm{\θ}}_i}}$

R _αβ＝R _βα＝0

In formula, θ _ifor the incidence angle of ray, ε=ε _r-j60 σ λ, ε _rfor medium relative dielectric constant, σ is medium conductance.

(3). diffraction ray field intensity calculates

Run into edge or the tip of scattering object once electromagnetic wave, ray phenomenon will be produced.Geometric theory of diffraction, based on the Fermat's principle promoted, obtains corresponding diffraction law, thus can utilize this law to define and calculate diffraction field ^[67].

Edge diffraction law can be defined as: in homogeneous medium, and diffraction ray is equal with the angle of edge (tangent line) with incident ray with the angle of edge (tangent line).

What main consideration was made up of two planes below directly splits edge diffraction situation.

υ is the interior angle split, and with the edge split for z-axis, x-axis is positioned in the plane of splitting, s ₁for source point is to the distance of Diffraction Point, s ₂for the distance of Diffraction Point is put in field.At Diffraction Point D place, diffraction field initial value can be designated as:

E ^d(D)＝D·E ⁱ(D)

In above formula, incident wave is E the last script holder at D place ⁱ(D), D is called diffraction matrix.In ray basis coordinates system, D is the matrix of 2 × 2.According to above formula, the field account form of field point F is as follows:

E ^d(F)＝E ^d(D)A _d(s ₂)exp(jks ₂)

Diffraction Point between showing up a little electromagnetic diffusion coefficient be A _d(s ₂), can be expressed as: s ₂for the distance that Diffraction Point is shown up a little, next the calculating of diffraction coefficient D is discussed.

By plane of incidence and diffraction plane generate plane, E ⁱ(D) end, in-field, Diffraction Point place value is expressed as, E ^d(D) diffraction field initial value is expressed as:

$E^i\left(D\right)={\widehat{\mathrm{\α}}}_1{E}_{\mathrm{\α}}^i+{\widehat{\mathrm{\β}}}_1{E}_{\mathrm{\β}}^i=\left[\begin{array}{c}{E}_{\mathrm{\α}}^i\\ E_{\mathrm{\β}}^i\end{array}\right]$

$E^d\left(D\right)={\widehat{\mathrm{\α}}}_1{E}_{\mathrm{\α}}^d+{\widehat{\mathrm{\β}}}_1{E}_{\mathrm{\β}}^d=\left[\begin{array}{c}{E}_{\mathrm{\α}}^d\\ E_{\mathrm{\β}}^d\end{array}\right]$

D is now 2 × 2 matrixes.

$D=\left[\begin{array}{cc}{D}_{\mathrm{\α}\mathrm{\α}}& D_{\mathrm{\α}\mathrm{\β}}\\ D_{\mathrm{\β}\mathrm{\α}}& D_{\mathrm{\β}\mathrm{\β}}\end{array}\right]=-\left[\begin{array}{cc}{D}_e& 0\\ 0& D_m\end{array}\right]$

The orthogonal polarization diffraction coefficient of electric field is designated as D _e=D _{α α}; Meanwhile, the horizontal polarization diffraction coefficient of electric field is designated as D _m=D _{β β}.Cross polarization coefficient D _{α β}=D _{β α}=0 represents along the axial diffraction of α and β.

D can be provided by consistency geometric theory of diffraction _eand D _mcomputing formula as follows, in formula, the physical significance of each parameter is as follows.

$D^{e,m}=D_1+D_2+R_n^{e,m}{D}_3+R_0^{e,m}{D}_4$

In above formula:

$D_1(L,\mathrm{\φ},{\mathrm{\φ}}^{\′},{\mathrm{\β}}_0,n)=-\frac{e^{-j(\mathrm{\π}/4)}}{2n\sqrt{2\mathrm{\π}k}{\mathrm{sin\β}}_0}\cot \[\frac{\mathrm{\π}+(\mathrm{\φ}-{\mathrm{\φ}}^{\′})}{2n}\]\×F\[{\mathrm{kL\α}}^{+}(\mathrm{\φ}-{\mathrm{\φ}}^{\′})\]$

$D_2(L,\mathrm{\φ},{\mathrm{\φ}}^{\′},{\mathrm{\β}}_0,n)=-\frac{e^{-j(\mathrm{\π}/4)}}{2n\sqrt{2\mathrm{\π}k}{\mathrm{sin\β}}_0}\cot \[\frac{\mathrm{\π}-(\mathrm{\φ}-{\mathrm{\φ}}^{\′})}{2n}\]\×F\[{\mathrm{kL\α}}^{-}(\mathrm{\φ}-{\mathrm{\φ}}^{\′})\]$

$D_3(L,\mathrm{\φ},{\mathrm{\φ}}^{\′},{\mathrm{\β}}_0,n)=-\frac{e^{-j(\mathrm{\π}/4)}}{2n\sqrt{2\mathrm{\π}k}{\mathrm{sin\β}}_0}\cot \[\frac{\mathrm{\π}+(\mathrm{\φ}+{\mathrm{\φ}}^{\′})}{2n}\]\×F\[{\mathrm{kL\α}}^{+}(\mathrm{\φ}+{\mathrm{\φ}}^{\′})\]$

$D_4(L,\mathrm{\φ},{\mathrm{\φ}}^{\′},{\mathrm{\β}}_0,n)=-\frac{e^{-j(\mathrm{\π}/4)}}{2n\sqrt{2\mathrm{\π}k}{\mathrm{sin\β}}_0}\cot \[\frac{\mathrm{\π}-(\mathrm{\φ}+{\mathrm{\φ}}^{\′})}{2n}\]\×F\[{\mathrm{kL\α}}^{-}(\mathrm{\φ}+{\mathrm{\φ}}^{\′})\]$

$R_e(\mathrm{\θ},{\mathrm{\ϵ}}^{\′})=\frac{cos\mathrm{\θ}-\sqrt{{\mathrm{\ϵ}}^{\′}-{\sin }^2\mathrm{\θ}}}{cos\mathrm{\θ}+\sqrt{{\mathrm{\ϵ}}^{\′}-{\sin }^2\mathrm{\θ}}}$

$R_m(\mathrm{\θ},{\mathrm{\ϵ}}^{\′})=\frac{{\mathrm{\ϵ}}^{\′}cos\mathrm{\θ}-\sqrt{{\mathrm{\ϵ}}^{\′}-{\sin }^2\mathrm{\θ}}}{{\mathrm{\ϵ}}^{\′}cos\mathrm{\θ}+\sqrt{{\mathrm{\ϵ}}^{\′}-{\sin }^2\mathrm{\θ}}}$

In above formula, be the vertical of n face and horizontal reflection coefficient, incidence angle is φ '; for the vertical of O face and horizontal reflection coefficient.β ₀for incident ray splits with it edge angle.φ and φ ' is respectively incident ray and diffraction ray and the angle directly splitting angle.

$L=\frac{s_1{s}_2}{s_1+s_2}{\sin }^2{\mathrm{\β}}_0$

In above formula, s ₁for the distance from source point-to-point P, s ₂for the distance of field point-to-point P.

F (x) is transition function, and be the one distortion of fresnel integral, it is defined as:

$F\left(x\right)=2j\sqrt{x}{\∫}_{\sqrt{x}}^{\mathrm{\∞}}{e}^{-{\mathrm{j\μ}}^2}d\mathrm{\μ}x>0$

F _xprogressive expression formula be:

$F_x\&ap;e^{j(\mathrm{\&pi;}/4+x)}\&lsqb;\sqrt{\mathrm{\&pi;}x}-2{\mathrm{xe}}^{j\mathrm{\&pi;}/4}-\frac{2}{3}{x}^2{e}^{-j\mathrm{\&pi;}/4}\&rsqb;x<1$

$F_x\&ap;1+j\frac{1}{2x}-\frac{3}{4x^2}-j\frac{15}{8x^3}+\frac{75}{16x^2}x<1$

F when x>10 time _xmodulus value level off to 1.

${\mathrm{\&alpha;}}^{\&PlusMinus;}(\mathrm{\&phi;},{\mathrm{\&phi;}}^{\&prime;})=2{\cos }^2\&lsqb;\frac{2{\mathrm{\&pi;nN}}^{\&PlusMinus;}-(\mathrm{\&phi;}\&PlusMinus;{\mathrm{\&phi;}}^{\&prime;})}{2}\&rsqb;$

In above formula, N ^±it is the smallest positive integral meeting following equation

2πnN ^±-(φ±φ′)＝π

2πnN ^±-(φ±φ′)＝-π

In upper two formulas

$n=\frac{2\mathrm{\&pi;}-\mathrm{\&alpha;}}{\mathrm{\&pi;}}$

In formula, α splits angle in diffraction edge.

In theory, the method can reach an ideal resolution as 0.1 meter, but in practical application, the density of fingerprint base determines the precision of positioning result, so above-mentioned signal strength signal intensity forecasting process need not have too high resolution, in general, this resolution should be identical with fingerprint base density, and the present invention is set to 5 meters, so, while not affecting positioning precision, improve the real-time of system largely and reduce computation complexity.

Step 4, carries out coupling location by location fingerprint algorithm.

This some algorithm operates in the BJUTLocate application program developed by Beijing University of Technology, and program operation platform is Android4.0 and compatible version thereof.

(1). set up location fingerprint storehouse.

After obtaining predictive simulation received signal strength distribution map, derived by the manual drive test of the drive test signal strength data of 28 the location fingerprint sampled points that will allocate in advance.The signal strength signal intensity that the data result of each sampled point clicks 20 times at random by mouse in this region is done mean filter to determine, to reduce data error, the data generated are exported text to be derived.Finally location fingerprint database is inputed in finder, for further matching primitives provides data basis.

Specific implementation step is: first, and opening up a size is that the memory space of 4*30*5 byte is used for deposit position fingerprint database.Then, by emulated each with reference to subregion signal strength successively assignment or be directed in the array of corresponding numbering.Finally, at the end of this activity life cycle, this region will be automatically released, can not extra occupying system resources.

(2). position matching calculates

Due to our locating area complex structure, barrier is more, lacks large area open field, is relatively applicable to utilizing location fingerprint algorithm to locate.Nearest neighbor method is the basic algorithm of location fingerprint algorithm, possesses short, the advantage such as location algorithm is simple positioning time, but the positioning result due to this algorithm gets the RP coordinate nearest with tested point as estimated value, so error is relatively large, causes its positioning precision lower slightly.So in order to ensure relatively fast locating speed, the location algorithm that complexity is relatively little, possess good positioning precision again simultaneously, we select to adopt KNN (k-nearest neighbor) to position coupling.

K-nearest neighbor (KNN) is the innovatory algorithm based on nearest neighbor method, nearest neighbor method is the reference point selecting a database RSS vector nearest with test point RSSI corresponding, and k-nearest neighbor chooses reference point corresponding to the nearest database RSS vector of K from minimum range, the average coordinates then calculating this K reference point coordinate exports as the position of test point.By the formula of nearest neighbor method in the hope of the distance D between each reference point and test point, K value can be chosen in the result from small to large, with the formula calculate the result output of average as location of the position coordinates of its corresponding reference point.(x in formula _i, y _i) be the position coordinates of the reference point corresponding to database RSSI vector that i-th is selected.

In reality test, traditional location fingerprint algorithm cannot meet the requirement of precision and stability aspect, and after groping and inquire into after a while, the present invention has carried out following improvement to this algorithm:

(1) logical decision filter is used to carry out filtering to signal strength signal intensity original sample value.In general, in the process of establishing of fingerprint base, the value of part reference label can produce very strong logicality, such as, the signal strength values about this focus that the label of a distance focus 5 meters stores has the signal strength values about this focus that may store than the reference label of distance focus 10 meters of more than 90% large.Therefore, in actual test process, if there is the phenomenon contrary with the above results, then can be considered small probability event, system will be rejected this part sampled result automatically, positions by sampled result next time.(inventive point 4)

(2) carry out amplitude limiting processing to the raw signal strength received, when being less than-80dB to signal strength signal intensity, its amplitude can be limited in-80dB by system.This be due to this algorithm with WiFi signal intensity for standard positions, the feature of this signal is that stabilized soil pavement is directly proportional, although general intelligent terminal can receive the signal of minimum-93dB, but the error of these signals is excessive, larger impact can be produced to aligning accuracy, therefore, the present invention adopts clipping operation to process sampled signal, and threshold value is repeatedly test the empirical value that rear summary obtains.

Claims (1)

1., based on the indoor wireless positioning method of WiFi signal Strength Simulation and location fingerprint algorithm, it is characterized in that, comprise the following steps:

Step 1, utilizes ray tracing algorithm to indoor environment modeling

Select the bikini equation of plane $\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0,$ Whole region is made up of two horizontal planes and several vertical planes, in order to determine the coefficient of horizontal plane and vertical plane, chooses arbitrarily 3 point (x respectively in each plane ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x ₃, y ₃, z ₃), bring the coordinate of each point into plane bikini equation, composition 3 × 3 determinants, make it solve x, y, z coefficient separately, are finally expressed as the general equation Ax+By+Cz+D=0 (A of plane ²+ B ²+ C ²≠ 0), calculation procedure is as follows:

First planar get arbitrarily 3 points, its coordinate is substituting to plane bikini equation $\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0,$ Then by determinant decomposition computation $\&DoubleRightArrow;\left\{\begin{array}{c}(x-x_1)\&lsqb;(y_2-y_1)(z_3-z_1)-(z_2-z_1)(y_3-y_1)\&rsqb;\\ -(y-y_1)\&lsqb;(x_2-x_1)(z_3-z_1)-(z_2-z_1)(x_3-x_1)\&rsqb;\\ +(z-z_1)\&lsqb;(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\&rsqb;\end{array}\right\},$ Equation coefficient A, B, C, D show the most at last

$\&DoubleRightArrow;Ax+By+Cz+D=0\&DoubleRightArrow;\left\{\begin{array}{c}A=(y_2-y_1)(z_3-z_1)-(z_2-z_1)(y_3-y_1)\\ B=(z_2-z_1)(x_3-x_1)-(x_2-x_1)(z_3-z_1)\\ C=(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\\ D=x_1\&lsqb;(z_2-z_1)(y_3-y_1)-(y_2-y_1)(z_3-z_1)\&rsqb;\\ +y_1\&lsqb;(x_2-x_1)(z_3-z_1)-(z_2-z_1)(x_3-x_1)\&rsqb;\\ -z_1\&lsqb;(x_2-x_1)(y_3-y_1)-(y_2-y_1)(x_3-x_1)\&rsqb;\end{array}\right.$

One by one the concrete equation of all horizontal planes and vertical plane and the domain of definition are showed by the method, form Indoor environment solid geometric pattern

Step 2, by carrying out propagation path tracking to every bar ray, calculates its multipath transmisstion track

Every bar ray only considers that direct projection, primary event and secondary reflection, a diffraction and second time diffraction, primary event and a diffraction combine this several multipath transmisstion state, and wherein diffraction only considers wedge diffraction;

When carrying out propagation forecast with ray tracking method, the field intensity of acceptance point is exactly all rays through acceptance point superposition sum; May be direct path, reflection path, diffraction path in every bar ray path, also may be the mixed path of direct projection, reflection, diffraction; After route searching completes, just carry out the calculating of field intensity according to all propagation paths of gained; According to the difference in path, calculating is divided into direct projection field intensity, reflection field intensity and diffraction field intensity three parts;

Be the total field intensity expression formula of received field point below:

E _total＝∑E _x

$E_x={\mathrm{xG}}_{tx}{G}_{rx}{L}_x\left(n\right)\underset{y}{\&Pi;}\stackrel{\&OverBar;}{R}\left({\mathrm{\&theta;}}_{yx}\right)\underset{z}{\&Pi;}\stackrel{\&OverBar;}{D}\left({\mathrm{\&phi;}}_{zx}\right)E_0$

E in above formula _xfor xth bar ray is at the electric field intensity of acceptance point; E ₀for launching electric field vector; L _x(n) be xth bar ray arrive acceptance point through the decay of path n at free space; for the reflection coefficient of xth article ray y secondary reflection, incidence angle is θ _yx; for the diffraction coefficient of xth article ray the z time diffraction, incidence angle is φ _zx; G _txand G _rxthe gain of transmitting antenna and reception antenna respectively;

Step 3, use RanPlaniBuildNET software to calculate the field intensity of continuous space any point, field intensity resolution is set to 5 meters;

Step 4, carries out coupling location by location fingerprint algorithm

Use weighting k-nearest neighbor to add weight factor, be used for weighing the percentage contribution that different Neighbor Points positions test point

Try to achieve the distance of different reference point and test point, relatively and choose the reference point that wherein K minimum value is corresponding, then the coordinate of test point is calculated by following formula;

$(x,y)=\underset{i=1}{\overset{K}{\&Sigma;}}{w}_i(x_i,y_i)$

Wherein, w _irepresent the weight factor of i-th reference point in position fixing process; w _icomputing formula as follows:

$w_i=\frac{1/D_i^2}{\underset{i=1}{\overset{K}{\&Sigma;}}1/D_i^2}$

W _ivalue depend on the Euclidean distance of RSS between reference point and test point, i.e. D _ivalue;

Logical decision filter is used to carry out filtering to signal strength signal intensity original sample value:

The signal strength values about this focus that the signal strength values about this focus that near label of distance focus the stores reference label far away than distance focus stores is large, if there is the phenomenon contrary with the above results, automatically this part sampled result is rejected, positioned by sampled result next time;

And amplitude limiting processing is carried out to the raw signal strength received, amplitude is limited in-80dB.