# Differential radio map-based robust indoor localization

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## Abstract

While wireless local area network-based indoor localization is attractive, the problems concerning how to capture the signal-propagating character in the complex dynamic environment and how to accommodate the receiver gain difference of different mobile devices are challenging. In this article, we solve these problems by modeling them as common mode noise and develop a localization algorithm based on a novel differential radio map approach. We propose a differential operation to improve the performance of the radio map module, where the location is estimated according to the difference of received signal strength (RSS) instead of RSS itself. The particle filter algorithm is adopted to realize the target localization and tracking task. Furthermore, to calculate the particle weight at arbitrary locations, we propose a local linearization technique to realize continuous interpolation of the radio map. The indoor experiment results demonstrate the effectiveness and robustness of our approach.

### Keywords

Indoor localization differential radio map RSS particle filter### Abbreviations

- CDF
cumulative distribution function

- DRMBL
differential radio map-based Bayesian localization

- GPS
global positioning system

probability distribution function

- RSS
received signal strength

- SDM
signal-distance map

- WLAN
wireless local area network.

## Introduction

Ubiquitous computing and communication have become popular with the development of wireless communication technology over the last decade. The need for location information to capture contexts and configure them into the computing and communication processes, coupled with the unavailability of global positioning system (GPS) in indoor environment, has triggered increased research interest in indoor localization. Recently, numerous localization systems have been developed based on the received signal strength (RSS) of the wireless local area networks (WLANs). The advantage of these systems is that the cost of deploying a specialized infrastructure is avoided. However, building an indoor localization system based on WLAN is a challenging problem due to the complex indoor signal propagation character and different hardware solutions of different mobile devices.

Radio map-based approach is the most widely adopted method to realize indoor localization [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The essential idea is to construct the radio map by dividing the whole deployment area into cells and then collecting the RSS measurements from various access points (APs) at each cell, and thus a mobile device can be localized by matching the observed RSS vector with the radio map. In the indoor environment, the RF signal propagation is unpredictable and affected by several factors, such as the presence and movement of human beings, relocation of furniture, multi-path fading, humidity and temperature variations, and closing or opening doors. In such a dynamic environment, the radio map obtained in one time period may not be applicable to other time periods. To solve this problem, Chen et al. [9] built multiple radio maps under various environmental conditions and used sensors to identify the current environment so as to select the most approximate map. Yin et al. [10] offset the variational environmental factors by adding some reference points as sniffers to capture the dynamic characters of the environment and rebuilt the radio map with regression method. Although these methods partially overcome the negative effect of dynamic environment, the need for specific infrastructures, such as the environmental sensors and sniffers, makes these methods impractical. More recently, Fang and Lin [11] adopted a temporal sequence of RSS samples as the character vector of the radio map so as to overcome the multipath problem. While this approach demonstrates the effectiveness for the multipath effect, it is of little use for other problems. The question of how to adapt to the dynamic complex environment without any additional infrastructure is a promising and challenging problem. Because with the changing of environment, it is most likely that the RSS measurements in one location from different APs are prone to shift in the same direction, we can model the dynamic of the indoor environment as the common mode noise. Inspired by the fact that differential signals are widely used in the circuit design to restrain the common mode noise, we adopt the difference of RSS from different APs as the characteristic signal of the radio map. Suppose the RSS measurement vector from three APs are (*RSS*_{1}, *RSS*_{2}, *RSS*_{3}). Instead of treating it as the fingerprint to realize localization, we adopt the differential vectors (*RSS*_{1}*- RSS*_{2}, *RSS*_{1}*- RSS*_{3}, *RSS*_{2}*- RSS*_{3}) as fingerprint. Compared with the traditional RSS vector, the differential vector can be effectively adapted to the dynamic indoor environment. Furthermore, it can accommodate the receiver gain difference of different mobile devices. We are aware that the receiver gains of even the same type of devices are different, let alone different types of devices. If the device used in the localization phase is different from that used in the radio map building phase, then the estimation error will be increased dramatically. Because the difference of receiver gain offsets the RSS measurements in the same direction, we can also model it as common mode noise.

In this article, we propose a novel robust indoor localization algorithm under the framework of Bayesian filter. The particle filter (PF) [12, 13] is adopted to achieve the localization and tracking task, which makes full use of the history observation to improve the estimation accuracy. The differential radio map is used for building the observation likelihood for the PF algorithm so as to solve the dynamic environment and different receiver gain problem. For the sake of predicting signal strength measurements at arbitrary locations so as to calculate particle weight and improve localization accuracy, we also adopt a local linearization technique to realize continuous interpolation of the radio map.

This article is organized as follows. Section II provides a brief overview of the indoor localization problem. In Section III, the definition of the differential radio map is given, and the localization architecture is described from the view of system. The detailed implementation of our differential radio map-based PF algorithm is presented in Section IV. Section V validates our algorithm by evaluations. Finally, the conclusion is drawn in Section VI.

## Related works

Indoor localization with WLAN has been an active research area in the last decade. Honkavirta et al. [14] presented a survey of location fingerprinting methods, and Seco et al. [15] reviewed the indoor localization algorithms from the aspect of mathematic. In this section, we give a brief overview of some key research findings in this area. Considering the needs of building the radio map, we divide the methods into map-based and non-map based algorithms.

The principle of the radio map based method is to fingerprint each cell of the deployment area with a RSS measurement vector from various APs. A mobile device is then localized by matching the observed RSS against the radio map. To the best of our knowledge, radio map-based indoor localization was first introduced by Bahl and Padmanabhan [1]; they proposed the well-known RADAR system and realized the localization using the deterministic fingerprint. Since then some schemes have been proposed to reduce the manual calibration effort and make the radio map more robust so as to improve the localization accuracy. To reduce manual effort, Deasy and Scanlon [2] proposed a technique to estimate the radio map using a signal propagation model. They used an instrument to measure the signal propagation model parameters and built the simulated radio map automatically. Compared with the traditional measured radio map, although the building of the simulated radio map is time efficient, the localization accuracy degenerates significantly. Tsai et al. [3] also adopted the signal propagation model and the interpolation technique to build the map. Chai and Yang [4] proposed a scheme to reduce the sample location in the radio map building phase so as to reduce the manual effort and developed an interpolation technique to effectively patch a radio map. Philipp [5] introduced a collaborative way to build the radio map with the collaboration of users, each user could create and manage the map, and the whole map can be built gradually with the participation of more and more users. Recently, Chintalapudi et al. [6] also developed a collaborative localization system named EZ which did not require any knowledge about the RF environment. EZ adopted an improved genetic algorithm to solve the constraint equations defined by signal propagation models so as to calculate the parameters of the APs and training points. However, it requires the mobile device equipped with GPS, and it can work well only if there are enough APs to provide excellent coverage. In order to make the radio map more informative, Wu et al. [7] adopted the probability distribution function (PDF) as the fingerprint of the map. Youssef and Agrawala [8] also employed a stochastic description of the radio map. As has been discussed above, with the purpose of adapting the radio map to the dynamic environment, Chen et al. [9], Yin et al. [10], and Fang and Lin [11] have made some pioneering research contributions. As a continuation of these schemes, our proposed approach adopts the differential radio map to make the algorithm more robust and a local linearization technique to realize continuous interpolation of the radio map.

Besides the above research studies, some schemes based on the deterministic and proba-bilistic framework have also been developed. Lim et al. [16] used the truncated singular value decomposition to calculate the signal-distance map (SDM) based on the online measurements between the APs. Although the dynamic SDM makes it possible to capture the challenging dynamic indoor environment, the requirements of the high AP density and the modification of commercial AP's software make the scheme impractical. Hossain et al. [17] proposed a robust localization algorithm that could make use of multiple wireless techniques. Schwaighofer et al. [18] first adopted the Gaussian process (GP) as a non-parametric tool to realize the approximation of the radio map of cellular network. Ferris et al. [19] introduced the GP into the WLAN-based indoor localization. Compared with other regression models, the GP takes into account the noise of the observation and provides the ability to approximate nonlinear signal propagation model. Madigan et al. [20] adopted a Bayesian hierarchical approach to realize indoor localization, which eliminated the need of knowing the locations of the training points. Huang et al. [21] proposed a similar Bayesian algorithm and introduced the stochastic properties of measurement errors and the reliability of the measurement data into the factor graph framework so as to improve the accuracy. Wymeersch et al. [22] also proposed a Bayesian localization algorithm and took the cooperation of the nodes into consideration to improve the accuracy. Feng et al. [23] employed the compressive sensing theory to analyze the localization problem. The localization problem is modeled as a sparse question and can be solved by the L1 minimization. While these methods cut down the measurement effort and partially adapt to the dynamic environment, they still require effort in terms of placing sniffers, modifying commercial AP's software, obtaining the knowledge of AP placement, and of complex computation.

## Differential radio map and system architecture

In this section, we define the differential radio map and analyze its ability to restrain the dynamic environmental noise and receiver gain difference. The architecture of the proposed localization system is presented thereafter.

### Differential radio map

where *M* is the total number of training points, *p*_{ i } and *R*_{ i } indicate the location and fingerprint of the *i* th training point, respectively, *N*_{ i } is the detected AP list at the *i* th training point, *R*_{ ij } is a Gaussian PDF represented by Open image in new window with the mean *μ*_{ ij } , and covariance Open image in new window , which is used to approximate the RSS measurements collected at the *i* th training point and transmitted by the *j* th AP.

*R*

_{ i }directly for localization, we adopt the differential fingerprint Open image in new window which takes the

*R*

_{ i }as input, and it is calculated as follows:

where *R*_{ im } is the strongest RSS measured at the *i* th training point (the measurement with lower ID is adopted when equal RSSs are measured), and *R*_{ ij } *-R*_{ im } is represented by Open image in new window .

*R*

_{ ij }is defined by

where *G* is the receiver gain, *P*_{ j } is the transmitting power (*dBm*) of the *j* th AP, *L*_{ j } is the signal attenuation power (*dBm*) at the distance of 1 m, *β* is the path loss exponent, *d*_{ ij } is the Euclidean distance between the *i* th training point and *j* th AP, and *v* represents the measurement noise. *G* + *P*_{ j } *- L*_{ j } is always represented by one symbol and is called the received power at the distance of 1 m in other studies. To analyze the feature of the differential operation, we use three symbols to represent each factor here. The dynamic indoor environment always causes the change of parameters *L*_{ j } and *β*, and the change of these parameters incur the change of the *R*_{ ij. } As for different types of device, the receiver gain *G* is different, and thus the change of device causes the change of *R*_{ ij } , as well.

where *P*_{ j } *- P*_{ m } is a constant which does not change with environment. While *L*_{ j } and *L*_{ m } change with the environment, they always offset to the same direction. Consequently, the change of *L*_{ j } *-L*_{ m } is not significant compared with the change of *L*_{ j } and *L*_{ m } . As for 10*β* (log_{10}*d*_{ ij } *-* log_{10}*d*_{ im } ), since log_{10}*d*_{ ij } *-* log_{10}*d*_{ im } is less than log_{10}*d*_{ ij } and log_{10}*d*_{ im } , the change must be insignificant, too. From Equation 4, we can see that the term *G* is eliminated in the expression. Therefore, the differential RSS scheme is immune to the dynamic indoor environment, and can solve the problem caused by different receiver gains of multi-devices.

### System architecture

*x*

_{ t }is the current estimated location information,

*y*

_{ t }is the current observation,

*p*(

*x*

_{t- 1}|

*y*

_{t- 1}) is the posterior PDF estimation of time instant

*t -*1,

*p*(

*x*

_{ t }

*|y*

_{t- 1}) and

*p*(

*x*

_{ t }

*|y*

_{ t }) are the prior and posterior PDF estimations of time instant

*t*, respectively.

*y*

_{1},...,

*y*

_{ t }. The essential of the Bayesian filter is the prediction process and observation update process, which are defined as follows:

where the term *p* (*x*_{ t }*|x*_{t-1}) represents the motion model, which describes the motion of the mobile device, and *p* (*y*_{ t }*|x*_{ t } ) represents the observation likelihood model, which describes the likelihood of observing a differential RSS measurement vector *y*_{ t } at a location *x*_{ t } . We describe the detailed models in the next section.

## Implementation of the algorithm

This section first gives a brief introduction of the PF algorithm, and then defines the motion model and observation model in detail.

### PF algorithm for localization and tracking

*x*

_{ t }with associated normalized weight Open image in new window . Then, the posterior PDF

*p*(

*x*

_{ t }

*|y*

_{ t }) can be approximated as

*δ*() is the Dirac delta function. Suppose we have the proposal distribution

*q*(

*x*

_{ t }

*|x*

_{t-1},

*y*

_{ t }), then the predicted location Open image in new window can be generated based on the previous location Open image in new window and the latest observation

*y*

_{ t }as follows:

Most articles in the literature define the proposal distribution as *q* (*x*_{ t }*|x*_{t-1}, *y*_{ t } ) = *p* (*x*_{ t }*|x*_{t-1}), which only considers the motion model and neglects the latest observation *y*_{ t } . For simplicity, we follow this scheme. Interested readers could find out the methods of designing advanced proposal distribution in [25]. Now, the question is how to define the motion model Open image in new window and the observation likelihood model Open image in new window for the particles.

### Motion model

*x*

_{ t }can be represented by (

*X*

_{ t }

*, Y*

_{ t }). Suppose the location states of the previous two time instants are,

*x*

_{t-2}and

*x*

_{t-1}, the predicted velocity Open image in new window and direction Open image in new window of the mobile device can be estimated as follows:

*v*

_{max}is the velocity threshold of the mobile device and generally set as 1

*m*/

*s*. The motion model of the particles can be written as

where *n*_{ t } is the noise, Open image in new window . The new particles are generated in the fan-shaped area. Meanwhile, to cope with the circumstance such as the swerve of the mobile device, we randomly select 80% particles that participate in the prediction defined by Equation 12, and let the rest 20% particles randomly move in the circular area, with the last estimation as center and *v*_{max} as radius.

### Observation likelihood model

*x, y, r*) coordinate, where (

*x, y*) is the 2D location, and

*r*is RSS measurement. The equation is defined as

*a*

_{ x },

*a*

_{ y }, and

*a*

_{ r }are the coefficients of the plane equation, and

*c*is a non-zero constant and set as 1 in this article. The RSS measurements of the four vertices and their locations are known, therefore, they can be used to calculate the coefficients of the hyperplane equation. Suppose the locations of the four vertices are (

*x*

_{1},

*y*

_{1}), (

*x*

_{2},

*y*

_{2}), (

*x*

_{3},

*y*

_{3}), and (

*x*

_{4,}

*y*

_{4}), the mean values of the RSS measurements from one AP are

*r*

_{1},

*r*

_{2},

*r*

_{3}, and

*r*

_{4}. We have a constraint matrix in the following form:

The coefficients of the hyperplane equation can be solved with the least square algorithm as Open image in new window , where ()^{-1} and ()^{T} represent the matrix inverse and transpose, respectively. After building the hyperplane equation for every AP in each of the square training cells, the mean value of RSS fingerprint at an arbitrary location can be calculated with Equation 13, and the average value of the four vertices' covariance is set as the covariance of the location.

*j*th AP is Open image in new window , the observed differential RSS measurement from the

*j*th AP is Open image in new window , then the likelihood for the

*j*th AP is Open image in new window . Suppose the RSS measurements from different APs are independent, the observation likelihood can be expressed as

where *n* is the number of detected APs. The exponent 1/*n* is used to smooth the likelihood so as to avoid the occurring of overconfident estimate. We calculate the observation likelihood values for all the particles and adopt Open image in new window as the new particle weight, and then, normalize it to ensure the summation of weights is equal to 1.

*x*

_{ t }can be calculated as Open image in new window . To avoid the occurrence of degeneration problem, we adopt the adaptive systematic resample method [25] for further optimizing the quality of the particles. The outline of our differential radio map-based Bayesian localization (DRMBL) algorithm is summarized in Table 1.

DRMBL algorithm

1. Initialization: |
---|

Adopt the estimation of RADAR as the initial estimation. |

2. While ( |

2.1 Prediction update |

A. Estimate the velocity and direction using Equations 10 and 11 |

B. Make prediction using Equation 12 |

2.2 Observation update |

A. Calculate the observation likelihood function of each particle with Equation 16 |

B. Calculate the normalized weight for each particle |

2.3 Adopt the weighted mean of the particles as the current location estimation |

2.4 Resample, if necessary |

End |

## Experimental evaluation

In this section, we start by giving a detailed presentation of our testbed. Then, we evaluate the proposed improvement strategies under different conditions. For simplicity and comparison, the deterministic fingerprint-based RADAR algorithm adopts the weighted *k*-nearest neighbor technique, abbreviated as KNN, and the algorithm that adopts probabilistic fingerprint localization technique is abbreviated as PL. Furthermore, to evaluate the effectiveness of our differential strategy, the differential strategy is also applied to the KNN and PL algorithms. We define the improved algorithms as DRMKNN and DRMPL, respectively.

### Experiment setup

*×*29 meters. The TP-LINK TL-WR340G

_{+}APs are adopted, and there are six detectable APs on the floor. We use an IBM ThinkPad X60 laptop with Windows XP operating system as the mobile device. A TP-LINK TL-WN322G wireless card is adopted to gather RSS in the radio map building phase, and a 4965AGN card and a TL-WN322G wireless card are used in the localization phase. Unless otherwise specified, we adopted the data collected by 4965AGN in the following evaluations. We designed the software for collecting RSS based on the NDIS Miniport [27].

The radio map has 164 locations along the corridor and 70 locations inside the room. We placed the training points 1.2 m apart and collected 10 samples at each point with a time interval of 1 s. The default parameters for the algorithms are as follows: the parameter *k* of KNN is 4, and the number of particles used in the DRMBL is 1000.

### Evaluation results

Comparison of localization error

Algorithm | Median (m) | Average (m) | Stand deviation (m) | 90% (m) | Max (m) |
---|---|---|---|---|---|

KNN | 2.42 | 2.78 | 1.89 | 5.28 | 7.34 |

DRMKNN | 1.97 | 2.28 | 1.85 | 4.19 | 9.95 |

PL | 2.26 | 2.60 | 1.86 | 4.82 | 7.50 |

DRMPL | 1.92 | 2.34 | 2.12 | 4.61 | 10.23 |

DRMBL | 1.49 | 2.04 | 1.75 | 4.17 | 6.80 |

### Discussion

We highlight some of the experience on the DRMBL algorithm, including the differential strategy, the density of training points, and the characteristic of the PF algorithm.

*N*APs are detected, ideally there are Open image in new window pairs of differential RSS measurements. For simplicity, we select the AP with the strongest RSS as the reference AP and select

*N -*1 differential RSS measurements relative to it according to Equation 2. Computational resources permitting, one can utilize all the differential measurements to improve the performance. The performance of the differential strategy is greatly affected by the reference AP. Therefore, the selection of the most appropriate reference AP is vital for the DRMBL algorithm. We have verified four criteria: AP with the strongest RSS, AP with the weakest RSS, AP with the minimum standard deviation, and AP with the maximum standard deviation. Table 3 illustrates that the criterion of selecting the AP with the strongest RSS is superior to others.

Comparison of the reference AP selection criterions

criterion | Median (m) | Average (m) | Stand deviation (m) | 90% (m) | Max (m) |
---|---|---|---|---|---|

Strongest RSS | 1.43 | 2.01 | 1.71 | 4.27 | 6.80 |

Weakest RSS | 1.91 | 2.36 | 1.71 | 4.72 | 7.16 |

Minimum standard deviation | 1.66 | 2.06 | 1.64 | 4.12 | 7.13 |

Maximum standard deviation | 1.73 | 2.18 | 1.79 | 4.32 | 8.08 |

## Conclusion

To address the problem of realizing accurate localization in complex dynamic environment in the WLAN which is made up of different types of devices, we proposed a novel DRMBL algorithm under the Bayesian framework. We proposed a differential strategy to overcome the common mode noise and a continuous interpolation technique to accurately realize the particle weight calculation. The experiments validated our proposed schemes, and revealed that DRMBL algorithm could achieve reasonable localization results under challenging background conditions. The schemes proposed in this article are generic and could be adopted by other localization systems.

## Notes

### Acknowledgements

This study was supported by the National Natural Science Foundation of China under grant numbers 60871046 and the National Hi_Tech Research and Development 863 program of China under grant numbers 2008AA092701. The authors thank the constructive discussions with their group members during the writing of the article. The authors would also like to thank the reviewers for their useful suggestions and comments.

## Supplementary material

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