CN103152823B - A kind of wireless indoor location method - Google Patents

A kind of wireless indoor location method Download PDF

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CN103152823B
CN103152823B CN201310060708.1A CN201310060708A CN103152823B CN 103152823 B CN103152823 B CN 103152823B CN 201310060708 A CN201310060708 A CN 201310060708A CN 103152823 B CN103152823 B CN 103152823B
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corridor
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CN103152823A (en
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杨铮
吴陈沭
刘云浩
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Tsinghua University
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Abstract

本发明提出一种无线室内定位方法,包括步骤:利用智能手机自动采集无线指纹数据和用户移动数据,形成指纹集F和距离矩阵D′,并进行预处理;根据预处理后的指纹集F和距离矩阵D′,构建指纹空间;生成无应力平面图,进行关键特征提取,以及进行空间坐标转换,其中,关键特征提取包括走廊识别、房间识别和参考点匹配,空间坐标转换包括楼层级的转换和房间级的转换。本发明的无线室内定位方法无需对定位区域进行人工的现场勘测,可以方便地由系统中的多个用户协同提供指纹信息,其定位结果精度高,逻辑性好,并且在查询与平时移动时产生的冗余信息均可作为升级信息。

The present invention proposes a wireless indoor positioning method, comprising the steps of: using a smart phone to automatically collect wireless fingerprint data and user movement data, forming a fingerprint set F and a distance matrix D', and performing preprocessing; according to the preprocessed fingerprint set F and The distance matrix D′ constructs the fingerprint space; generates a stress-free floor plan, extracts key features, and performs spatial coordinate transformation. Among them, key feature extraction includes corridor identification, room identification, and reference point matching, and spatial coordinate transformation includes floor-level conversion and Room-level transformations. The wireless indoor positioning method of the present invention does not need manual on-site survey of the positioning area, and multiple users in the system can conveniently provide fingerprint information cooperatively. All redundant information can be used as upgrade information.

Description

一种无线室内定位方法A wireless indoor positioning method

技术领域technical field

本发明属于无线室内定位领域,涉及一种无线室内定位方法。The invention belongs to the field of wireless indoor positioning and relates to a wireless indoor positioning method.

背景技术Background technique

手机的普及和普适计算的推广催生了大量关于无线室内定位的研究。目前大多数的室内定位方法利用接收信号强度(ReceivedSignalStrength,RSS)来确定位置。而RSS指纹可以很容易地从现成的无线网络设备(比如WiFi或ZigBee兼容的设备)获得。The popularity of mobile phones and the promotion of ubiquitous computing have spawned a large number of researches on wireless indoor positioning. Most current indoor positioning methods use received signal strength (Received Signal Strength, RSS) to determine the position. And RSS fingerprints can be easily obtained from off-the-shelf wireless network devices (such as WiFi or ZigBee compatible devices).

传统的无线指纹定位技术采用两阶段的模式。第一个阶段是训练阶段,或称为信号采集阶段,即采用人工的方法预先将室内各个位置上的无线信号强度(如不同无线路由的Wi-Fi信号强度或Zig-Bee信号强度)进行多次记录,并将记录结果处理后存储在数据库中对应物理位置的条目中。由于无线信号传播和室内情况的不确定性,信号强度数据的采集需要大量多次的重复。同时,物理位置的精确程度也影响到最终定位结果的准确性,需要消耗大量的人力和时间进行准备和现场勘查(SiteSurvey),提前建立无线信号地图(RadioMap)。经过第一阶段的训练,指纹数据库建立好以后,系统进入第二阶段,即实际的服务阶段。用户可以在已有无线信号分布图的区域获得自己的无线指纹信息,并将该信息作为查询的依据发送给定位服务模块。通过定位算法,将用户发送的无线指纹信息与数据库中的无线指纹进行比对,返回相似度最接近的位置信息给用户。The traditional wireless fingerprint positioning technology adopts a two-stage model. The first stage is the training stage, or called the signal acquisition stage, that is, the wireless signal strength (such as the Wi-Fi signal strength or Zig-Bee signal strength of different wireless routes) at various positions in the room is artificially measured in advance. record, and store the record result in the entry corresponding to the physical location in the database. Due to the uncertainty of wireless signal propagation and indoor conditions, the acquisition of signal strength data requires a large number of repetitions. At the same time, the accuracy of the physical location also affects the accuracy of the final positioning result, which requires a lot of manpower and time for preparation and site survey (SiteSurvey), and the establishment of a wireless signal map (RadioMap) in advance. After the first stage of training, after the fingerprint database is established, the system enters the second stage, which is the actual service stage. The user can obtain his own wireless fingerprint information in the area where the wireless signal distribution map exists, and send the information to the positioning service module as the basis of the query. Through the positioning algorithm, the wireless fingerprint information sent by the user is compared with the wireless fingerprint information in the database, and the location information with the closest similarity is returned to the user.

由于无线指纹定位技术利用已有网络设施进行定位,不增加系统的额外开销,因此国内外学者对无线指纹定位方法进行了大量深入的研究。但如上所述,现有的无线指纹定位技术还存在以下的缺陷:Since the wireless fingerprint positioning technology utilizes the existing network facilities for positioning without increasing the additional cost of the system, scholars at home and abroad have conducted a lot of in-depth research on the wireless fingerprint positioning method. But as mentioned above, the existing wireless fingerprint positioning technology also has the following defects:

(1)需要进行高成本、低效率的人工现场勘测(1) High-cost and low-efficiency manual site surveys are required

现场勘测需要对定位区域的每一位置进行无线信号指纹的采样与人工标注,耗时费力,而且难以覆盖定位区域的所有位置。On-site survey requires wireless signal fingerprint sampling and manual labeling for each position in the positioning area, which is time-consuming and laborious, and it is difficult to cover all positions in the positioning area.

(2)对环境变化以及无线信号波动的容忍性差(2) Poor tolerance to environmental changes and wireless signal fluctuations

室内环境的一大特征是环境多变,且无线信号传播特性复杂,信号波动性大。基于现场勘测的方法,难以适应环境的动态变化;传统的方法直接利用无线信号指纹之间的欧式距离作为特征,难以适应无线信号的波动性。One of the characteristics of the indoor environment is that the environment is changeable, and the wireless signal propagation characteristics are complex, and the signal volatility is large. The method based on site survey is difficult to adapt to the dynamic changes of the environment; the traditional method directly uses the Euclidean distance between wireless signal fingerprints as a feature, which is difficult to adapt to the volatility of wireless signals.

(3)无法实现房间级别的逻辑定位(3) Logical positioning at the room level cannot be achieved

传统的方法大多旨在实现绝对坐标的定位,无法实现区分不同的房间。而事实上,房间信息在实际中具有更大的应用价值。Most of the traditional methods are aimed at the positioning of absolute coordinates, and cannot distinguish between different rooms. In fact, room information has greater application value in practice.

当前,智能手机拥有强大的计算和通信能力,内置各种各样功能丰富的传感器,并且几乎随时随地和用户绑定在一起。因此,手机可以被视为用户和环境之间的一个越来越重要的信息的接口。通过智能手机及其内置的传感器,不仅可以感知丰富的环境数据,还能捕获用户的运动信息,这位非现场勘测型的室内定位提供了可能。At present, smartphones have powerful computing and communication capabilities, built-in various sensors with rich functions, and are bound to users almost anytime and anywhere. Therefore, the mobile phone can be regarded as an increasingly important information interface between the user and the environment. Through the smartphone and its built-in sensors, it can not only perceive rich environmental data, but also capture the user's motion information, which makes it possible for off-site survey-type indoor positioning.

发明内容Contents of the invention

本发明旨在至少在一定程度上解决上述技术问题之一或至少提供一种有用的商业选择。为此,本发明的目的在于提出一种具有数据采集灵活方便,定位结果逻辑性好的无线室内定位方法。The present invention aims at solving one of the above technical problems at least to a certain extent or at least providing a useful commercial choice. Therefore, the object of the present invention is to propose a wireless indoor positioning method with flexible and convenient data collection and good logic of positioning results.

根据本发明实施例的一种无线室内定位方法,包括以下步骤:S1.利用智能手机自动采集无线指纹数据和用户移动数据,形成指纹集F和距离矩阵D′,并进行预处理;S2.根据预处理后的所述指纹集F和距离矩阵D′,构建指纹空间;S3.生成无应力平面图,进行关键特征提取,以及进行空间坐标转换,其中,所述关键特征提取包括走廊识别、房间识别和参考点匹配,所述空间坐标转换包括楼层级的转换和房间级的转换。A wireless indoor positioning method according to an embodiment of the present invention includes the following steps: S1. Using a smart phone to automatically collect wireless fingerprint data and user movement data to form a fingerprint set F and a distance matrix D', and perform preprocessing; S2. The preprocessed fingerprint set F and distance matrix D′ construct a fingerprint space; S3. Generate a stress-free plan, perform key feature extraction, and perform spatial coordinate transformation, wherein the key feature extraction includes corridor identification and room identification Matching with the reference point, the spatial coordinate transformation includes floor-level transformation and room-level transformation.

在本发明的一个实施例中,所述S1进一步包括:S11.通过智能手机采集无线网络的信号以及加速度传感器和方向传感器的读数,假设区域中有m个无线网络接入点,则所述智能手机在区域内某个位置的得到的RSS指纹记为一个m维的向量f=(s1,s2,...,sm),其中si表示第i个无线网络接入点的RSS值,又定义d′ij为fi和fj之间的距离,即为用户在两个位置之间行走的步数,在指纹收集阶段结束后,得到指纹集F={fi,i=1...n},其中n是指纹的条数,以及距离矩阵D′=[d′ij];S12.对所述指纹集F进行预处理,对两条指纹fi=(s1,s2,...,sm)和fj=(t1,t2,...,tm),定义fi和fj差异度为若δij小于预定阈值∈,则fi和fj在指纹空间生成过程中被当作相同的点,否则被当作不同的点;S13.对所述距离矩阵D′进行预处理,根据最短路径算法计算每对指纹间的最短距离,即如果对在fi和fj之存在某个中间节点fk,满足d′ij>d′ik+d′kj,则d′ij被更新为d′ik+d′kjIn one embodiment of the present invention, the S1 further includes: S11. Collecting the signal of the wireless network and the readings of the acceleration sensor and the direction sensor through the smart phone, assuming that there are m wireless network access points in the area, the smart The RSS fingerprint obtained by the mobile phone at a certain position in the area is recorded as an m-dimensional vector f=(s 1 ,s 2 ,...,s m ), where s i represents the RSS of the i-th wireless network access point value, and define d′ ij as the distance between f i and f j , that is, the number of steps the user walks between the two locations. After the fingerprint collection phase is over, the fingerprint set F={f i ,i= 1...n}, where n is the number of fingerprints, and the distance matrix D′=[d′ ij ]; S12. Preprocess the fingerprint set F, for two fingerprints f i =(s 1 , s 2 ,...,s m ) and f j =(t 1 ,t 2 ,...,t m ), define the difference between f i and f j as If δ ij is less than the predetermined threshold ∈, f i and f j are regarded as the same point in the fingerprint space generation process, otherwise they are regarded as different points; S13. Preprocess the distance matrix D′, according to the shortest The path algorithm calculates the shortest distance between each pair of fingerprints, that is, if there is an intermediate node f k between f i and f j and satisfies d′ ij >d′ ik +d′ kj , then d′ ij is updated to d ′ ik +d′ kj .

在本发明的一个实施例中,所述S2包括:根据预处理后的所述指纹集F和距离矩阵D′,通过MDS算法将所有指纹映射到一个d维的欧几里得空间。In one embodiment of the present invention, the S2 includes: according to the preprocessed fingerprint set F and the distance matrix D', map all the fingerprints to a d-dimensional Euclidean space through the MDS algorithm.

在本发明的一个实施例中,所述走廊识别包括:利用中间度获取走廊上的指纹,其中,根据指纹间的距离,建立最小生成树T,计算所述最小生成树上各点的中间度,中间度高的部分视为走廊上的指纹,记为走廊指纹集Fc,其中所述中间度B(v)定义为:对于一个由顶点集V和边集E构成的图G=(V,E),其中,σst为从s到t的最短路径数,σst(v)为从s到t且经过v的最短路径数。In one embodiment of the present invention, the corridor identification includes: using betweenness to obtain fingerprints on the corridor, wherein, according to the distance between fingerprints, a minimum spanning tree T is established, and the betweenness of each point on the minimum spanning tree is calculated , the part with high betweenness is regarded as the fingerprint on the corridor, which is recorded as the corridor fingerprint set F c , where the betweenness B(v) is defined as: For a graph G=(V ,E), Among them, σ st is the number of the shortest path from s to t, and σ st (v) is the number of the shortest path from s to t passing through v.

在本发明的一个实施例中,所述房间识别包括:利用聚类获取房间指纹集,其中,在所有指纹空间中去除所述走廊指纹集Fc,采用K-means算法对剩下的指纹F-Fc进行聚类,得到k个k个群集(记为i=1,2,...,k),聚类后认为同一个中的所有点来自同一个房间。In one embodiment of the present invention, the room identification includes: using clustering to obtain a room fingerprint set, wherein the corridor fingerprint set F c is removed from all fingerprint spaces, and the K-means algorithm is used to analyze the remaining fingerprints FF c clustering, get k k clusters (denoted as i=1,2,...,k), after clustering, consider the same All points in are from the same room.

在本发明的一个实施例中,所述参考点匹配包括:利用房间的门作为建立无应力平面图和指纹空间之间联系的关键参考点,其中,首先定义 为房间门内外离门最近的点,则定义房间门指纹集所述FD中的所有指纹在最小生成树T中可以被组织成一条链,故将所述FD表示为向量形式FD=(f1,f2,...,fk),而在无应力平面图中,定义PD=(p1,p2,...,pk)为走廊上离各个门最近的采样点,各个所述采样点在PD中出现的顺序为沿着走廊从一侧到另一侧,由于从FD到PD的映射为相对应或者刚好相反顺序对应,实现了参考点匹配确定了无应力平面图中某个房间指纹集与平面图中的某个房间的对应。In one embodiment of the present invention, the reference point matching includes: using the door of the room as a key reference point for establishing the connection between the stress-free floor plan and the fingerprint space, wherein, firstly, define and is the point closest to the door inside and outside the room door, then define the room door fingerprint set All fingerprints in the F D can be organized into a chain in the minimum spanning tree T, so the F D is represented as a vector form F D =(f 1 , f 2 ,...,f k ), and In the stress-free plan view, define P D =(p 1 ,p 2 ,...,p k ) as the sampling point closest to each door in the corridor, and the order in which each sampling point appears in P D is along From one side of the corridor to the other, since the mapping from F D to P D is corresponding or just in reverse order, the reference point matching is realized to determine the fingerprint set of a room in the stress-free plan and a certain room in the plan corresponding to.

在本发明的一个实施例中,所述楼层级的转换包括:利用一个变换矩阵来实现无应力平面图和指纹空间可视化图的楼层级的转换,其中,假设在FD中的一条指纹的坐标为xi=[xi 1xi 2...xi d]T,其中d为指纹空间的维数,与之相应的位置的坐标yi=[yi 1yi 2...yi d]T,定义A为d×d的变换矩阵,B=[b1b2...bd]T,由于有k=|FD|条等式yi=Axi+B,将所述k条等式重写成Hiz=Gi,其中Hi=[xi T1],z=[AB]T,Gi=yi T,联合所述k条等式,有Hz=G,其中Hi和Gi为H和G的第i行,由最小二乘法解得求得A和B,从而对于坐标为x=[xi 1xi 2...xi d]T的一条指纹,离Ax+B最近的采样点可视为它的实际位置。In one embodiment of the present invention, the conversion at the floor level includes: using a transformation matrix to realize the conversion at the floor level of the stress-free plan view and the fingerprint space visualization map, wherein it is assumed that the coordinates of a fingerprint in FD are x i =[x i 1 x i 2 ... x i d ] T , where d is the dimension of the fingerprint space, and the coordinates of the corresponding position y i =[y i 1 y i 2 ... y i d ] T , define A as the transformation matrix of d×d, B=[b 1 b 2 ...b d ] T , since there are k=|F D | equations y i = Axi +B, all The above k equations are rewritten as H i z=G i , where H i =[ xi T 1], z=[AB] T , G i =y i T , combined with the k equations, Hz= G, where H i and G i are the i-th row of H and G, solved by the least square method Obtain A and B, so that for a fingerprint whose coordinates are x=[x i 1 x i 2 ... x i d ] T , the sampling point closest to Ax+B can be regarded as its actual position.

在本发明的一个实施例中,所述房间级的转换包括:进一步利用MDS算法将来自同一个房间的指纹变换到一个d维的空间,使对应房间的采样点形成一个d维的无应力平面图,将离房间门最近和最远的点作为参考点,可以确定指纹房间与物理房间之间的变换关系,通过对所有房间逐一重复上述操作,实现了各个房间的无应力平面图和指纹空间可视化图的房间级的转换。In one embodiment of the present invention, the room-level conversion includes: further using the MDS algorithm to transform the fingerprints from the same room into a d-dimensional space, so that the sampling points of the corresponding room form a d-dimensional stress-free plan , using the nearest and farthest points from the room door as reference points, the transformation relationship between the fingerprint room and the physical room can be determined. By repeating the above operations for all the rooms one by one, the stress-free floor plan and the fingerprint space visualization map of each room are realized. room-level transformations.

本发明的无线室内定位方法无需对定位区域进行人工的现场勘测,可以方便地由系统中的多个用户协同提供指纹信息,其定位结果精度高,逻辑性好,并且在查询与平时移动时产生的冗余信息均可作为升级信息。The wireless indoor positioning method of the present invention does not need manual on-site survey of the positioning area, and multiple users in the system can conveniently provide fingerprint information cooperatively. All redundant information can be used as upgrade information.

本发明的附加方面和优点将在下面的描述中部分给出,部分将从下面的描述中变得明显,或通过本发明的实践了解到。Additional aspects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

附图说明Description of drawings

本发明的上述和/或附加的方面和优点从结合下面附图对实施例的描述中将变得明显和容易理解,其中:The above and/or additional aspects and advantages of the present invention will become apparent and comprehensible from the description of the embodiments in conjunction with the following drawings, wherein:

图1是本发明实施例的室内空间定位方法的流程图。Fig. 1 is a flowchart of an indoor space positioning method according to an embodiment of the present invention.

图2是本发明实例所提供的2D指纹空间示意图。Fig. 2 is a schematic diagram of the 2D fingerprint space provided by the example of the present invention.

图3是本发明实例所提供的3D指纹空间示意图。Fig. 3 is a schematic diagram of the 3D fingerprint space provided by the example of the present invention.

图4是本发明实例所提供的在室内平面图上进行采样的结果示意图。Fig. 4 is a schematic diagram of the results of sampling on the indoor plan provided by the example of the present invention.

图5是本发明实例所提供的平面图采样点生成的2D无应力平面图。Fig. 5 is a 2D stress-free plan view generated by the sample points of the plan view provided by the example of the present invention.

图6是本发明实例所提供的平面图采样点生成的3D无应力平面图。Fig. 6 is a 3D stress-free plan view generated by the sample points of the plan view provided by the example of the present invention.

图7是本发明实例所提供的3D指纹空间的最小生成树示意图。Fig. 7 is a schematic diagram of the minimum spanning tree of the 3D fingerprint space provided by the example of the present invention.

图8是本发明实例所提供的指纹空间除去走廊部分的聚类结果示意图。Fig. 8 is a schematic diagram of the clustering results of the corridor part removed from the fingerprint space provided by the example of the present invention.

具体实施方式detailed description

下面详细描述本发明的实施例,所述实施例的示例在附图中示出,其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的,旨在用于解释本发明,而不能理解为对本发明的限制。Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

在本发明的描述中,需要理解的是,术语“中心”、“纵向”、“横向”、“长度”、“宽度”、“厚度”、“上”、“下”、“前”、“后”、“左”、“右”、“竖直”、“水平”、“顶”、“底”“内”、“外”、“顺时针”、“逆时针”等指示的方位或位置关系为基于附图所示的方位或位置关系,仅是为了便于描述本发明和简化描述,而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作,因此不能理解为对本发明的限制。In describing the present invention, it is to be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", " Orientation or position indicated by "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc. The relationship is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, therefore It should not be construed as a limitation of the present invention.

此外,术语“第一”、“第二”仅用于描述目的,而不能理解为指示或暗示相对重要性或者隐含指明所指示的技术特征的数量。由此,限定有“第一”、“第二”的特征可以明示或者隐含地包括一个或者更多个该特征。在本发明的描述中,“多个”的含义是两个或两个以上,除非另有明确具体的限定。In addition, the terms "first" and "second" are used for descriptive purposes only, and cannot be interpreted as indicating or implying relative importance or implicitly specifying the quantity of indicated technical features. Thus, a feature defined as "first" and "second" may explicitly or implicitly include one or more of these features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

在本发明中,除非另有明确的规定和限定,术语“安装”、“相连”、“连接”、“固定”等术语应做广义理解,例如,可以是固定连接,也可以是可拆卸连接,或一体地连接;可以是机械连接,也可以是电连接;可以是直接相连,也可以通过中间媒介间接相连,可以是两个元件内部的连通。对于本领域的普通技术人员而言,可以根据具体情况理解上述术语在本发明中的具体含义。In the present invention, unless otherwise clearly specified and limited, terms such as "installation", "connection", "connection" and "fixation" should be understood in a broad sense, for example, it can be a fixed connection or a detachable connection , or integrally connected; it may be mechanically connected or electrically connected; it may be directly connected or indirectly connected through an intermediary, and it may be the internal communication of two components. Those of ordinary skill in the art can understand the specific meanings of the above terms in the present invention according to specific situations.

在本发明中,除非另有明确的规定和限定,第一特征在第二特征之“上”或之“下”可以包括第一和第二特征直接接触,也可以包括第一和第二特征不是直接接触而是通过它们之间的另外的特征接触。而且,第一特征在第二特征“之上”、“上方”和“上面”包括第一特征在第二特征正上方和斜上方,或仅仅表示第一特征水平高度高于第二特征。第一特征在第二特征“之下”、“下方”和“下面”包括第一特征在第二特征正下方和斜下方,或仅仅表示第一特征水平高度小于第二特征。In the present invention, unless otherwise clearly specified and limited, a first feature being "on" or "under" a second feature may include direct contact between the first and second features, and may also include the first and second features Not in direct contact but through another characteristic contact between them. Moreover, "above", "above" and "above" the first feature on the second feature include that the first feature is directly above and obliquely above the second feature, or simply means that the first feature is horizontally higher than the second feature. "Below", "beneath" and "under" the first feature to the second feature include that the first feature is directly below and obliquely below the second feature, or simply means that the first feature has a lower level than the second feature.

本发明属于无线室内定位领域,涉及一种非现场勘测型的无线室内定位技术的实现方法。本发明是利用智能手机为载体,配合多种嵌入式传感器,通过非现场勘测型的指纹定位算法,基于用户移动路径推导出无线指纹之间的物理距离,并基于此物理距离利用MDS算法生成指纹空间系统,再将其转换为物理坐标,实现对室内用户进行定位服务的一项发明。The invention belongs to the field of wireless indoor positioning, and relates to a method for realizing an off-site survey type wireless indoor positioning technology. The present invention uses a smart phone as a carrier, cooperates with a variety of embedded sensors, and uses an off-site survey type fingerprint positioning algorithm to deduce the physical distance between wireless fingerprints based on the user's moving path, and uses the MDS algorithm to generate fingerprints based on the physical distance Space system, and then convert it into physical coordinates to realize an invention of positioning service for indoor users.

如图1所示,本发明实施例的室内空间定位方法包括如下步骤。As shown in FIG. 1 , the indoor space positioning method according to the embodiment of the present invention includes the following steps.

S1.利用智能手机自动采集无线指纹数据和用户移动数据,形成指纹集F和距离矩阵D′,并进行预处理。具体地,进一步包括:S1. Use the smart phone to automatically collect wireless fingerprint data and user movement data to form a fingerprint set F and a distance matrix D′, and perform preprocessing. Specifically, further include:

S11.采集数据S11. Collect data

在收集阶段,用户不需要进行特殊的训练,只需要像往常一样行走在建筑中进行日常活动。用户携带的手机会在行走路径上的各个点收集WiFi的RSS特征。同时,利用手机集成的加速度传感器推算出用户各个采样点之间的行走步数,以此确定各点之间的物理距离。具体地,假设在区域A内有m个无线网络接入点。对于区域A内的各个位置,RSS指纹可以定义为一个m维的向量f=(s1,s2,...,sm),其中,si表示第i个无线网络接入点的RSS值。另外,我们约定,如果该位置无法监测到第i个无线网络接入点,si的值设为0。定义d′ij为fi和fj之间的距离,计算过程为:d′ij默认为正无穷;当用户在某一位置记录fi,他步行至另一位置记录fj,d′ij即为用户在两个位置之间行走的步数。在指纹收集阶段结束后,我们得到一个指纹集F={fi,i=1...n}(n是指纹的条数)和一个距离矩阵D′=[d′ij]。During the collection phase, the user does not need special training, and just needs to walk in the building and carry out daily activities as usual. The mobile phone carried by the user will collect the RSS characteristics of WiFi at various points on the walking path. At the same time, the acceleration sensor integrated in the mobile phone is used to calculate the number of walking steps between each sampling point of the user, so as to determine the physical distance between each point. Specifically, it is assumed that there are m wireless network access points in area A. For each location in area A, the RSS fingerprint can be defined as an m-dimensional vector f=(s 1 ,s 2 ,...,s m ), where s i represents the RSS of the i-th wireless network access point value. In addition, we agree that if the i-th wireless network access point cannot be monitored at this location, the value of si is set to 0. Define d′ ij as the distance between f i and f j , the calculation process is: d′ ij is positive infinity by default; when the user records f i at a certain location, he walks to another location to record f j , d′ ij That is, the number of steps the user walks between two locations. After the fingerprint collection phase is over, we get a fingerprint set F={f i ,i=1...n} (n is the number of fingerprints) and a distance matrix D′=[d′ ij ].

S12.对指纹集进行预处理S12. Preprocessing the fingerprint set

为了构建指纹空间,需要对数据进行预处理。用户动作通常是任意的和无规则的,步行路径可能是交叉的。因此,指纹可能会重叠。预处理过程合并相似的指纹,其中“相似”意味着它们很可能来自相同(或者非常接近)位置。我们用δ表示指纹间的差异,对两条指纹fi=(s1,s2,...,sm)和fj=(t1,t2,...,tm),定义它们的差异度为In order to construct the fingerprint space, the data needs to be preprocessed. User actions are usually arbitrary and irregular, and walking paths may intersect. Therefore, fingerprints may overlap. The preprocessing process merges similar fingerprints, where "similar" means that they are likely to come from the same (or very close) location. We use δ to represent the difference between fingerprints. For two fingerprints f i =(s 1 ,s 2 ,...,s m ) and f j =(t 1 ,t 2 ,...,t m ), define Their difference is

δδ ijij == || || ff ii -- ff jj || || 11 == ΣΣ kk == 11 mm || sthe s kk -- tt kk ||

对fi和fj,如果它们的差异度δij小于预定义的阈值∈,它们在指纹空间生成过程中被当作相同的点。否则,fi和fj被当作不同的点。For f i and f j , if their degree of difference δ ij is less than a predefined threshold ∈, they are regarded as the same point in the fingerprint space generation process. Otherwise, f i and f j are treated as distinct points.

S13.对距离矩阵进行预处理S13. Preprocessing the distance matrix

我们需要对从加速度传感器得到的原始的数据进行预处理来计算步行距离。理论上,可以通过对加速度的二次方对时间进行积分得到距离。但是,由于噪声的存在,误差会迅速地积累。为了避免误差的积累,我们采用通过加速度传感器的数值来计算步数的方法,将步数作为步行距离的指标。对于指纹fi和fj,如果没有一个用户走过一条连接它们的路径,它们间的距离将不可用。然而,fi和fj可以通过多条用户路径连通起来。因此,可以用连接fi和fj的最短路径的长度来估计d′ij。另外,已测得的d′ij也可能被更新。例如,我们采用经典的Floyd-Warshall算法(最短路径算法)来计算每对指纹间的最小距离。该算法复杂度为O(n3),n为指纹的条数。如果对某个中间结点k使得,d′ij>d′ik+d′kj,则d′ij被更新为d′ik+d′kj。这样做可以消除用户绕行或者来回踱步造成的误差。为了方便起见,我们仍然用D′表示处理过的距离矩阵。We need to preprocess the raw data from the accelerometer to calculate the walking distance. Theoretically, the distance can be obtained by integrating the time with the quadratic acceleration. However, due to the presence of noise, errors can accumulate rapidly. In order to avoid the accumulation of errors, we use the method of calculating the number of steps through the value of the acceleration sensor, and use the number of steps as an indicator of walking distance. For fingerprints f i and f j , if none of the users walked a path connecting them, the distance between them will not be available. However, f i and f j can be connected through multiple user paths. Therefore, d′ ij can be estimated by the length of the shortest path connecting f i and f j . In addition, the measured d' ij may also be updated. For example, we use the classic Floyd-Warshall algorithm (shortest path algorithm) to calculate the minimum distance between each pair of fingerprints. The algorithm complexity is O(n 3 ), where n is the number of fingerprints. If for an intermediate node k such that d' ij >d' ik +d' kj , then d' ij is updated to d' ik +d' kj . Doing so eliminates errors caused by the user walking around or pacing back and forth. For convenience, we still denote the processed distance matrix by D′.

S2.根据预处理后的指纹集F和距离矩阵D′,构建指纹空间S2. Construct the fingerprint space according to the preprocessed fingerprint set F and the distance matrix D′

具体地,将D′作为输入,MDS算法将所有指纹映射到一个d维的欧几里得空间。d取2和3时的指纹空间分别如图1、图2所示。Specifically, taking D′ as input, the MDS algorithm maps all fingerprints to a d-dimensional Euclidean space. The fingerprint spaces when d is 2 and 3 are shown in Figure 1 and Figure 2, respectively.

S3.指纹空间与实际位置的匹配S3. Matching of fingerprint space and actual location

S31.无应力平面图生成S31. Stress-free plan generation

在建筑学和建筑工程中,平面图是一张说明建筑物中房间、空间和其他物理特征之间关系的俯视图。在平面图中,墙壁之间的距离常会被画出来说明房间大小和墙的长度。由于墙壁和其他障碍物的影响,两个位置在平面图上的距离不一定与它们之间的步行距离相等。为了解决这个问题,我们引入了无应力平面图。如图3所示,在平面图上,我们将感兴趣的区域用网格划分,进行平均采样。根据基于指纹的定位方法的特征,网格的间距通常可以取1-3米。间距取太大会降低定位的准确度,而取太小对准确度带来的提升微乎其微。通过计算各个采样点之间的距离,我们得到了一个距离矩阵D=[dij],其中dij表示在平面图上,两个采样点pi和pj之间的步行距离。将D作为输入,MDS算法将所有采样点映射到一个d维的欧几里得空间。在无应力平面图中,两点之间的欧几里得距离反映它们在实际平面图中相应的位置之间的步行距离。为了方便观察,取d为2和3,所生成的无应力平面图分别如图4、图5所示。In architecture and building engineering, a floor plan is a top view illustrating the relationships between rooms, spaces, and other physical features in a building. In floor plans, the distance between walls is often drawn to illustrate the size of the room and the length of the walls. Due to walls and other obstructions, the distance between two locations on the floor plan is not necessarily equal to the walking distance between them. To solve this problem, we introduce stress-free floor plans. As shown in Figure 3, on the plan view, we divide the area of interest with a grid and perform average sampling. According to the characteristics of the fingerprint-based positioning method, the grid spacing can usually be 1-3 meters. If the spacing is too large, the accuracy of positioning will be reduced, while if it is too small, the accuracy will be improved little. By calculating the distance between each sampling point, we get a distance matrix D=[d ij ], where d ij represents the walking distance between two sampling points p i and p j on the planar graph. Taking D as input, the MDS algorithm maps all sampling points to a d-dimensional Euclidean space. In a stress-free plan view, the Euclidean distance between two points reflects the walking distance between their corresponding locations in the actual plan view. For the convenience of observation, d is taken as 2 and 3, and the generated stress-free plan views are shown in Fig. 4 and Fig. 5, respectively.

S32.关键特征抽取S32. key feature extraction

分为三个步骤:走廊识别、房间识别、参考点匹配Divided into three steps: corridor identification, room identification, reference point matching

(1)走廊识别(1) Corridor identification

在一个建筑中,走廊连接了各个房间。用户从一间房间走向另一间通常必须要穿过走廊。走廊在现实空间中的这一特性也反应到了无应力平面图和指纹空间上。在走廊采集到的指纹在指纹空间中处于关键位置。考虑到图论中的集中性(centrality),这些指纹有一个较大的集中性值。在图论中,点的集中性可以取度数、中间性、紧密度等。本发明实例采用中间性来获取走廊上的指纹。从概念上来说,如果一个点出现在任意一条最短路径上的概率较大,那么它有着较高的中间性。对于一个由顶点集V和边集E构成的图G=(V,E),中心度定义为In a building, corridors connect rooms. Users often have to walk through corridors to get from one room to another. This character of the corridors in real space is also reflected in the stress-free floor plan and fingerprint space. The fingerprints collected in the corridor are at a key position in the fingerprint space. Considering centrality in graph theory, these fingerprints have a large centrality value. In graph theory, the concentration of points can take degree, betweenness, compactness, etc. Examples of the present invention use betweenness to acquire fingerprints in hallways. Conceptually, a point has high betweenness if it has a high probability of appearing on any shortest path. For a graph G=(V,E) consisting of a vertex set V and an edge set E, the centrality is defined as

BB (( vv )) == ΣΣ sthe s ≠≠ νν ≠≠ tt ∈∈ VV σσ stst (( νν )) σσ stst

其中,σst为从s到t的最短路径数,σst(v)为从s到t且经过v的最短路径数。Among them, σ st is the number of the shortest path from s to t, and σ st (v) is the number of the shortest path from s to t passing through v.

根据指纹间的距离,我们建立一棵最小生成树T,如图6所示。利用中间性将所有指纹分成两部分,中间性高的那部分视为走廊上的指纹,这部分指纹集记作FcAccording to the distance between fingerprints, we build a minimum spanning tree T, as shown in Figure 6. Use the betweenness to divide all fingerprints into two parts, the part with high betweenness is regarded as the fingerprint in the corridor, and this part of the fingerprint set is denoted as F c .

(2)房间识别(2) Room identification

在所有指纹中去掉Fc,我们观察到剩下的指纹可以组成几个群集,不同群集之间的指纹在空间上分隔。考虑到计算效率,我们采用K-means算法对剩下的指纹进行聚类。取K的值为平面图上的房间数,F-Fc被聚成了k个群集(记为i=1,2,...,k),如图7所示。聚类后,我们认为同一个中的所有点来自同一个房间,接下来还需要利用参考点匹配确定这个房间对应平面图的哪一个。Removing Fc from all fingerprints , we observe that the remaining fingerprints can form several clusters, with the fingerprints between different clusters being spatially separated. Considering the computational efficiency, we use the K-means algorithm to cluster the remaining fingerprints. Taking the value of K as the number of rooms on the floor plan, FF c is gathered into k clusters (denoted as i=1,2,...,k), as shown in Figure 7. After clustering, we consider the same All the points in are from the same room, and then we need to use reference point matching to determine which one of the floor plan this room corresponds to.

(3)参考点匹配(3) Reference point matching

本发明实例利用房间的门作为建立无应力平面图和指纹空间之间联系的关键参考点。我们按如下定义 The inventive example utilizes the door of the room as a key reference point for establishing the connection between the stress-free floor plan and the fingerprint space. We define as follows

这样,可看作门内外离门最近的点。定义FD中的所有指纹在最小生成树T中可以被组织成一条链,这样,我们可以将FD表示为向量形式FD=(f1,f2,...,fk)。在无应力平面图中,定义PD=(p1,p2,...,pk)为走廊上离各个门最近的采样点,点在PD中出现的顺序为沿着走廊从一侧到另一侧。这样,从FD到PD的映射只有两种情况:相对应或者刚好相反。定义l=(l1,l2,...,lk-1),li=||pi+1-pi||,l’=(l’1,l’2,...,l’k-1),li=||p′i+1-p′i||。定义l与l’的相似度为s1,计算方法为so, It can be regarded as the point closest to the door inside and outside the door. definition All fingerprints in F D can be organized into a chain in the minimum spanning tree T, so that we can express F D as a vector form F D =(f 1 ,f 2 ,...,f k ). In the stress-free plan view, define P D =(p 1 ,p 2 ,...,p k ) as the sampling point closest to each door in the corridor, and the order in which points appear in P D is along the corridor from one side to the other side. In this way, the mapping from F D to PD has only two situations: corresponding or just opposite. Define l=(l 1 ,l 2 ,...,l k-1 ), l i =||p i+1 -p i ||, l'=(l' 1 ,l' 2 ,... ,l' k-1 ), l i =||p′ i+1 -p′ i ||. Define the similarity between l and l' as s 1 , and the calculation method is

ll ·&Center Dot; ll ′′ || || ll || || || || ll ′′ || ||

用同样的方法计算l和l’的相反向量的相似度,记为s2。如果s1≥s2,则认为FD到PD各点相对应;否则,认为FD到PD各点刚好相反。Use the same method to calculate the similarity of the opposite vectors of l and l', denoted as s 2 . If s 1 ≥ s 2 , it is considered that the points from F D to PD are corresponding; otherwise, the points from F D to PD are just opposite.

S33.空间坐标转换S33. Space coordinate conversion

分为两步:楼层级的转换、房间级的转换Divided into two steps: conversion at the floor level and conversion at the room level

(1)楼层级的转换(1) Conversion at the floor level

从无应力平面图和指纹空间的可视化图中可以看到,它们的结构非常相似,但是有一些微小的变化,如平移、旋转和反射。我们利用一个变换矩阵来实现楼层级的匹配。As can be seen from the stress-free plan view and the visualization of the fingerprint space, their structures are very similar, but with some minor changes such as translation, rotation, and reflection. We utilize a transformation matrix to achieve floor-level matching.

假设在FD中的一条指纹的坐标为xi=[xi 1xi 2...xi d]T,d为指纹空间的维数。与之相应的位置的坐标yi=[yi 1yi 2...yi d]T。定义A为d×d的变换矩阵,B=[b1b2...bd]T。我们有k=|FD|条等式Assume that the coordinates of a fingerprint in F D are x i =[ xi 1 x i 2 ... x i d ] T , and d is the dimension of the fingerprint space. The coordinates of the corresponding position y i =[y i 1 y i 2 ... y i d ] T . Define A as a d×d transformation matrix, B=[b 1 b 2 ...b d ] T . We have the equation k=|F D |

yi=Axi+By i =Ax i +B

我们将这k条等式重写成We rewrite these k equations as

Hiz=Gi H i z=G i

其中Hi=[xi T1],z=[AB]T,Gi=yi T。联合这k条等式,有Where H i =[x i T 1], z=[AB] T , G i =y i T . Combining these k equations, we have

Hz=GHz=G

Hi和Gi为H和G的第i行。H i and G i are the ith rows of H and G.

由最小二乘法可得It can be obtained by the method of least squares

zz ‾‾ == (( Hh TT Hh )) -- 11 Hh TT GG

这样,我们可以得到A和B。对于坐标为x=[xi 1xi 2…xi d]T的一条指纹,离Ax+B最近的采样点可视为它的实际位置。In this way, we can get A and B. For a fingerprint whose coordinates are x=[x i 1 x i 2 ... x i d ] T , the sampling point closest to Ax+B can be regarded as its actual position.

(2)房间级的转换(2) Room-level conversion

前面提到,本发明实例将指纹通过聚类分到了不同的指纹房间中,且通过参考点匹配,得到了指纹空间与平面图上物理空间之间的一一对应关系。再次利用MDS,将来自同一个房间的指纹变换到一个d维的空间。同样地,使对应房间的采样点形成一个d维的无应力平面图。将离房间门最近和最远的点作为参考点,可以确定指纹房间与物理房间之间的变换关系。通过对所有房间重复此步骤,我们实现了房间级的转换。As mentioned above, the example of the present invention classifies fingerprints into different fingerprint rooms through clustering, and obtains the one-to-one correspondence between the fingerprint space and the physical space on the plan through matching of reference points. Using MDS again, the fingerprints from the same room are transformed into a d-dimensional space. Similarly, the sampling points corresponding to the room form a d-dimensional stress-free plan. Taking the nearest and farthest points from the room door as reference points, the transformation relationship between the fingerprint room and the physical room can be determined. By repeating this step for all rooms, we achieve room-level transformations.

综上所述,本发明的无线室内定位方法无需对定位区域进行人工的现场勘测,可以方便地由系统中的多个用户协同提供指纹信息,其定位结果精度高,逻辑性好,并且在查询与平时移动时产生的冗余信息均可作为升级信息。To sum up, the wireless indoor positioning method of the present invention does not require manual on-site survey of the positioning area, and multiple users in the system can conveniently provide fingerprint information collaboratively. Redundant information generated during normal movement can be used as upgrade information.

需要说明的是,流程图中或在此以其他方式描述的任何过程或方法描述可以被理解为,表示包括一个或更多个用于实现特定逻辑功能或过程的步骤的可执行指令的代码的模块、片段或部分,并且本发明的优选实施方式的范围包括另外的实现,其中可以不按所示出或讨论的顺序,包括根据所涉及的功能按基本同时的方式或按相反的顺序,来执行功能,这应被本发明的实施例所属技术领域的技术人员所理解。It should be noted that any process or method descriptions described in flowcharts or otherwise described herein can be understood as representing codes including one or more steps of executable instructions for implementing specific logical functions or processes. modules, segments or parts, and the scope of the preferred embodiments of the present invention includes further implementations, which may be performed out of the order shown or discussed, including in substantially simultaneous fashion or in reverse order depending on the functions involved. function, which should be understood by those skilled in the art to which the embodiments of the present invention belong.

在本说明书的描述中,参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中,对上述术语的示意性表述不一定指的是相同的实施例或示例。而且,描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

尽管上面已经示出和描述了本发明的实施例,可以理解的是,上述实施例是示例性的,不能理解为对本发明的限制,本领域的普通技术人员在不脱离本发明的原理和宗旨的情况下在本发明的范围内可以对上述实施例进行变化、修改、替换和变型。Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be construed as limitations to the present invention. Variations, modifications, substitutions, and modifications to the above-described embodiments are possible within the scope of the present invention.

Claims (6)

1. a wireless indoor location method, is characterized in that, comprises the following steps:
S1. utilize smart mobile phone automatically to gather wireless fingerprint data and user's Mobile data, formed fingerprint collection F and Distance matrix D ', and carry out preliminary treatment;
S2. according to pretreated described fingerprint collection F and Distance matrix D ', build fingerprint space, wherein, described S2 comprises: according to pretreated described fingerprint collection F and Distance matrix D ', the Euclidean space all fingerprint map tieed up to a d by MDS algorithm;
S3. the Euclidean space tieed up according to described d generates unstressed plane graph, carries out key feature extraction, and carries out space coordinate conversion,
Wherein, described key feature extracts and comprises corridor recognition, room identification and reference point coupling, described space coordinate conversion comprises the conversion of floor-level and the conversion of room-level, described reference point coupling comprises: utilize the door in room as setting up the critical reference points contacted between unstressed plane graph and fingerprint space, wherein, first define with for inside and outside room door from the point that door is nearest, then define room door fingerprint collection described F din all fingerprints can be organized into a chain in minimum spanning tree T, therefore by described F dbe expressed as vector form F d=(f 1, f 2..., f k), and in unstressed plane graph, definition P d=(p 1, p 2..., p k) on corridor from each nearest sampled point, described in each, sampled point is at P dthe order of middle appearance is along corridor from side to opposite side, due to from F dto P dbe mapped as corresponding or just reverse order is corresponding, achieve reference point coupling and determine the corresponding of certain room fingerprint collection and certain room in plane graph in unstressed plane graph.
2. wireless indoor location method as claimed in claim 1, it is characterized in that, described S1 comprises further:
S11. the signal of wireless network and the reading of acceleration transducer and direction sensor is gathered by smart mobile phone, suppose there be m wireless network access point in region, then described smart mobile phone RSS fingerprint obtained of certain position in region is designated as the vector f=(s of a m dimension 1, s 2..., s m), wherein s irepresent the RSS value of i-th wireless network access point, define d ' again ijfor f iand f jbetween distance, be the step number that user walks between the two positions, after the fingerprint-collection stage terminates, obtain fingerprint collection F={f i, i=1 ... n}, wherein n is the number of fingerprint, and Distance matrix D '=[d ' ij];
S12. preliminary treatment is carried out, to two fingerprint f to described fingerprint collection F i=(s 1, s 2..., s m) and f j=(t 1, t 2..., t m), definition f iand f jdiversity factor is if δ ijbe less than predetermined threshold, then f iand f jin the generative process of fingerprint space, be taken as identical point, otherwise be taken as different points;
S13. to described Distance matrix D ' carry out preliminary treatment, the beeline between often pair of fingerprint is calculated according to shortest path first, if namely at f iand f jcertain intermediate node of existence f k, meet d ' ij>d ' ik+ d ' kj, then d ' ijbe updated to d ' ik+ d ' kj.
3. indoor orientation method as claimed in claim 1, it is characterized in that, described corridor recognition comprises: utilize the fingerprint on degree acquisition corridor, centre, wherein, according to the distance between fingerprint, set up minimum spanning tree T, calculate the middle degree of each point on described minimum spanning tree, the part that centre degree is high is considered as the fingerprint on corridor, is designated as corridor fingerprint collection F c, wherein said middle degree B (v) is defined as: the figure G=(V, E) be made up of vertex set V and limit collection E for, wherein, σ stfor the shortest path number from s to t, σ stv () is from s to t and through the shortest path number of v.
4. indoor orientation method as claimed in claim 1, it is characterized in that, the identification of described room comprises: utilize cluster to obtain room fingerprint collection, wherein, remove described corridor fingerprint collection F in all fingerprint spaces c, adopt K-means algorithm to remaining fingerprint F-F ccarry out cluster, obtain individual the trooping of k k and (be designated as i=1,2 ..., k), think same after cluster in institute a little from same room with them.
5. indoor orientation method as claimed in claim 1, it is characterized in that, the conversion of described floor-level comprises: utilize a transformation matrix to realize the conversion of the floor-level of unstressed plane graph and fingerprint spatial visualization figure, wherein, suppose at F din the coordinate of a fingerprint be x i=[x i 1x i 2x i d] t, wherein d is the dimension in fingerprint space, the coordinate y of corresponding position i=[y i 1y i 2y i d] t, definition A is the transformation matrix of d × d, B=[b 1b 2b d] t, owing to there being k=|F d| bar equation y i=Ax i+ B, is rewritten as H by described k bar equation iz=G i, wherein H i=[x i t1], z=[AB] t, G i=y i t, combine described k bar equation, have Hz=G, wherein H iand G ifor i-th row of H and G, solved by least square method try to achieve A and B, thus be x=[x for coordinate i 1x i 2x i d] ta fingerprint, can be considered its physical location from the sampled point that Ax+B is nearest.
6. indoor orientation method as claimed in claim 1, it is characterized in that, the conversion of described room-level comprises: utilize MDS algorithm the fingerprint from same room with them to be transformed to the space of a d dimension further, the sampled point in corresponding room is made to form the unstressed plane graph of a d dimension, by as a reference point with point farthest recently from room door, the transformation relation between fingerprint room and physical room can be determined, by repeating aforesaid operations one by one to all rooms, achieve the conversion of the unstressed plane graph in each room and the room-level of fingerprint spatial visualization figure.
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