Magicol: Indoor Localization Using Pervasive Magnetic Field and Opportunistic WiFi Sensing

粗略翻译，方便快速阅读
abstract
Anomalies of the omnipresent earth magnetic (i.e., geomagnetic) field in an indoor environment, caused by local disturbances due to construction materials, give rise to noisy direction sensing that
hinders any dead reckoning system. In this paper, we turn this unpalatable phenomenon into a favorable one. We present Magicol, an indoor localization and tracking system that embraces the local disturbances of the geomagnetic field. We tackle the low discernibility
of the magnetic field by vectorizing consecutive magnetic signals on a per-step basis, and use vectors to shape the particle distribution in the estimation process. Magicol can also incorporate WiFi signals to achieve much improved positioning accuracy for
indoor environments with WiFi infrastructure. We perform an in-depth study on the fusion of magnetic and WiFi signals. We design a two-pass bidirectional particle filtering process for maximum accuracy, and propose an on-demand WiFi scan strategy for energy
savings. We further propose a compliant-walking method for location database construction that drastically simplifies the site survey effort. We conduct extensive experiments at representative indoor environments, including an office building, an underground
parking garage, and a supermarket in which Magicol achieved a 90 percentile localization accuracy of 5 m, 1 m, and 8 m, respectively, using the magnetic field alone. The fusion with WiFi leads to 90 percentile accuracy of 3.5 m for localization and 0.9mfor
tracking in the office environment. When using only the magnetism, Magicol consumes 9× less energy in tracking compared to WiFi-based tracking.

我们提出的Magicol室内定位和跟踪系统，可以抵抗地磁场的干扰。①我们在每一个步骤的基础上通过对连续磁信号进行向量化处理来解决磁场低分辨的问题，利用向量来模拟粒子的分布形状。②为了更好的定位精度，Magicol也将WiFi信号强度纳入考量中。我们对磁性和WiFi信号的融合进行了深入的研究。为达到最高的精度，我们设计了一个双通双向粒子滤波过程，并且为了节能提出了一种按需扫描WiFi信号强度的策略。③我们进一步提出了一个融合步行的方法来建设位置数据库的算法，大大简化了场地测量工作。
I. INTRODUCTION
ACCURATE and pervasive indoor positioning can significantly improve our everyday life. Examples include local searching for position of interest (POIs) in a shopping mall, navigating to a meeting room
in an unfamiliar office building, and finding a car in a parking garage. WiFi [1]–[4], cellular [5]–[7], or even FM [8], [9] based approaches have shown great promise but may not be as effective when the signals are weak or not available, as is the case in
an underground parking garage. The WiFi scans are also known to be energy expensive.
精确和普及的室内定位可以显着改善我们的日常生活。 示例包括在购物中心中本地搜索感兴趣的位置（POI），导航到不熟悉的办公大楼中的会议室以及在停车库中找到汽车。 基于Wi-Fi [1] - [4]，蜂窝[5] - [7]或甚至FM [8]，[9]的方法表现出巨大的希望，但是当信号弱或不可用时， 是在地下停车场的情况。 WiFi扫描也被认为是能量昂贵的。
The (geo-)magnetic field is omnipresent, and thus can potentially be leveraged for a pervasive positioning technology for an indoor environment without any dependency on infrastructure. There are several
ways to exploit the geomagnetism for localization purposes. One is to obtain the walking direction from the magnetic field, typically used in an inertial sensor based tracking (i.e., dead reckoning) system [10]–[12]. However, the direction sensing inside a
building is extremely noisy due to the geomagnetic field anomalies caused by the local disturbances of ferromagnetic building materials [13], [14]. Another way, in contrast, is to exploit the magnetic field anomalies as distinctive signatures. But these systems
either require customized hardware [15] or work under specific scenarios [16], [17]. The magnetic field anomalies are also used to discriminate indoor and outdoor environment in [18], and as indoor landmarks in [12].
（地理）磁场是无所不在的，因此可以潜在地用于室内环境的普遍定位技术，而不依赖于基础设施。 有几种方法利用地磁用于本地化目的。 一个是从磁场获得步行方向，通常用于基于惯性传感器的跟踪（即航位推算）系统[10] - [12]中。 然而，由于由铁磁性建筑材料的局部扰动引起的地磁场异常，建筑物内的方向感测非常嘈杂[13]，[14]。 相反，另一种方法是利用磁场异常作为区别性标记。 但这些系统需要定制的硬件[15]或在特定的情况下工作[16]，[17]。
磁场异常也用于区分室内和室外环境[18]，和作为室内地标[12]。
In this paper, we present the design and evaluation of Magicol—a magnetic field based indoor localization and tracking system for smartphone users. Recognizing that the indoor geomagnetic field anomalies
are omnipresent, location specific and temporally stable, Magicol leverages the locally disturbed magnetic signals as location-specific signatures. It uses the magnetometer commonly found on smartphones, without resorting to special hardware. Through magnetic
sensing that consumes very little energy, Magicol is energy efficient and applicable to almost every indoor venue.

在本文中，我们提出对Magicol的设计和评估——一个为智能手机用户设计的基于磁场的室内定位和追踪系统。认识到室内地磁场的异常是无所不在的，
Magicol利用局部干扰的磁信号作为特定位置的标签。它使用智能手机上常见的磁强计量器，不用求助特殊的硬件。Magicol通过消耗很少能量的磁检测器，高效节能，适用于几乎所有的室内场所。
To make Magicol a reality, we must address three major challenges. First, the magnetic signal has a very limited discernibility. A single observation cannot be reliably used as a unique location signature.
In Magicol, we leverage user motion to vectorize multiple observations to form a higher dimensional signature. This vector is then matched against a pre-established magnetic signal map (M-Map), a location database built offline with mappings between magnetic
signals and their locations, to localize the user. A user may walk arbitrarily, in different directions and with different strides, and may stop from time to time. To ensure tractable complexity, the vectorization is performed on a per-step basis, and the
matching process is realized through an augmented particle filter (APF) in which the similarity between the signal vector and that in the M-Map is used to weigh particles. We design a novel map-constrained, positionaware, and inertial-based (MPI) particle
motion model to avoid using absolute (indoor) heading directions that are known to be noisy. We further use dynamic time warping in APF to address practical issues such as variations in spatial sampling density, devices, and usage patterns.

为了实现Magicol系统，我们必须解决三大挑战。首先，磁信号的辨别性非常有限。一个单一的观察值作为一个独特的位置特征是不可靠的。在Magicol里，我们利用用户的运动信息来向量化多个观察值形成一个高维的特征。这个向量之后被用来与预先建立的磁信信号强度地图（M-Map）匹配来定位用户，M-Map利用磁信号和它们的位置之间的映射离线建立位置数据库。用户可以在不同的方向以不同的步伐任意行走，并可能会不时停止。为了确保可行的复杂度，向量化是在每一个步骤的基础上进行的，匹配过程是通过改进的粒子滤波（APF）实现，信号向量和M-map之间的相似性是通过带权重的粒子来衡量的。
20000
我们设计了一种新的地图限制，positionaware，是一种基于惯性（MPI）粒子的运动模型，可以避免使用绝对（室内）前进方向，这种绝对方向已被验证是带有噪声的。我们进一步在粒子滤波上使用动态时间规划来解决实际问题，例如空间采样密度，设备和使用模式的变化。
Secondly, while Magicol works without dependency on a WiFi infrastructure, but it can work even better in dense WiFi AP deployment environments, an issue that has not been exploited. We show the WiFi
and magnetic signals are indeed complementary: WiFi signals are distinctive across distant locations whereas magnetic field are more locally discriminative. We then explore a few intuitive ways of magnetic-WiFi fusion, which uses a rough WiFi localization
estimate to confine initial particle distribution and also considers the WiFi fingerprint similarity in the course of APF. In particular, we design a
two-pass, bidirectional particle filtering method to fuse the WiFi and magnetic localization. Given a WiFi scan result and a background logged motion trace with unknown starting position, the first pass aims to obtain a good estimate of the starting
position via backward particle filtering on the reversed motion trace with particles initially distributed around theWiFibased location estimate. The resultant starting position is in return used to ensure better initialization of the forward particle filtering
process in the second pass.
其次，虽然Magicol不依赖WiFi基础设施工作，但它在WiFi AP部署密集的环境中工作效果更好，这是一个尚未被开发的问题。WiFi和磁信号实际上是互补的：WiFi信号在远距离的分辨能力是显着的，而磁场在局部范围更容易被区分。然后，我们探讨了一些直观的磁场和WiFi融合方法，它使用粗略的WiFi定位来限制初始粒子分布范围，并考虑APF过程中的WiFi指纹相似性。特别是，我们设计了一个双通双向粒子滤波方法来融合WiFi和磁场定位。给定WiFi扫描结果和后台记录的具有未知起始位置的运动轨迹，第一步目标在于通过在反向运动轨迹上的反向粒子滤波获得起始位置的良好估计，其中这些粒子是使用基于WiFi的位置估计初始化的。所得到的起始位置用于第二步中正向粒子滤波过程的初始化。
Thirdly, as in radio based localization systems, the location database (i.e., M-Map in Magicol) needs to be constructed in advance. This is a non-trivial problem and has been actively studied recently
[19], [20]. In addition, the low discernibility of the magnetic field entails a densely collected database. We propose a
compliant-walk (CW) based site survey solution. A surveyor only needs to walk normally along pre-planned survey paths. The phone collects inertial sensor readings and magnetic signals automatically during the walk. The system estimates the actual walking
traces from the sensor data, and matches the data against the paths through dynamic programming. This fixes the positions of the steps, from which positions of magnetic signals are interpolated. With CW, the survey task is significantly simplified for an ordinary
phone user. This method is also applicable to other localization means such as WiFi-based fingerprinting.
第三，正如基于无线电的定位系统，需要预先构建位置数据库（即，Magicol中的M-Map）。 这是一个具有价值的问题，最近受到研究[19]，[20]。 此外，磁场的低可辨别性需要密集收集的数据库。 我们提出一个以融合步行（CW）为基础的位置测量方案。 测量员只需要沿着预先计划的测量路径正常行走。
手机在步行期间自动收集惯性传感器读数和磁场信号。 系统根据传感器数据估计实际步行轨迹，并且通过动态规划将数据与路径匹配。固定的步伐形态可以揭示从哪个位置开始磁信号强度发生变化。使用CW，普通电话用户的调查任务显著简化。该方法还适用于其他定位手段，例如基于WiFi的指纹识别。
In summary, the contributions of Magicol are threefold:
总之，Magicol的贡献有三个方面：
• We perform an in-depth study of the indoor magnetic field properties and propose effective techniques to exploit the anomalies of the magnetic field for localization and handle several practical challenges.

• We propose a novel two-pass bidirectional particle filtering process to fuse magnetic and WiFi signals for more accurate indoor positioning and tracking.

• We devise a compliant-walk based location database construction method which significantly lowers the bar for ordinary smartphone users to conduct site surveys.

•我们对室内磁场特性进行深入研究，并提出有效的技术来利用磁场的异常进行定位，并应对若干实际挑战。
•我们提出一种新型双向双通粒子滤波过程来融合磁信号和WiFi信号，从而实现更准确的室内定位和跟踪。
•我们制定了一个基于步行一致的位置数据库构建方法，这显著降低了普通智能手机用户进行现场调查的标准。
 
II. INSIGHT ON
GEOMAGNETISM
对磁场的探索
In this section, we provide some measurement study on the properties of the indoor magnetic field, some are favorable for indoor localization purpose, whereas others bring challenges to actual exploration.
在本节中，我们对室内磁场的性质进行一些测量研究，一些是有利于室内定位的目的，而另一些对实际勘探带来挑战。
A. Favorable Geomagnetic Field Properties
A.有利的地磁场性质
Locally Disturbed yet Stable Magnetic Field:
Indoor magnetic fields have been found to exhibit certain anomalies due to the disturbances caused by building construction materials and electrical appliances. The patterns of disturbance are different across different locations. In addition, the magnetic
field, including the local disturbances, is very stable over time as long as the internal layout remains unchanged. Fig. 1 clearly demonstrates these properties, where the magnetic signals were collected during walks along a straight corridor in an office
building at different times of day, and on two different dates that were two months apart. The local disturbance and the stability over time make the magnetic field a potential candidate for localization purpose. We note that it has been reported and preliminary
explored in many previous work (e.g., [13]–[15], [17], [18], [21]–[24]), we include them here for completeness.
有局部干扰但稳定的磁场：由于建筑材料和电器产生的干扰，室内磁场会表现出特定的异常。 不同位置的干扰模式是不同的。 此外，只要内部布局保持不变，局部干扰的磁场随时间变化是非常稳定的。图1清楚地表明了这些性质，其中磁信号是沿着办公楼内的竖直走廊在一天的不同时间和相隔两个月的两个不同日期期间被收集。局部扰动和随时间的稳定性使得磁场成为用于定位目的的潜在候选。我们注意到，在许多以前的工作（例如，[13]
- [15]，[17]，[18]，[21] - [24]）中已经报道并初步探讨，我们在这里包括它们的完整性。
Limited Impact of Mobile Objects:
Indoor environments are usually highly dynamic, due to mobile objects such as people, cars, elevators, and on/offs of electrical appliances. We studied the impact they have on the magnetic field in typical scenarios. The results are shown in Fig. 2. Fig.
2(a) shows the impact of cars, with data having been collected along the red line that was about 1 meter away from the car. We collected data twice: at 4PM when the garage was full of cars, and at 12AM when the garage was almost empty. We can see that cars
have little impact on the magnetic field that is 1 meter away. We also measured the influences of people and grocery carts in a supermarket.As can be seen in Fig. 2(b), there was no visible
impact from trolleys and people walking by. On the contrary, the fluctuation of magnetic measurement is much larger and obvious during user walking. We also collected magnetic signals in an elevator lobby with 12 running elevators at a 1-meter distance from
the elevator doors. In Fig. 2(c), comparing with drastic fluctuations of magnetic values during walking, running elevators do not bring serious impacts when the user is standing still. That means the elevator infrastructure had a more significant impact on
the magnetic field whereas the moving cabin had little impact. In summary, our experiments confirm that the impact of mobile objects is very limited, and have barely no impact at a distance of one meter away.
移动对象的有限影响：由于诸如人，汽车，电梯和电器的开/关等移动对象，室内环境通常是高度动态的。 我们研究了它们在典型情况下对磁场的影响。 结果示于图1和 图2。 图2（a）示出了汽车的影响，其中数据是沿着离汽车约1米的红线收集的。 我们收集数据两次：在下午4点当车库充满了汽车，和上午12时，当车库几乎是空的。我们可以看到车对1米外的磁场影响不大。
我们还测量了人们和杂货店在超市的影响。
如图2（b）所示，手推车和人行走没有明显的影响。 相反，在用户行走期间，磁测量的波动更大和更明显。 我们还在电梯大厅收集了磁信号，在离电梯门1米的地方有12部电梯。 如图2（c）所示，与步行时的磁性值的急剧变动相比，使用者静止时，运行电梯不会带来严重的影响。
这意味着电梯基础设施对磁场有更显着的影响，而移动的舱室几乎没有影响。 总之，我们的实验证实移动物体的影响非常有限，并且在距离一米外几乎没有影响。
B. Challenges in Using the Magnetic Field
B.使用磁场的挑战
Low Discernibility of Magnetic Signals:
The strength of (geo-)magnetic field is usually very weak, commonly within a few tens of uT. Hence, singlemagnetic signal offers very limited discernibility. Taking the iPhone 4 trace shown in Fig. 3(a) as an example. If we randomly pick one magnitude,
say 48, we will find many locations with magnitude 48 in the rather short trace.
磁信号的低分辨性：（地理）磁场的强度通常非常弱，通常在几十uT内。因此，单磁信号提供的可辨别性非常有限。以图3（a）中所示的iPhone 4轨迹为例，如果我们随机选取一个幅值，例如48，我们将在相当短的轨迹中找到许多幅值为48的位置。
The magnetic field is directional, and a magnetometer measures 3-D magnetic signals. It is natural to think of using the 3-D signal to increase the discernibility. However, it is hard to do so in practice
because the frame of reference of the magnetometer may not always align with the global coordinate system. To ensure the alignment, it would require either to accurately track the device attitude all the time or to constrain the device usage to some fixed
attitude (e.g., hand-held horizontally with Y-axis towards heading direction). The former is difficult due to sensor drift and the latter severely affects user experiences. Therefore, only the magnitude of the magnetic signal may be used in practice.
磁场有方向的，并且磁力计测量3-D磁信号。想到使用3-D信号来增加可辨别性是很自然地。 然而，在实践中很难这样做，因为磁力计的参考系与全局坐标系可能不总是一致的。为了确保坐标系一致，将需要始终精确地跟踪装置方向或者将以某种固定姿态使用装置到（例如，水平地手持，Y轴朝向方向）。前者由于传感器漂移而实现困难，后者严重影响用户体验。
因此，在实践中可以仅使用磁信号的幅值。
Device Diversity and Usage Diversity:
We found that for the same magnetic field, different devices will show different readings. This is clearly demonstrated in Figs. 3 and 4. Fig. 3(a) shows the magnitude of the collected magnetic signals along exactly the same path using different smartphones.
For the same device, if the data was collected at different device attitudes, then the resulting signals vary. This is confirmed in Fig. 3(b), where the data was collected with different attitudes along the same path. Note that during the experiments, we stood
still for 10 seconds before walking to discriminate sensor noise and magnetic field variation. Such diversity in terms of devices and usage further impair discernibility.
设备和使用方式多样性：我们发现，对于相同的磁场，不同的设备显示不同的读数。这在图3和图4中清楚地示出。图3（a）显示出了使用不同的智能手机沿着完全相同的路径收集的磁信号的幅度。对于相同的设备，如果以不同的使用姿态（手机和人的相对方向）收集数据，则所得到的信号也会变化。如图3（b）所示，其中沿着相同路径以不同的使用姿态收集数据。注意，在实验过程中，我们在走前静止10秒钟，以区分传感器噪声和磁场变化。在设备和使用方面的这种多样性进一步削弱了可辨别性。
Statistical results of the deviation of magnetic field measurement are shown in Fig. 4. In Fig. 4 we can see that compared with temporal influence, deviations of magnetic measurement among different
devices and attitudes are larger. However, deviation values are relatively stable with different trace lengths, and variances of deviation are small that result in steep slopes of all three CDF curves.
磁场测量偏差的统计结果如图4所示。从图4可以看出，与时间影响相比，不同器件和使用姿态会使磁测值差异更大。然而，偏差值对于不同长度的迹线是相对稳定的，并且偏差的变化小，导致三个CDF曲线都带有陡峭斜率。
As a brief summary, the magnetic field has favorable intrinsic properties (i.e., stability and local disturbance) to serve as a localization modality. However the low discernibility of magnetic signals
make it rather challenging to explore the magnetic signal directly, e.g., using fingerprinting techniques.The device and usage diversities further pollute the sensed magnetic strength.
简要概述，磁场具有有利的内在特性（即，稳定性和局部干扰）以用作定位模式。然而，磁信号的低可辨别性使得直接探测磁信号变得相当具有挑战性。例如使用指纹技术。设备和使用姿态的多样性进一步干扰感测到的磁强度。
 
III. MAGICOL
OVERVIEW
MAGICOL概述
The insights into indoor geomagnetism indicate both opportunities and challenges when utilizing a magnetic field for localization purposes. On one hand, features such as the ubiquitousness, the location-specific,
temporally stable and undisturbed anomalies clearly reveal the potential of using magnetic signals as location signatures. On the other hand, the low discernibility, device and usage diversity impose real challenges that we need to overcome.
对室内地磁的研究表明将磁场用于定位时所面对的机遇和挑战。优势：无处不在，位置特异性，时间稳定性，未受干扰的异常的特征清楚地揭示了使用磁信号作为位置特征的可能性。劣势：低可辨别性，设备和使用姿态的多样性增加了使用难度。
In this section, we provide an overview of Magicol—an indoor localization system for mobile phone users that exploits the globally available geomagnetic field. Magicol consists of a mobile client and
a backend Cloud service. The mobile client has two operating modes: online and offline. The overall architecture of Magicol is depicted in Fig. 5.
在本节中，我们提供了Magicol的概述 - 利用全球可用的地磁场的手机用户的室内定位系统。Magicol由一个移动客户端和一个后端云服务组成。移动客户端有两种操作模式：在线和离线。Magicol的总体架构如图5所示。
Mobile Client:
TheMagicol client performs background data logging (to facilitate immediate localization) of IMU sensor data and, opportunistically, the WiFi sensing results. To save memory and communication costs, it performs motion state detection and keeps a window
of the most recent walking information (e.g., step length, turning angle of the step) and the corresponding magnetic signals. Walking state detection is well studied and we employ the step detection techniques and personalized step model developed by Li
et al. [25]. The mobile client may operate in online mode if network access is available. In this mode, the background logged data is sent to the Cloud service to obtain a location fix; it may also operate in offline mode when there is no network access
and the location database is downloaded beforehand. In this mode, the location is resolved locally on the device using a local location inference engine.
手机客户端：Magicol客户端执行IMU传感器数据的背景记录（以便立即定位），并且选择性地执行WiFi传感检测。为了节省内存和通信成本，它执行运动状态检测并且只保持最新的步行信息（例如，步长，转向角度）和相应的磁信号。行走状态检测是很重要的研究，我们采用步伐检测技术和由Li等人开发的个人化步态模型。如果网络访问可用，则移动客户端可以在在线模式下操作。在此模式下，将后台记录的数据发送到云服务以获取位置修订;
当没有网络接入但已预先下载位置数据库时，它也可以在离线模式下操作。在此模式下，使用本地位置推断引擎在设备上解析位置。
Cloud Service:
Cloud service consists of two subsystems: location database construction and a location inference engine. The location database consists of the magnetic fingerprint map (M-Map) that contains <position, magnetic field strength>
tuples and the radio map which stores the WiFi information. The M-Map construction
subsystem solves the location database construction problem through a simple yet efficient
compliantwalking- based (CW) site surveying method (Section VI). The subsystem further consists of three modules: survey plan creation, user trace estimation, and trace matching.
云服务：云服务包括两个子系统：位置数据库构造和位置推断引擎。位置数据库由包含<位置，磁场强度>元组的磁场指纹地图（M-Map）和存储WiFi信息的无线电地图组成。M-Map构造的子系统能够通过基于步态融合（CW）的场地测量方法（第VI部分）解决位置数据库构造问题。子系统还包括三个模块：创建测量计划，用户运动轨迹估计和跟踪轨迹匹配。
The location inference engine receives and resolves location queries from mobile clients. As a common module for both the mobile client (in offline mode) and the backend Cloud service, it resolves a
user's location by matching the magnetic signals against the M-Map. The location resolution process is achieved through an
augmented particle filter that operates on a per-step basis (Section IV). Depending on the availability of other opportunistically sensed signals (e.g., WiFi), it may leverage and fuse them with the magnetic field-based localization process (Section
V).
位置推断引擎接收并解析来自移动客户端的位置查询请求。作为移动客户端（在离线模式下）和后端云服务的通用模块，它通过将磁信号与M-Map相匹配来推断用户的位置。位置分辨过程通过一个在每一步基础上进行操作的改进粒子滤波器实现（第IV部分）。其他随机感测信号（例如，WiFi）如果可以使用，其可以将它们与基于磁场的定位过程融合（第V部分）。
 
IV. TRACKING
WITH
MAGNETIC
FIELD
In this section, we present the tracking engine that resolves user's location through observed magnetic signals and the IMU data using particle filtering. In addition to aforementioned low discernibility
of the magnetic signal, device and usage diversities, it further faces challenges caused by different spatial sampling density due to different walking speed or sensor sampling rate. We elaborate concrete techniques that overcome all these challenges.
在本节中，我们提出了通过观察到的磁信号和使用粒子滤波的IMU数据来推断用户位置的跟踪引擎。除了上述磁信号的低可辨别性，装置和使用姿态多样性之外，它还面临由于不同的步行速度或传感器采样率而由不同的空间采样密度带来的挑战。我们制定克服所有这些挑战的具体算法。
A. Step-Based Vectorization
To improve the discernibility of (geo-)magnetic signals, one common method is to increase the spatial coverage of measurements. Unlike [15] where the authors obtained a 12-D vector magnetic signal using a special customized hardware,
which implies not applicable to mobile phones, we propose to vectorize
multiple temporal observations into a high dimensional vector signal. This vector signal has increased spatial coverage due to
the fact that the user is walking. Let's again take Fig. 3(a) as an example. Now suppose the device observes three consecutive samples with magnitude {47, 48, 49}. There are only two possible locations (highlighted with red circles) with similar observations.
The discernibility is indeed improved. Obviously, the longer the trace we vectorize, the more discriminative the resulting vector signal will be.

为了改善（地理）磁信号的可辨别性，一种常用的方法是增加测量的空间覆盖率。[15]中作者使用特殊定制的硬件采集了12-D向量磁信号，这种方式不适用于移动电话，与此不同，我们提出将多个时间的观测值向量化为高维矢量信号。由于用户在行走的事实，该向量信号具有更广的空间覆盖。以图3（a）为例。现在假设设备观察到三个幅值为{47,48,49}的连续样本。只有两个可能的位置（用红色圆圈突出显示）具有相似的观察结果。所以确实改善了可辨别性。显然，我们向量化的轨迹越长，得到的向量信号越有辨别力。

We incorporate the step model and vectorize all the samples
within the same step as a vector for three reasons. First, when performing a vector comparison, it makes sense only when both vectors cover a similar spatial distance. Thus, we need to have an estimate of the spatial coverage of the step vector. Such
information is readily available from IMU-based tracking. Second, all the samples within the same step always have the same motion direction. This is the fundamental reason that we can combine them into one vector. Third, using step model naturally handles
the discontinuity in the walking process.
我们之所以结合步态模型并在同一步中将所有样本向量化为向量，有三个原因。首先，当执行向量比较时，仅当两个向量覆盖类似的空间距离时才有意义。因此，我们需要估计步向量的覆盖空间。这样的信息容易从基于IMU的跟踪获得。第二，同一步骤内的所有样本总是具有相同的运动方向。这是我们可以将它们组合成一个向量的根本原因。第三，使用步态模型可以自然地处理步行过程中的不连续。
B. Magnetic Vector Matching With DTW
利用DTW匹配磁场向量
The magnetic field is sampled continuously while walking. Due to possibly different walking speeds and different sampling rates, different number of samples may result for the same spatial coverage. We refer to this as
spatial sampling density variation issue. Fig. 6 demonstrates this problem. In our experiments, we walked along the same path at different speeds while sampling the magnetometer at a fixed frequency. We found that fast walking led to shorter traces
and fewer samples, whereas slow walking yielded long traces and more samples. This translates to different spatial sampling density because the walks covered the same path. Different temporal sampling frequencies will further complicate the phenomenon.

磁场在步行时连续采样。由于不同的步行速度和不同的采样率，对于相同的覆盖空间可能产生不同数量的样本。我们将其称为空间采样密度变化问题。图6演示了这个问题。在我们的实验中，我们沿着相同的路径以不同的速度走，同时以固定频率采样磁力计。我们发现，快速步行导致更短的痕迹和更少的样品，而缓慢的步行导致长的痕迹和更多的样品。这转化为不同的空间采样密度，因为步行覆盖相同的路径。不同的时间采样频率将进一步使该现象复杂化。

The spatial sampling density variation makes it difficult to directly compare two vectors that cover the same spatial range, as they are likely to have different dimensionalities. However, a closer
look at Fig. 6 reveals that, despite the different spatial sampling densities, their shapes look similar. Therefore, in Magicol, we adopt dynamic time warping (DTW) to compare two vectors. DTW is a proven effective algorithm for measuring similarity between
two sequences that may vary in time or speed.
空间采样密度变化使得难以直接比较覆盖相同空间范围的两个向量，因为它们可能具有不同的维度。然而，仔细观察图6，尽管不同的空间采样密度，它们的形状看起来相似。 因此，在Magicol中，我们采用动态时间扭曲（DTW）来比较两个向量。 DTW是用于测量可能在时间或速度上有差别的两个序列之间的相似性的有效的算法。
Handling the Diversities:
We further handle the device diversity and usage diversity issues, identified in Section II, with a simple mean removal technique: both the signal vector and the candidate vector have their mean removed before applying DTW. The rationale is that, despite
the diversities in measured magnetic strengths, the shape of the resulting magnetic signal sequences are all similar for the same path, as confirmed in both Figs. 3 and 6. Therefore, we can rely on the shape of the local magnetic field instead of their absolute
values.
处理多样性：我们使用平均删除技术进一步处理在第二部分中提到的设备和使用姿态多样性问题：在应用DTW之前，信号向量和候选向量都被去除了平均值。如图3和图6中所证实的，原理是尽管测量的磁强度的多样性，所得到的磁信号序列的形状对于相同的路径都是类似的。因此，我们可以依赖于局部磁场的形状而不是它们的绝对值。
In brief, to match a magnetic signal vector collected in one step, we compose a mean-removed candidate vector in the database. The candidate vector consists of a set of successive geomagnetic samples
spread over the travelling path of each particle. These samples cover the same spatial distance of that step. We then remove the means of both the measurement vector and the candidate vector, and apply DTW to calculate their similarity.
简而言之，为了匹配在某一个步中收集的磁信号向量，我们在数据库中去除平均的候选向量。候选向量由在每个粒子的行进路径上分布的一组连续的地磁样本组成。在该步中这些样本覆盖了相同的空间距离。然后我们去除测量向量和候选向量的平均值，并运用DTW计算它们的相似性。
 
C. Particle Motion Model粒子运动模型
Particle filtering is commonly adopted in tracking applications. In these work, particles are
uniformly driven by externally sensed absolute heading directions, which is often the fusion result from compass and gyroscope. However, due to the magnetic field anomalies, the heading direction, even after fusion, is still very noisy, as
evidenced in Fig. 7.
粒子滤波在跟踪应用中是常用的。在这些工作中，粒子一致由外部感测的绝对方向驱动，这通常是来自罗盘和陀螺仪的融合结果。然而，如图7所示，由于磁场异常，即使在融合之后，前进方向仍然充满噪声。
Magicol also adopts particle filtering. Unlike existing tracking systems that fuse the magnetometer and the gyroscope to obtain a compromised result, Magicol makes separate use of them to best exploit
the strength of each sensor modality: the gyroscope can reliably tell relative walking direction; magnetic field anomalies can serve as useful location features.

Magicol还采用粒子滤波技术。不像现有的跟踪系统将磁力计和陀螺仪融合以获得折衷的结果，Magicol分开使用它们使得更好地利用每个传感器的测量强度：陀螺仪可以可靠地指示相对行走方向; 磁场异常可以用作有利的定位特征。
Based on the observation that a user is very likely to follow the main direction of the path and is very likely to continue walking in a consistent direction rather than making random turns, we come
up with a map-constrained, position-aware, inertial-based (MPI) particle motion model to drive particles. In this MPI motion model, as illustrated in Fig. 8, the direction _u
of a newborn particle (e.g., Particle A and D) is determined by the direction _upw
of the pathway it is on; and that of a resampling particle (e.g., Particle B and C) is that of the previous step plus the relative direction change _ugyro
during this step, hence the term inertial-based. The relative direction is obtained from the gyroscope using the technique presented in Section VI.

基于观察结果，用户很可能遵循路径的主方向，并且很可能继续沿着一致的方向行走而不是随机转向，我们想出了一个地图约束，position-awar（位置感知），基于惯性的（MPI）粒子运动模型来驱动粒子。如图8所示，在该MPI运动模型中新生颗粒（例如，颗粒A和D）的方向_u由其所在的路径的方向_upw确定;
而重采样粒子的方向（例如，粒子B和C）是前一步骤的方向加上在该步的相对变化方向_ugyro得到的，因此是基于惯性的。相对方向是从陀螺仪获得的，使用第VI节中提出的技术。
Note that the gyroscope may occasionally give a false positive conclusion of turns due to the possibility of sudden attitude change (e.g., change holding hands), but it seldom misses the detection of
real turns. Therefore, if the gyroscope indicates no turn, we may significantly reduce (or even eliminate) the possibility of a direction turn (e.g., Particle B); whereas when the gyroscope indicates a turn, we will increase the probability of a turn in direction
but still retain a certain probability of the original direction (e.g., Particle C). If the turn indication is a false alarm, then the particles will soon hit the wall and die. Clearly, Magicol makes more use of the map information than existing tracking systems.
It uses not only the walls to kill incorrectly moved particles, but also uses the pathway directions to better initialize a particle's direction.
注意，陀螺仪可能由于突然的姿态的改变（例如，改变持机手势）而偶尔给出错误的转弯判断，但是它很少丢失对真实转弯的检测。因此，如果陀螺仪指示没有转向，我们可以显着地减少（或甚至消除）方向转向的可能性（例如，粒子B）; 而当陀螺仪指示转弯时，我们将增加方向转弯的概率，但仍保持原始方向的某一概率（例如，粒子C）。 如果转向指示是假警报，则颗粒将很快撞击壁并死亡。显然，Magicol比现有的跟踪系统更多地使用地图信息。
它不仅使用墙壁来杀死不正确移动的粒子，而且还使用路径方向更好地初始化粒子的方向。
D. Augmented Particle Filter改进的粒子滤波
All these techniques are combined into an augmented particle filter that executes on a per-step basis. The state of a particle includes its current location _p
= {x, y} and also the heading direction _u. The observations are obtained from the mobile client, include step information (step length, relative direction change) and the magnetic fingerprint vector collected during the step.

所有这些技术被组合形成在每一步基础上执行的改进的粒子滤波器。粒子的状态包括其当前位置_p = {x，y}以及方向_u。观察值从移动客户端获得，包括当前步的步态信息（步长，相对方向变化）和在步骤期间收集的磁指纹向量。
Particle Movement:
With new step input, location of each particle is updated as follows:
粒子运动：当新的步态信息输入时，每个粒子的位置更新如下：




is a probabilistic selection function that instantiates the direction of a newborn particle according to its position.


accounts for possible direction errors that are also assumed to follow a Gaussian distribution with zero mean and variance set to 10◦.
l is the estimated step length and δ obeys a Gaussian distribution with zero mean and variance set to 0.2l
to capture the possible error of step length estimation.


是概率选择函数，其根据其位置实例化新生粒子的方向。考虑到可能的方向误差，

设定为遵循具有均值为零和方差为10°的高斯分布。l是估计的步长，δ服从均值为零和方差为0.2l的高斯分布，以避免步长估计的可能误差。
Particle Weight Assignment:
The weight of a particle is set to
粒子重量分配：粒子的重量设置为



where d is the resulting DTW distance and
σ is a parameter that reflects the overall disturbance intensity of the indoor magnetic field. Particularly, if a particle hits a wall, its weight will be significantly reduced (×0.01, but not eliminated).

其中d是所得到的DTW距离，σ是反映室内磁场总干扰强度的参数。 特别地，如果颗粒撞击壁，其重量将显着降低（×0.01，但未消除）。

Particle Resampling:
Once after particle weight updating, we conduct weight-based importance sampling over the entire set of particles. This way, particles moving at wrong directions will eventually be killed as the mismatches between the magnetic signals will continuously
reduce their weight.
粒子重采样：粒子重量更新之后，我们对整个粒子集进行基于权重的重要性采样。这样，在错误方向移动的粒子将最终被杀死，因为磁信号之间的错误匹配将连续地减小它们的重量。
Position Decision Strategy:
The distribution of particles reflects the likelihood of the real position. There two common ways to determine the position from particle distribution: one is to use the position of the particle with maximum weight; the other is to perform a weighted average
on all particles' positions using their own weights. Through experiments, we found that the former method locks on the user more quickly but may fluctuate more during the tracking process, whereas the latter method takes longer time to lock on but gives more
steady position during tracking. In Magicol, we use a hybrid method: initially go after the particle with maximum weight, and switch to weighted average once it converges. We use the weighted average of top 50% most weighted particles.
位置决策策略：粒子的分布反映了实际位置的可能性。有两种常用的从粒子分布确定位置的方法：一种是使用具有最大重量的粒子的位置;另一种是使用它们自己的权重对所有粒子的位置执行加权平均。通过实验，我们发现前一种方法更快地锁定用户，但是在跟踪过程中可能更多地波动，而后一种方法需要更长的时间来锁定，但在跟踪期间给出更稳定的位置。在Magicol中，我们使用混合方法：首先追踪具有最大权重的粒子，并且一旦收敛，就切换到加权平均。我们使用前50％最大加权粒子的加权平均值。
V. FUSION
WITH
WIFI
Tracking using only the magnetic field and inertial sensors is universally applicable. However, given the wide deployment of WiFi, we may obtain both WiFi and magnetic signals simultaneously in many
venues. In this section, we study the fusion of WiFi and magnetic signal towards even better positioning and tracking accuracy.
仅使用磁场和惯性传感器的跟踪是普遍适用的。然而，鉴于WiFi的广泛部署，我们可以在许多场所同时获得WiFi和磁信号。在本节中，我们研究WiFi和磁信号的融合，以便达到更好的定位和跟踪精度。
A. Rationale of Fusion融合理论
The fundamental reason that Magicol can be combined with a WiFi-based localization method lies in their complementary location resolving capabilities. Conceptually, WiFi is a short range radio. It is guaranteed that remote locations
will see different radio environment (less or no common APs), whereas nearby locations will share similar radio environment. On the contrary, the geomagnetic field is global. Remote locations may have similarmagnetic fields,whereas nearby locations may have
different ones due to the local disturbance to the magnetic field.

Magicol可以与基于WiFi的定位方法相结合的根本原因在于它们的位置解析能力的差异性。从概念上讲，WiFi是一个短距离无线电。保证远程位置将看到不同的无线电环境（更少或没有公共AP），而附近的位置将共享类似的无线电环境。相反，地磁场是全局的。远程位置可以具有类似的磁场，而附近位置可能由于对磁场的局部干扰而具有不同的磁场。

This concept is better illustrated in Fig. 9, which shows the normalized distances in the signal space between every pair of locations sequentially sampled from two distant parallel corridors. From
Fig. 9(a), we can see that the distances between neighboring locations can be large for those locations where the magnetic field is indeed disturbed. However, distant locations may also observe similar magnetic signals, especially when their magnetic fields
are less disturbed. On the other hand, as shown in Fig. 9(b), WiFi signals are usually similar for nearby locations, but quite different for faraway locations. If we consider both the magnetic and the WiFi signals, the resultingdistances
(in the signal space) will be a blend of the two signals, as evidenced in Fig. 9(c). This clearly indicates the potential of combining the WiFi and magnetic signals.
这个概念在图9中更好地显示出。从两个远距平行走廊顺序采样的每对位置之间的信号空间中的归一化距离。如图9（a）所示，我们可以看出，对于磁场确实被干扰的那些位置，相邻位置之间的距离可以是大的。然而，远处位置也可以观察到类似的磁信号，特别是当它们的磁场较少干扰时。另一方面，如图9（b）所示，WiFi信号通常对于附近位置是相似的，但对于远距离位置是相当不同的。如图9（c）所示，如果我们考虑磁信号和WiFi信号，则（在信号空间中）所得到的距离将是两个信号的混合。这清楚地表明了组合WiFi和磁信号的潜力。
 
B. Intuitive Fusion Methods直观的融合方法
Given the complementary properties of magnetic field and WiFi, it is natural to think of a few possible ways to fuse them. The first way is to use WiFi for a rough position estimation and constrain
particle distribution to a proximity of the WiFi location estimate. This is particular helpful at the initial of tracking and lead to faster convergence. The second way is to incorporate the similarity of WiFi signals to weigh particles during the filtering
process. For instance, the weight of a particle is set to
由于磁场和无线的互补特性，这是很自然的想到的几个可能的融合方式。第一种方式是使用WiFi的粗略位置估计约束粒子分布到邻近的位置。这是对跟踪初始化特别有帮助，并且导致更快的收敛。二是使用WiFi信号的相似性来衡量颗粒的过滤过程。例如，一个粒子的重量被设置为



where dm and dw are the distance in signal space for the magnetic and WiFi signals, respectively. σm and σw are parameters adjusting the impact of signal distances. A third way is to hybrid the first
two by weighing particles with both signal modalities but also constrain the particle distribution to be within a proximity of WiFi location estimate.
其中dm和dw分别是磁信号和WiFi信号在信号空间中的距离。σm和σw是调整信号距离的影响的参数。第三种方式混合前两种方法，是通过用两种信号模态来衡量粒子的权重，但是也将粒子分布限制在WiFi位置估计的接近值内。
C. Fusion for Better Accuracy更准确的融合
It is well known that theWiFi localization results are jumpy— measurements of two neighboring positions can lead to quite different actual position estimates. This affects the performance of fusion using the intuitive methods
presented above. To achieve better accuracy, we propose a two-pass bidirectional particle filtering
(TBPF) process to fuse WiFi and magnetic signals during tracking, where magnetic signals are available (e.g., logged in the background) when a WiFi scan is performed. The cost we pay is more computation.

众所周知，WiFi定位结果是跳跃的 -
两个相邻位置的测量可能导致完全不同的实际位置估计。这影响使用上述直观方法的融合的性能。为了实现更好的精度，我们提出了在跟踪期间融合WiFi和磁信号的双向双向粒子滤波（TBPF）过程，在磁信号和WIFI信号同时可得到的情况下使用（例如，在后台记录中可查询到）。这种方式需要更多的计算量。

Two-Pass Bidirectional Particle Filtering:
Fig. 10 illustrate the TBPF process. In the first pass, we first obtain the rough location estimate
P0 using WiFi signals, and apply a
backward particle filtering along the reversed motion trace. In this pass, the hybrid fusion scheme mentioned above is adopted. The locality-preserving property of WiFi guarantees the true po sition to be near
P0. Therefore, we distribute initial particles only within a proximity of
P0, i.e., a circle centered at
P0 with radius
R. With the backward particle filtering process, we obtain a good estimate of the starting position
Pt of the logged trace. In the second pass, we perform a
forward particle filtering along the motion trace normally, but initialize all the particles to be within a circle around
Pt with radius
r. Finally, we perform a post-filtering process and retain only the particles that fall within the range
R_ to
P0. The weighted average of these particles and obtain the final localization result
P_ 0.

双向双向粒子滤波：图10显示出了TBPF的过程。在第一遍中，我们首先使用WiFi信号获得粗略估计的位置P0，并且沿着反向运动轨迹应用反向粒子滤波。在此过程中，采用上述的融合方案。WiFi的局部位置保护属性保证真实位置在P0附近。因此，我们只在P0附近分布初始粒子，即以P0为中心，以R为半径的圆形范围。使用反向粒子滤波处理，我们获得记录轨迹的起始位置Pt的良好估计。在第二遍中，我们通常沿着运动轨迹执行正向粒子滤波，但是将所有粒子初始化在Pt周围的具有半径r的圆内。最后，我们执行后滤波处理并且仅保留落入以P0为中心R_为半径的圆形范围内的粒子。计算这些颗粒的加权平均值并获得最终定位结果P_0。

Note that the same background logged motion trace are used twice in the TBPF. This makes the particle filtering in the second pass biased. In general, the bias will lead to either better or worse results.
It is thus crucial to apply the final postfiltering process (i.e., selecting particles within radius
R_ to
P0). This selection implicitly uses some truth information—the true location must be around
P0, and ensures the bias is favorable.
注意，在TBPF中使用两次相同的运动轨迹。这使得在第二遍中的粒子滤波被偏置。一般来说，偏差会导致更好或更差的结果。因此，最终应用后过滤过程（即，选择P0半径R_内的粒子到）是至关重要的。这个选择隐含地使用一些真值信息 - 真实位置必须在P0附近，并且确保偏差是有利的。
VI. M-MAP
CONSTRUCTION
The conventional site survey approach suffers from low efficiency as the surveyor needs to first fix the location before collecting any sensor readings. SLAM techniques (either employing robots [26]
or via crowdsourcing [19], [20]) suffer from poor initial accuracy and slow convergence. We believe that site survey is an effective method because the surveyor is more dedicated to the task. Our idea is to lower the bar such that ordinary mobile phone users
can do the survey job at high efficiency.
常规的现场勘测方法效率较低，因为勘测者需要在收集传感器读数之前先固定位置。使用SLAM技术（使用机器人[26]或通过众包[19]，[20]）会造成初始精度差和收敛慢的问题。我们认为现场勘测是一种有效的方法，因为测量师更专注于任务。我们的想法是降低阻碍，使普通手机用户可以高效地完成调查工作。
To this end, we devise a simple
compliant-walking-based data collection method: the surveyor simply walks along a preplanned survey path from the starting point to the end point with the phone in a fixed body position. The system records all the IMU data including accelerations,
gyroscope readings, and magnetic signals from the magnetometer during the walk. The actual user trace is then estimated and matched against the preplanned path to fix the location of each step. Then locations of all collected magnetic signals are interpolated
from neighboring step positions.
为此，我们设计了一种简单的基于融合步行的数据收集方法：测量员简单地沿着预先计划的测量路径从起点到终点，手机处于固定的身体位置。在步行期间，系统记录所有IMU数据，包括来自磁力计的加速度，陀螺仪读数和磁信号强度。然后估计实际用户轨迹并与预计划路径匹配以固定每一步的位置。然后，在相邻的步进位置内插入所有收集的磁信号强度。
Note that here we focus on the design of the
compliantwalking- based site survey method. Businesses that wish to build an indoor location system can utilize crowdsourcing or outsource the survey task to crowd tasking platforms, such as Amazon Mechanical Turk [27] to quickly bootstrap their services.
We leave the design of incentive models of site survey as our future work.

注意，这里我们专注于设计基于compliantwalking的现场调查方法。希望建立室内定位系统的企业可以利用众包或将调查任务外包给任务分配平台，例如亚马逊机械设备[27]，以快速启动其服务。我们将设计现场调查的激励模型做为我们的未来工作 。
Survey Plan Creation:
Given a venue map, we need to first come up with a survey plan that covers all paths (of interest). It can be generated manually or following some simple rule such as a right-hand or left-hand wall follower rule [28]. Considering the spatial coverage,
the path is through the middle for narrow pathways, whereas for extra wide path segments or open spaces, we add additional survey paths that are parallel to the middle one but separated by about 3 meters. This is empirically determined by experiments and is
supported by the achievable accuracy of Magicol shown in Section VII.
测量计划创建：给定一个场地地图，我们首先需要制定一个涵盖所有感兴趣路径的调查计划。它可以手动生成或遵循一些简单的规则，如right-hand或left-hand墙追踪规则[28]。考虑到空间覆盖，路径从狭窄的路径中间通过，而对于宽阔的路径段或开放空间，我们添加与中间平行的间隔约3米的附加测量路径。这是由实验确定的，并由Magicol的可实现精度支持，如第七节所示。
Walking Trace Estimation:
Walking trace estimation using IMU sensors is a well-studied topic. The estimation consists of step detection, step length estimation, and step direction estimation. We adopt the techniques used in [25]. However, instead of inferring the heading direction
from the magnetometer, we estimate the relative heading direction change in that step using gyroscope. As the device may be put in any attitude, we convert the sensor readings from the device's body frame to its vehiclecarried North East Down (NED) frame [29],
which is close to the local World Coordinate System. The conversion matrix is obtained by estimating the gravity in the device's body frame by taking the average acceleration over the past several steps. Since the turning action always happen along the horizontal
plane that is perpendicular to the gravity, we can estimate the turning angle by integrating the Z-axial rotation in the vehicle-carried NED frame. A negative or positive turning angle indicates a direction change towards the left or right, regardless of the
device's actual attitude.
步行轨迹估计：使用IMU传感器的步行轨迹估计是一个很好的研究话题。估计任务包括步伐检测，步长估计和步行方向估计。我们采用[25]中使用的技术。然而，我们使用陀螺仪来估计该步骤中的相对前进方向变化，而不是从磁力计推断前进方向。由于设备可以处于任何姿态，我们将传感器读数从设备主体框架转换为设备自带的世界坐标系（NED）框架[29]。通过获取过去几步的平均加速度来估计装置的主体框架中的重力来获得转换矩阵。由于转弯动作总是沿着垂直于重力的水平面发生，我们可以通过将主体携带的NED框架中的Z轴旋转积分来估计转向角。负转角或正转角指示朝向左或右的方向改变，而不管装置的实际姿态如何。
Turn Detection:
We apply a running detection window (empirically set to 7 steps) to the resulting walking traces. We identify a candidate turn if the sum of the angle changes within the detection window exceeds a threshold, say 30 degrees. A real turn may lead to multiple
candidate turns. We further merge the consecutive turns and perform a local search such that any additional steps belonging to the same turn are included. This ensures the integrity of the turn and improves the detection accuracy of the turning angle. The
turning point is set at the step with the sharpest angle changes.
转向检测：我们将一个检测窗口（经验设置为7步）应用到最终得到的步行痕迹上。如果在检测窗口内的角度变化的总和超过一个阈值，例如30度，我们认定其为一个候选转向。一个真正的转向可能会导致多个候选转向。我们进一步合并连续的转弯，并执行一个本地搜索，这样，属于同一个转向的任何的步伐都包括在内。这保证了转向的完整性，提高了转向角的检测精度。转折点设置在最清晰的角度变化的那步。
Trace Matching via Dynamic Programming:
We match an estimated user trace to its corresponding pre-planned path by first matching the turns because the turns are the most salientfeatures of a user trace. We have two lists
of turns: one ground truth turn list (G) obtained from the pre-planned paths and one candidate turn list
(C) from the estimated user traces. Taking Fig. 11 as an example, we have
基于动态编程的跟踪匹配：通过首先路径转向匹配，我们将估计的用户轨迹与其对应的预先规划的路径匹配，因为转弯是用户轨迹最突出的特征。我们有两个转弯列表：从预先计划的路径获得的一个根据地况得到的转弯列表（G）和来自估计的用户轨迹的一个候选转弯列表（C）。如图11所示，我们有
The start and end points are directly matched and the overall length of the estimated trace is scaled to have the same length as the pre-planned path. When matching intermediate turns, there are two
major sources of errors in walking trace estimation: one is walking distance errors that arise from the incorrect detection of steps or errors in step length estimation, and the other is angle detection errors due to instantaneous errors such as a hand shake,
sensor drift, and imperfect walking. To consider both error sources, we define the following penalty function for matching the
jth turn in
C to the ith turn in
G:
开始点和结束点直接匹配，并且估计轨迹的总长度被缩放为具有与预先计划的路径相同的长度。当匹配中间转弯时，在步行轨迹估计中存在两个主要的误差源：一个是由步长的错误检测或步长估计中的误差引起的步行距离误差，另一个是由于瞬时误差引起的角度检测误差，例如手抖，传感器漂移和不规范的行走姿势。为了考虑这两个误差源，我们定义以下惩罚函数用于匹配C中的第j个弯道与G中的第i个弯道：
 
With a given penalty function, the sequence matching problem can be effectively handled using dynamic programming. With the algorithm, the example in Fig. 11 would generate the following optimal matching
results:
配合给定的惩罚函数，可以使用动态规划来有效地处理序列匹配问题。如图11所示，利用该算法，将生成以下最优匹配结果：
Magnetic Field Map Construction:
After fixing the turns' positions, we calculate the location of the intermediate steps proportionally according to their estimated step length and the overall distance between two bounding turns. The location of each fingerprint is then interpolated from
the locations of the two bounding steps, proportional to their time differences. The final M-Map is constructed by extrapolating the magnetic field strength on the survey path towards both sides until reaching the walls. For wide pathways, multiple parallel
survey paths may exist. Magnetic field strengths at intermediate locations are interpolated according to their distances to each bounding path. For crossroads and turning areas, the average of the interpolated strengths (from different survey paths) is used.
Fig. 13 shows the 2-D view of the resultingM-Map for an office building (refer to Fig. 12(a)), which is used in the evaluation in Section VII. From the figure, we can clearly see the locallyspecific disturbances of the indoor magnetic field.
磁场地图构造：在固定弯道位置之后，我们根据它们的估计步长和两个固定弯道之间的总距离成比例地计算中间步伐的位置。然后，从两个已确定步的位置与它们的时间差成比例地内插每个指纹的位置。最终的M-Map通过在测量路径上向两侧外推磁场强度直到到达壁来构造。对于宽阔的路径，可能存在多个并行测量路径。根据它们到每个边界路径的距离来内插中间位置处的磁场强度。对于十字路口和转弯区域，使用插值强度的平均值（来自不同的测量路径）。图。图13示出了用于办公楼（参见图12（a））的结果M-Map的2-D视图，其用于第VII部分中的评估。从图中，我们可以清楚地看到室内磁场的局部特异性干扰。
 
VII. SYSTEM EVALUATION
In this section we will first present micro-benchmark results on the key components of the Magicol system, and then evaluate the system in a variety of representative indoor environments, to understand
its effectiveness and limitations. Due to space constraints, we put the evaluation of map construction and complexity and energy consumption analysis in Appendix.
在本节中，我们将首先提供关于Magicol系统关键模块的微基准测试结果，然后在各种典型的室内环境中评估系统，以了解其有效性和局限性。 由于空间限制，我们将地图构造和复杂性及能耗分析的评价纳入附录。
A. Implementation
We implemented a Magicol client on HTCMazaa smartphone with a 1 GHz processor and 576MB RAM, running Windows Phone 7.5, and the Magicol Cloud service on a Dell PC, with a 2.8 GHz processor and 4G RAM,
running Windows 7. We adopted KLD-sampling [30] to change the number of particles on-the-fly on the basis of their distribution. The initial number of particles was 3000.

Background Data Logging: The mobile client performed continuous background IMU sampling and walking state detection [25].When the user was detected to be walking, the step information and the magnetic
field signals were logged. The IMU sampling frequency was set to 30 Hz for both the accelerometer and the magnetometer, and 50 Hz for the gyroscope. When the user issued a location query, a WiFi scan was also conducted. As will be shown later, only a short
duration (e.g. 30 seconds) of the latest walking trace was usually sufficient to localize the user. Therefore, we may only need to keep a small buffer for the walking trace.
我们在运行Windows Phone 7.5的1GHz处理器和576MB内存的HTCMazaa智能手机上实现了一个Magicol客户端，在运行Windows 7的2.8 GHz处理器和4G内存的戴尔PC上安装了Magicol Cloud服务端。我们在传输过程中基于KLD采样[30]的分布来改变粒子数量。
背景数据记录：移动客户端在后台执行连续IMU采样和行走状态检测[25]。当用户被检测为行走时，记录步骤信息和磁场信号。对于加速度计和磁力计，IMU采样频率设置为30Hz，对于陀螺仪设置为50Hz。当用户发出位置查询时，进行WiFi扫描。如稍后将示出的，仅最近的步行轨迹的短持续时间（例如30秒）通常足以定位用户。因此，我们可能只需要为步行轨迹保留一个小缓冲区。
B. Localization Using Magnetic Field Only
Testing Environment and Ground Truth Acquisition: We extensively evaluated the system performance in three representative indoor environments: an office floor, an Underground Parking Lot (UPL) and a
supermarket, with a testing area of about 4000 m2, 3850 m2, and 1900 m2, respectively. Floor maps of the three testing environments are shown in Fig. 12, along with survey paths using dashed lines and one typical walking trace using solid lines. The supermarket
was huge and we walked only a portion of it, as shown in the red rectangle in the upper picture in Fig. 12(c). Overall, we collected more than 100 indoor walking traces with a total walking distance of 25 kilometers. To obtain the ground truth of walking,
we set up many landmarks and obtain their real positions in advance, and record the time (by tapping on the phone screen) when passing by those landmarks. Localization error is then obtained by computing the Euclidian distance between the estimated positions
and the ground truth. The results were compared with the Dead Reckoning (DR) based localization system [25]. Note that we have used exactly the same step detection and step length estimation techniques. Thus, the performance differences are purely due to our
way of leveraging the magnetic field.
Localization With Long Traces: We walked many traces in the whole area with randomly picked starting points and made random turns. These walks were relatively long, around 2 minutes. Fig. 14(a) shows
the cumulative distribution function (CDF) of localization errors for the three testing environments. We can see that Magicol significantly and consistently outperformed the Dead Reckoning system for all testing environments. For the office floor, the 80 percentile
error of Magicol was 4 m while it was around 9.5 m for DR; For the supermarket, performances of bothMagicol and DR are still reasonably good as the 80 percentile errors were approximately 3.5 m and 10 m, respectively. However, because supermarket was a more
complex and sophisticated environment, both CDF curves increased more slowly afterwards. For the UPL, Magicol achieved extremely good accuracy—the 80 percentile of error was only 1 m. This is due to the more severe magnetic field anomalies in the UPL. The
accuracy of DR was also good for the UPL, and the 80 percentile error was about 4 m. The reason was due to the simple layout of the pathways.

Fig. 14(b) shows the intermediate localization results (during particle filtering) against the walking time for typical traces, for all three environments. From the figure, we can see that Magicol exhibited
a steadier performance: after the initial convergence process, it rarely diverged again. But for DR, there were several spikes after the initial convergence. The reason was due to the erroneous externally sensed direction. This phenomenon indicates an interesting
difference between Magicol and conventional tracking-based systems: conventional tracking-based systems rely on turns to kill unlikely particles [25], while Magicol performs equally well for straight walking traces, thanks to the continuous sensing of the
magnetic field.
Localization Performance vs Trace Length: Fig. 14(b) indicates that Magicol can localize a user after about 20 seconds of walking. This suggests that we may not need to log very long motion traces.
We thus evaluated the localization performance of Magicol at different logged trace lengths. We collected 5 long traces in each testing environment and randomly selected a portion of them to emulate motion traces with different lengths. Fig. 14(c) shows the
average localization error at different trace lengths for both Magicol and DR for the three testing environments.We can see that Magicol typically achieved good accuracy for log lengths longer than 20 seconds and the resulting localization error was only a
fewmeters, whereas the perfor mance of DR wasmuch worse even with much longer traces. As the length of logged trace has a direct impact on the execution of the augmented particle filtering (see Appendix), this indicates another advantage of Magicol over conventional
DR.
Robustness among Different Users: The above experimental results on tracking and location accuracy were based on the traces mainly collected by two of our authors. To examine Magicol's robustness when
used by other people that may have different stride lengths and walking speeds, we employed five other users (4 male and 1 female) with different heights (between 1.60 m to 1.87 m) and asked them to walk along the same path (around 40 seconds) in the office
environment. The CDF of the localization error for all five users are plotted in Fig. 15. From the figure we can see that the five CDF curves are very close, and they are consistent with the experimental results from our own walks. This demonstrates the robustness
and practicality of Magicol.
 
C. Magnetic-WiFi Fusion
Among the three testing environments, only the office floor had dense enough WiFi AP deployment that WiFi-based localization methods worked. Specifically, there was only one AP in the UPL and 3 APs
in the subarea of the supermarket. This evidently showcases the pervasive applicability of Magicol. Therefore, we only studied the combination of Magicol (i.e., using normal particle filtering) andWiFi-based schemes for the office floor. We used Radar [1]
and EZ [3] in our experiments. RADAR is an RSS fingerprinting scheme. An incoming measurement is matched against all fingerprints in the database.We used the K-NN method (K = 5) to estimate location. EZ is a model-based scheme. It infers various propagation
model parameters based on a large number of measurements in advance. An incoming measurement is applied to the model to obtain the estimated position. We have used the same compliant-walking method (in Section VI) to construct the M-Map and the WiFi location
database, and to compute the model parameters with the same set of collected data.
Localization Accuracy with Magnetic-WiFi Fusion: Fig. 16 shows the point localization accuracy of Radar, EZ, Magicol, and when fused withWiFi using TBPF. Radar and EZ affects TBPF's performance due
to different initial position. From the figure, we can see that Magicol (with a 40-second motion trace) can achieve comparable performance to Radar and EZ on its own. The combination leads to a more significant performance improvement than using any individual
method. When combined with Radar, the 90 percentile accuracy was about 5.3 m, which was about a 50% improvement over that of Radar (i.e., 10.1 m). Similarly, when combined with EZ, the 90 percentile accuracy improved to 3.9 m over the original 8 m accuracy
achieved using EZ only. From the figure, we can also observe that the combination is more powerful for those locations where individual method yields larger errors. This is due to the complimentary nature of magnetic and WiFi signals.
Tracking Performance With Magnetic-WiFi Fusion: We evaluate the tracking accuracy with different magnetic-WiFi fusion approaches, namely the hybrid method (Eqn. (4)) and the proposed TBPF method, where
we trace back for 15 steps upon each new WiFi scan. Experiments are conducted in the office environment due to its denseWiFi deployment. For comparison purpose, we also include the performances when only magnetic field or WiFi is used in tracking (with normal
PF) as benchmarks. Note that even though WiFi was continuously scanned, but it took about 2 seconds to obtain a fingerprint. Thus, there is about a 3-step interval between two subsequent fingerprints. Fig. 17 shows the performance gain of TBPF over normal
PF (which is adopted in the hybrid fusion approach) when magnetic field and WiFi are combined in tracking. Compared with the 90 percentile accuracy of 2.1 m obtained by magnetism based tracking which uses normal particle filtering only, we see that the TBPF
is very effective, achieving a 57% improvement with 90 percentile accuracy of less than 1 m. The intuitive hybrid performs slightly worse than using magnetism only, due to the jumpy nature of WiFi signal, but does help to suppress large errors. We animated
and visually examined the tracking process of some traces and found that the resulting distribution of TBPF is significantly more concentrated than the cases of single pass particle filtering. Compare against Fig. 16, we found that tracking accuracy significantly
outperforms that of point localization. It is reasonable due to the constraint imposed by dead reckoning between subsequent WiFi scans. The cost we pay is extra energy consumed by multiple WiFi scans.

To see the impact of WiFi scan frequency, we also tried to scanWiFi less frequently at roughly 10 seconds intervals (about 15 steps). The results are shown in Fig. 18. We can see that the performance
drops quickly, almost to that of using magnetic field only. It is expected as most of steps do not have a WiFi fingerprint. However, it is still helpful in confining relatively larger errors.
As a final remark, Magicol was initially implemented and evaluated on a Windows Phone. We have applied this technology in Travi-Navi [31] and also evaluated on a variety of Android mobile devices (including
Samsung Galaxy S2, S4, Note3, HTC Desire and HTC Droid Incredible 2). The results there confirmed that the design of Magicol is intrinsically immune to device diversities due to its leverage of the shape instead of the absolute sensed value of magnetic field.
 
VIII. RELATED WORK
Indoor localization is an extensively studied topic, mostly relying on certain infrastructure, and WiFi is mostly explored [1]–[4], [19], [20], [32]. We only review closely related work here.
IMU-Based Tracking: IMU-tracking (a.k.a., Dead Reckoning) is a well-studied topic for its infrastructure independency [10], [25], [33]–[35]. These systems handle the noisy walking directions caused
by locally disturbed indoor magnetic field through fusion with gyroscope readings to obtain compromised heading directions. A map is usually used to constrain the tracking error. In contrast, Magicol exploits the magnetic field anomalies as useful features,
and makes separate use of the gyroscope and the magnetometer. Magicol makes more use of the map for not only constraining the motion but also initializing directions of particles.
室内定位是一个广泛研究的主题，主要依赖于某些基础设施，目前基于WiFi的室内定位方法主要被探索[1] - [4]，[19]，[20]，[32]。 我们只在这里研究密切相关的工作。
基于IMU的跟踪：IMU跟踪（a.k.a.，航位推算）是其基础设施独立性研究的一个主题[10]，[25]，[33] - [35]。 这些系统通过由被局部扰动的室内磁场与陀螺仪相融合共同矫正带有噪声行走方向以获得校正后的航向方向。室内地图通常用于约束用户行为来减少跟踪误差。 相比之下，Magicol利用磁场异常作为有用的特征，并且单独使用陀螺仪和磁力计。 Magicol使用地图不仅限制运动状态，而且初始化粒子的方向。
Magnetism-Based Localization: Geomagnetism was exploited for localization [21] or tracking purpose in the robotics field using special hardware, [15], [16], [36], [37]. However, these techniques either
requires dense samples of magnetic vector which leads to tedious training overhead [21], or incur special hardware or draw on existing tracking techniques (e.g., odometric) which are not applicable to off-the-shelf smartphones (e.g., due to unpredictable human
behaviors, we do not know the heading direction and can no longer use magnetic output from X, Y, Z axis independently).
基于磁性的定位：在机器人领域使用地磁进行定位[21]或跟踪需要借助特殊的硬件，[15]，[16]，[36]，[37]。 然而，这些技术要么需要密集的磁矢量样本，这会导致冗长的训练开销[21]，或者需要特殊硬件或跟踪技术（例如，odometric），这不适用于现成的智能手机（例如，由于不可预测的人类行为，我们不知道航向，并且不能再使用来自X，Y，Z轴的磁输出。
For smartphones, the geomagnetic field anomalies were leveraged in a leader-follower scenario [13], [22]. In [23], the authors leveraged observations of the ambient magnetic field, but they only handled
simple one-dimensional (e.g., in a straight pathway) situations and did not handle many practical problems such as the various diversities that Magicol does. In [38], Glanzer et al. introduce a pedestrian navigation system with human motion recognition. However,
the pre-mapped magnetic field information is only used to correct the severe disturbance of indoor direction sensing. In [39], authors leverage magnetic signatures to identify locations and rooms. Although mobile phones are used to measure magnetic field intensity,
the system relies on pillars and only offers rough positioning result (e.g. room-level). Kim et al. explored geomagnetism for indoor localization in rather simplistic settings—a single corridor in a building, and assumed known user motion and the starting
point [17]. Grand et al. [24] propose a light-weight magnetic map construction method and use online particle filter to estimate the location of the handheld device. However authors mainly emphasis the disturbance of magnetic field whereas in Magicol, we jointly
consider efficient database construction, dynamic user motion behaviors, limited discernibility of magnetic field, and run the localization algorithm in a real-time manner. In addition, we further enhance Magicol using complementary WiFi-based techniques at
low energy cost.
对于智能手机，地磁场异常被利用在引导-跟随情境[13]，[22]。在[23]中，作者利用磁场的观测值，但他们只处理简单的一维（例如，在直线路径）情况，并没有处理许多实际问题，如Magicol的各种多样性。在[38]，Glanzer et al。介绍一种具有人体运动识别的行人导航系统。然而，预映射的磁场信息仅用于校正室内方向感测的严重干扰。在[39]中，作者利用磁性签名来识别位置和房间。虽然移动电话用于测量磁场强度，但系统依赖于支柱并且仅提供粗略的定位结果（例如，房间水平）。
Kim et al。探索地磁在室内定位在相当简单的环境 - 建筑物中的单个走廊，并假设已知的用户运动和起点[17]。 Grand et al。 [24]提出一种轻量磁地图构造方法，并使用在线粒子滤波器估计手持设备的位置。然而，作者主要强调磁场的干扰，而在Magicol，我们联合考虑有效的数据库构造，动态用户运动行为，磁场的有限可辨别性，并以实时方式运行定位算法。此外，我们进一步增强Magicol使用基于互补的WiFi技术在低能源成本。
Location Database Construction: SLAM has been heavily studied in the robotics field [26]. FootSLAM [11] used shoemounted inertial sensors to construct the internal map for an unknown building. Zee [19]
studied the same problem for mobile users using a crowdsourcing approach. Unloc [12] explored various types of natural landmarks detectable from sensor readings to calibrate user traces. These methods usually suffer from poor initial accuracy of the mapping,
and take long time to reach an acceptable accuracy. In contrast, our compliant-walking based approach aims at improving the efficiency (essentially, any path needs only one visit) and, at the same time, lowers the bar for site surveyors as they just need to
walk along a given path.