# MapSentinel: Can the Knowledge of Space Use Improve Indoor Tracking Further?

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## Abstract

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## 1. Introduction

- We build a non-intrusive location sensing network consisting of modified WiFi access points and ultrasonic calibration stations, which does not require the occupants to install any specialized programs on their smartphones and prevents the energy and occupant engagement issues.
- We propose an information fusion framework for indoor tracking, which theoretically formalizes the fusion of the floormap information and the noisy sensor data using Factor Graph. The Context-Augmented Particle Filtering algorithm is developed to efficiently solve the walking trajectories in real time. The fusion framework can flexibly graft floormap information onto other types of tracking systems, not limited to the WiFi tracking schemes that we will demonstrate in this paper.
- We evaluate our system in a large typical office environment, and our tracking system can achieve significant tracking accuracy improvement over the purely WiFi-based tracking systems.

## 2. MapSentinel Architecture

#### 2.1. WiFi Access Points

#### 2.2. Ultrasonic Calibration Stations

#### 2.3. Floormap Processing Engine

## 3. Information Fusion Framework

#### 3.1. Problem Formulation

- ${\mathcal{T}}_{k}({\mathbf{z}}_{k},{\mathbf{z}}_{k-1},{m}_{k},{m}_{k-1})=p\left({\mathbf{z}}_{k}\right|{\mathbf{z}}_{k-1},{m}_{k},{m}_{k-1})$: transition model, or the prior information on the state evolution over time. Inspired by Variable Structure Multiple Model Estimator in [23], we propose CDKM to capture the context-dependent characteristics of occupants’ motion in the indoor space.
- ${\mathcal{O}}_{k}({\mathbf{z}}_{k},{y}_{k})=p\left({y}_{k}\right|{\mathbf{z}}_{k})$: observation model, or how the unknown states and sensor observations relate. We will introduce PSMM where the relationship between locations and sensor observations is characterized by certain conditional probabilities and multiple sensor observations are combined via Bayes’ theorem.
- ${\mathcal{C}}_{k}({\mathbf{z}}_{k},{m}_{k})$: characteristic function that checks the validity of the correspondence between ${\mathbf{z}}_{k}$ and ${m}_{k}$ using the contextual floormap.

#### 3.2. Context-Dependent Kinematic Model

#### 3.3. Probabilistic Sensor Measurement Model

**WiFi Measurement.**In the free space, the WiFi signal strength is a log linear function of the distance between the transmitter and receiver. However, due to the multipath effect caused by obstacles and moving objects in the indoor environments, the log linear relationship no longer holds. Previous work has proposed to adding a Gaussian noise term to account for the variations arising from the multipath effect; however, the simple model-based method can hardly guarantee a reasonable performance in practice. Another popular way is to construct a WiFi database comprising WiFi measurements at known locations to fingerprint the space of interest, but it requires onerous calibration to ensure the accuracy. We propose a novel WiFi modeling method based on a relatively small WiFi training set to accommodate for the complex variations of WiFi signals in the indoor space. The key insight is to use Gaussian process (GP) to model the WiFi signal where the simple model-based method provides a prior over the function space of GP.

**Ultrasonic Measurement.**Essentially, each of the ultrasonic sensors in the ultrasonic station can output the distance to the occupant passing in front of it. However, due to the missing data and measurement noise, the distance measurement is not always steady. Here, we will consider the ultrasonic station to be a binary sensor to indicate the occupancy in its detection zone. To be specific, the likelihood function is modeled as

#### 3.4. Characteristic Function

## 4. Context-Augmented Particle Filter

**Prediction Step.**In the prediction phase, we generate the predicted particles by

**Update Step.**To update, each predicted particle ${\tilde{\mathbf{z}}}_{k}^{i}$ is assigned with a weight proportional to its likelihood.

**“Oracle” Design.**The oracle is supposed to be able to answer the query about the next possible contexts ${m}_{k}$, based upon which the position/velocity component of the state can be properly propagated according to different transition models. For computational efficiency, we adopt a simple discriminative model to produce ${\tilde{m}}_{k}$’s. Given a small database of WiFi fingerprints, we apply the K-Nearest Neighbors (K-NN) algorithm and a modified distance weighted rule to generate an empirical distribution of the context. To be specific, let the WiFi database be denoted by ${\left\{({m}^{j},{y}_{w}^{j})\right\}}_{j=1}^{{N}_{w}}$, and ${N}_{w}$ is the number of WiFi fingerprints. When the new WiFi observation ${y}_{k}$ is querying the possible contexts, the K nearest neighbors of ${y}_{k}$ are found among the given training set. Let these K nearest neighbors of ${y}_{k}$, with their associated context, be given by ${\left\{({m}^{{j}^{\prime}},{y}_{w}^{{j}^{\prime}})\right\}}_{{j}^{\prime}=1}^{K}$. In addition, let the corresponding distances of these neighbors from ${y}_{k}$ be given by ${d}^{{j}^{\prime}}$, ${j}^{\prime}=1,\cdots ,K$. The weight attributed to the ${j}^{\prime}$th nearest neighbor is then defined as

Algorithm 1 Context-Augmented Particle Filter |

function CAPF(${y}_{1:T},wifi\_database,reachable\_set$) |

Initialization: |

Uniformly generate N samples ${\left\{{\mathbf{z}}_{0}^{i}\right\}}_{i=1}^{N}$ |

Set ${m}_{0}^{i}=\mathcal{M}\left({\mathbf{z}}_{0}^{i}\right)$, ${w}_{0}^{i}={N}^{-1}$, $i=1,\cdots ,N$ |

for $k=1,\cdots ,T$ do |

for $i=1:N$ do |

Context Estimate: |

if ${\mathbf{z}}_{k-1}^{i}$ on the boundary of ${\left\{{m}_{b}\right\}}_{b=1}^{B}$ then |

Uniformly sample ${\tilde{m}}_{k}^{i}$ from ${\left\{{m}_{b}\right\}}_{b=1}^{B}$ |

else |

Sample ${\tilde{m}}_{k}^{i}$ from Equation (27) |

end if |

Prediction Step: |

${\tilde{\mathbf{z}}}_{k}^{i}\sim p\left({\mathbf{z}}_{k}\right|{\mathbf{z}}_{k-1}^{i},{\tilde{m}}_{k}^{i},{m}_{k-1}^{i})$ |

Discard particles ${\tilde{\mathbf{z}}}_{k}^{i}\notin reachable\_set\left({\mathbf{z}}_{k-1}^{i}\right)$ |

Update Step: |

Compute weight ${\tilde{w}}_{k}^{i}=p\left({y}_{k}\right|{\tilde{\mathbf{z}}}_{k}^{i})$ |

end for |

Normalize weights: ${w}_{k}^{i}=\frac{{\tilde{w}}_{k}^{i}}{{\sum}_{i=1}^{N}{\tilde{w}}_{k}^{i}}$ |

Resampling: |

Select N particle indices ${i}^{\prime}\in \{1,\cdots ,N\}$ according to weights ${\left\{{w}_{k}^{i}\right\}}_{i=1}^{N}$ |

Set ${\mathbf{z}}_{k}^{i}={\tilde{\mathbf{z}}}_{k}^{{i}^{\prime}}$ and ${w}_{k}^{i}={N}^{-1}$ |

Set ${m}_{k}^{i}=\mathcal{M}\left({\mathbf{z}}_{k}^{i}\right)$ |

Estimate: |

${\widehat{\mathbf{z}}}_{k}={\sum}_{i=1}^{N}{w}_{k}^{i}{\mathbf{z}}_{k}^{i}$ |

end for |

return ${\widehat{\mathbf{z}}}_{1:T}$ |

end function |

## 5. Performance Evaluation

**Experimental methodology.**In a real-world setting, we expect the occupant to carry the smartphone as they walk through various sections of an indoor space. Moreover, occupants are unlikely to walk continuously; they would walk between locations of special interest and dwell at certain locations for a significant length of time. Our experiment aims at emulating these practical scenarios in an office environment and incorporating all the contexts defined in our model. Therefore, the following routes were designed as the ground truth for evaluation: (1) A enters the office from the front gate and walks through the corridors to find her colleague (different CSs are included); (2) B enters the office from the side door, walks to her own seat, stays there for a while and exits the office from the front gate (CSs, SS are included); (3) C enters the office from the front gate, walks through corridors, takes some time at her office and goes to the open area (CSs, SS, FS are included). We asked the experimenter to behave as usual when walking in the space. At the same time, the WiFi APs and ultrasonic stations constantly collect the measurements and send them to the central server. To obtain the ground truth at the sampling time of the tracking system, we mark the ground with a 1 m grid on the pre-specified route and ask the experimenter to create lap times with a stopwatch when happening to be on the grid. By recording the starting time of the experiment, we can obtain the time stamp of each grid and then interpolate the ground truth at the sampling time.

**Does the “oracle” work?**The current context estimation done by the “oracle” is critical to the CAPF algorithm, as the tuple of the current and previous context jointly steer the states in our model. Here, we would like to evaluate the context prediction performance of the “oracle” we constructed in light of several design rules presented in the Section 4. Figure 6 illustrates the result of the context estimation for different walks. Since the context estimates are represented by a set of particles in the algorithm, we visualize the context estimate by the purple lines centered at the possible contexts, and the lengths of the purple lines are scaled by the proportions of the particles of different contexts. Ideally, the purple cloud should scatter around the ground truth context. Figure 6 suggests that the estimates given by the “oracle” can generally capture the ground truth. Evidently, the context estimate is not perfect, especially for the static space (SS). However, these approximate “ground truths” essentially present other possibilities of the current context and avoids particles trapping in the static space. We define the context estimation accuracy to be the ratio of the number of particles with correct context estimate to the total number of particles. The context estimation accuracy is calculated for each time step of the experiments, and the empirical distribution of the context estimation accuracy is illustrated in Figure 7, where the mean accuracy is $52.41\%$. With this noisy “oracle”, the system can achieve median tracking error of $1.96$ m, while the tracking error would be $1.84$ m if a perfect “oracle” was utilized. Therefore, our work has the potential to be further improved with a more advanced “oracle” design.

**MapSentinel’s tracking performance.**We aggregate the data from different walks and compare the performance of MapSentinel against the fusion system of WiFi and ultrasonic station without leveraging the floormap information, as well as the purely WiFi-based tracking system. The tracking error distributions are depicted in Figure 9. As can be seen, the MapSentinel achieves an essential performance improvement, $31.3\%$ over the WiFi tracking system and $29.1\%$ over the fusion scheme. Note that adding the ultrasonic calibration into the WiFi system is able to realize a small amount of accuracy increment. Due to the high degree of uncertainty of WiFi signals, the effect of ultrasonic calibration will not last for long. The map information elongates the effect of the ultrasonic calibration via imposing additional constraints to the motion, and that is why MapSentinel greatly enhances the tracking performance compared with the purely WiFi-based system. We also evaluate the tracking performance in different contexts, and the result is shown by boxplots in Figure 10. Here, “without map” means using the WiFi and ultrasonic sensing systems without taking into account the reachable set as well as the context-dependent kinematic model. A unified dynamical model, the free space model, is applied in this case, and a traditional particle filter is implemented to estimate the location. As can be readily read from the figure, the MapSentinel performs better in all contexts. More significant increase is achieved in constrained spaces and static spaces, as expected.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**MapSentinel architecture—WiFi APs keep tracking occupants’ locations, and the estimation is periodically refined using the ultrasonic stations deployed in the environment. Furthermore, the sensor measurements and the floormap information are combined via the information fusion algorithm to estimate location in real-time. The floormap processing engine helps transform the floormap to the information accessible to the fusion algorithm.

**Figure 2.**The measurements of ultrasonic stations deployed in the space. When the occupant is within the detection zone of the ultrasonic station, the sensor reading exhibits a smaller value.

**Figure 3.**Illustration of the configuration of the ultrasonic calibration station. The coordinator requests measurements at 1 Hz frequency through the IEEE 802.15.4 protocol, and deposits collected data to the local database. The ultrasonic station takes three independent measures from its sensor points to detect occupant presence in the vicinity.

**Figure 4.**A factor graph model representation of the dependencies among location, velocity, context and observation.

**Figure 5.**The floormap (

**top**) and corresponding contextual map (

**bottom**) of the testbed. Four different contexts (FS, SS, VCS, HCS) are defined and color coded as illustrated in the legend.

**Figure 6.**The context estimate produced by the “oracle" versus the ground truth context. The radius of the purple cloud is proportional to the number of particles of the estimated context which the cloud is centered around.

**Figure 7.**Normalized histogram of context estimation accuracy of the “oracle”. The mean accuracy is 52.41%.

**Figure 8.**The snapshots of the intermediate steps of the CAPF algorithm visualized. The location estimate, ground truth location, particles are presented by the red cross, blue circle, green dots, respectively. As before, the black square and white triangles give the positions of WiFi routers and ultrasonic stations.

**Figure 9.**Tracking performance of MapSentinel, the fusion system of WiFi and ultrasound sensor, the pure WiFi system. The median tracking accuracy of the MapSentinel is $1.96$ m, MapSentinel can achieve the performance improvement of $31.3\%$ over the purely WiFi-based tracking system, $29.1\%$ over the fusion system.

**Figure 11.**Tracking performance of different usage of floormap information. “RSC” stands for reachable set check. MapSentinel extracts the context information from the floormap, and simultaneously eliminates the particles falling outside the reachable set. MapSentinel is compared with the tracking system without using context information (i.e., only performing RSC) and the one without using the map information at all. The median tracking errors of MapSentinel, the system only performing RSC, and the one without exploiting the floormap information are $1.96$ m, $2.44$ m and $2.77$ m, respectively.

**Figure 12.**The velocity estimation for the MapSentinel and the WiFi+Ultrasound system. The vector indicates the speed and direction of the estimated motion.

Context | Symbols | Motion Characteristics |
---|---|---|

Free Space | FS | Move freely, e.g., rooms |

Constrained Space | CS | Move along canonical direction, e.g., corridors |

Static Space | SS | Stay static, e.g., cubicles |

Context Transition | Model Specification | |
---|---|---|

$\mathit{F}\mathbf{(}{\mathit{m}}_{\mathit{k}\mathbf{-}\mathbf{1}}\mathbf{,}{\mathit{m}}_{\mathit{k}}\mathbf{)}$ | $\mathit{Q}\mathbf{(}{\mathit{m}}_{\mathit{k}\mathbf{-}\mathbf{1}}\mathbf{,}{\mathit{m}}_{\mathit{k}}\mathbf{)}$ | |

${m}_{k-1}={m}_{k}=FS$ | ${F}_{0}$ | ${Q}_{0}$ |

${m}_{k-1}={m}_{k}=C{S}_{i}$ | ${F}_{0}$ | ${Q}_{i}$ |

${m}_{k-1}={m}_{k}=SS$ | ${F}_{1}$ | ${Q}_{0}$ |

${m}_{k-1}\ne {m}_{k}$ | ${F}_{0}$ | ${Q}_{0}$ |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jia, R.; Jin, M.; Zou, H.; Yesilata, Y.; Xie, L.; Spanos, C.
MapSentinel: Can the Knowledge of Space Use Improve Indoor Tracking Further? *Sensors* **2016**, *16*, 472.
https://doi.org/10.3390/s16040472

**AMA Style**

Jia R, Jin M, Zou H, Yesilata Y, Xie L, Spanos C.
MapSentinel: Can the Knowledge of Space Use Improve Indoor Tracking Further? *Sensors*. 2016; 16(4):472.
https://doi.org/10.3390/s16040472

**Chicago/Turabian Style**

Jia, Ruoxi, Ming Jin, Han Zou, Yigitcan Yesilata, Lihua Xie, and Costas Spanos.
2016. "MapSentinel: Can the Knowledge of Space Use Improve Indoor Tracking Further?" *Sensors* 16, no. 4: 472.
https://doi.org/10.3390/s16040472