Indoor location estimation is important for many applications, including home automation, security, and surveillance, to name a few. This is accomplished via sensors such as cameras and passive infrared (PIR) sensors, as well as radio frequency-based technologies such as Wi-Fi, Bluetooth, and radio frequency identification (RFID). Because of its ease of implementation, Wi-Fi technology is the most extensively used. Aside from Wi-Fi, a growing number of researchers are experimenting with the sensors embedded into mobile phones. To increase the performance of the localization, deep learning, probabilistic, and statistical algorithms are applied to the raw data collected from sensors and Wi-Fi access points. In this paper, we present a sensor-based indoor localization test-bed. We feed data from magnetometer sensors and Wi-Fi access points to Machine Learning (ML) algorithms. With our proposed method, we get a very high accuracy of 98%. Performance analysis of the ML-classifiers' dependence on the size of the test data set is also explored in detail.
Various fingerprinting approaches have recently been studied and deployed in real time
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Notably, majority of the aforementioned approaches are not stand-alone, i.e., these cannot be implemented independently. More precisely, Wi-Fi based localization requires the use of a network, which raises the concerns about data security. Furthermore, when a small number of access points are installed, using alone a Wi-Fi approach is not very efective. Also, these approaches necessitate prior knowledge of the Geo-graphical locations of the access points deployed indoors. Wireless fingerprinting-based localization is the most popular among all the localization techniques, due to its ease of deployment. The Radio Frequency signals (RF signatures) collected from the access points help in the prediction of the location accurately. Typically, RF measurement values and the Received Signal Strength (RSS) values of WiFi or Bluetooth or any other wireless technologies, are one and the same.
Indoor localization methods which are based on the signatures of magnetic field generally
assume that these magnetic fields do not vary much within a smaller range of altitudes; for
example, see [
Rest of the paper is structured as follows: Section 2 provides a synopsis of some related works. Section 3 discusses the motivation of the paper. The Experimental setup which includes brief description of the sensors used in this work is presented in Section 4. Section 5 presents the experimental results. Section 6 discusses some concluding remarks.
In recent past, extensive research has been conducted towards indoor localization and the
boosting of the prediction accuracy. In this, many researches have proposed a wide range of
novel schemes for Indoor Localization/Navigation which involve the technologies, to name but
a few, RF-ID[
In [
In [
The work in [
A Deep Learning based approach has been introduced in [
In general, in any positioning approach, the evaluation of the accuracy involves the calculation of the Euclidean distance between the true and estimated positions of the users. One major draw back in this is that the floor transitions are being ignored. Dealing with some more challenges in predicting an accurate position of users indoors, the work in [21] introduces a new methodology to measure the positioning error, which considers the length of the user’s path that connects the estimated position to the exact position using the visibility graph for the floor map, so as to compute the shortest distance, navigational meshes for the vector maps to identify similar paths with less computation time.
To improve the user localization accuracy using RSSI and the complexity over widely used ifngerprinting methods, an eficient compressive sensing based approach have been introduced in [22]. Localization using Least Square Lateration(LSL) method has been introduced in[23]. This paper also discussed a comparative analysis of the accuracy with LSL against that of with Pure lateration(PL), by utilizing diferent Gaussian noise parameters for varying number of access points and varying distance between the access points and user’s end device. Further, it has been proven (in the same paper) that least-square algorithm with curve fitting approach provides significant performance improvements when compared to PL. A novel scheme for localization based on the Angle Diference of Arrival information and triangulation using mmwaves indoors has been proposed in [24]. Also, it has been stated that their proposed algorithm outperforms very well at both vacant as well as ofice environments, by using a commercial 60-GHZ mm-wave test bed for their experiment. Though the results therein are promising, deploying the same for real time usage will be the bottleneck given that their equipment is expensive.
To study and understand the behaviour of the Earth’s magnetic field inside a room, a novel
methodology has been introduced in [
So far, several research papers have been published in the literature that use either RSSI [27]
and [28] or CSI data [
Recent works, such as [29] and [30], to name a few, have demonstrated that using magnetic signatures indoors, and more broadly in the corridors of even large buildings, is quite beneficial in terms of consistency and stability. Furthermore, the sensor signatures do not change over time. In addition, they are unafected by any changes in the objects, such as furniture in diferent locations and moving objects such as doors, windows, and user(s), etc. However, some extreme conditions can influence these signatures, for example large-scale reconstructions or the relocation of heavy metallic objects.
Motivated by the findings mentioned in previous section, we developed a novel machine learning-based approach that makes use of data from both magnetic sensors and Wi-Fi access points. Interestingly, our approach does not require any network connectivity for localization. Furthermore, in this work, we critically examined the dependence of ML classifiers’ location prediction on the altitudes from the surface at which sensors are placed.
We therefore aim to overcome majority of these limitations with a novel idea of combining the utility of both the magnetic field and Wi-Fi Beacon information to describe the indoor position.
Finally, for a further eficient localization indoors, we would like to emphasize that the following can be immensely helpful: 1. A detailed study on the magnetic field data analysis.
2. A study of more recent state-of-the-art
To begin, we gathered data points spanning an area of 364 sq.ft. In the corridors of a building, this area is subdivided into cells of size 4 sq.ft., resulting in a grid (matrix) of size 7× 13 (outdoors). Similarly, while working inside a room (indoors), data points from an area of 180 sq.ft., were divided into cells of 4 sq.ft. each, and resulting in a 5× 9 grid. The actual problem is posed as a multi-output and multi-label classification problem, i.e., predicting the co-ordinates (of the user’s position) on the grid based on inputs from both the magnetometer sensor (HMC5883L) and the Beacon RSSI values of the selected Wi-Fi access points. We divided the rest of the description of the experiment (its setup and the various elements involved) into four separate subsections for ease of exposition.
Honeywell HMC5885L magnetometer sensor is used in this work. This ’low power’ module is useful for a variety of general purposes, including measuring the magnetization of a material (for example, ferromagnetic materials, iron bars inside concrete pillars, and so on), measuring the field strength, and measuring the direction of the magnetic field at a point, among others. It is intended for magnetic field sensing with a digital interface for a wide range of real-time embedded applications at a low cost and with high resolution. Next, using the I2C interface, you can easily establish communication between the HMC5885L and microcontrollers. This sensor supports 3V to 5V Input-Output levels on I2C Serial Clock Line (SCL) and Serial Data Line (SDA) pins. The sensor’s output is measured in milli-Gauss units.
To collect sensor data and beacon information, we created an Embedded test bed that includes an RF enabled Wi-Fi module and a Magnetometer sensor. Following that, we connected an SD card module to the microcontroller to store the raw data from the sensor into files (.csv format), and these files contain both the magnetic field data (along the x, y, and z planes in reference to the sensor’s alignment with the test bed) and the Beacon information of three (nearest, chosen at random) selected Wi-Fi access points. The block level representation of our experimental setup is shown in Fig. 1. We collected magnetic field data and Wi-Fi beacon information in both outdoor and indoor environments of our research laboratory by placing the sensor at various altitudes.
The data we collected has six attributes: the first three are the data corresponding to the X, Y, and Z axes provided by the Magnetometer sensor, and the remaining three are provided by the Beacon RSSI values of the three selected Wi-Fi access points. Over the 364 sq.ft. area, we collected a total of 54,600 samples (chosen above, outdoors). Remember that this area has 7× 13 cells, each with a 4 sq.ft. area, and we collected 600 samples from each of these cells. Similarly, we classified the indoor floor into a 5x9 grid and collected (total of 20,250 samples) 450 samples at each cell of the grid. 4.2.1. Wi-Fi Data During each scan, the signal strength measurements of all nearby access points can be theoretically obtained. However, not all access points in a location are usually observed/captured in real time. The Service Set Identifier (SSID) of any nearby Wi-Fi access point, as well as its BSSI (MAC address) and Received signal strength Information, are immediately visible in the database obtained by scanning the Wi-Fi network coverage area (RSSI). In our paper, we only considered three access points that were closest to the data collection location. 4.2.2. Magnetic Field Data The data from the Magnetic field sensor used in this work yields three column vectors each with dimension equal to the number of samples taken:
H = [︀ H, H, H]︀ number of samples× 3 .
Above, H, H and H denote the position-measurements from the sensor along , and -axes, respectively. Recall, these measurements are noted in mG units.
In general, the raw measurements obtained from the magnetic field sensor can be used in two diferent ways: 1) to calculate the magnitude of H, i.e., the magnitude of each row in H, which is a point in 3-dimensional space; 2) to use H directly/explicitly. For the purpose of enhancing the accuracy. usually way 2) in the previous line is followed. For each 1 ≤ ≤ the number of samples, recall:
Magnitude of H[] = √︁
(H[])2 + (H[])2 + (H[])2, where H[] = (︀ H[], H[], H[])︀ ∈ R3.
The 2D-heat maps of the measurements are shown in Fig. 5. Fig. 5(a) corresponds to the experiment outdoors; while the remaining two correspond to indoors and the two diferent (a) (b) altitudes (2 feet and 4 feet) considered. Furthermore, for a better understanding, we have plotted the 3D-heat map for the experiment outdoors, see Fig. 6.
To verify the consistency of the measurements by the magnetic sensor (embedded on the test bed), the process will be repeated to collect a large number of signatures of the magnetic field in diferent columns of the grids in Fig. 5. From all of these sub figures, one observes: • The signatures collected across diferent columns on the floor can be seen from Fig. 3.
Clearly, there is a variation in the patterns in these two figures. • Consistency: Evidently, the patterns in the plots in Fig. 3 are not varying with the times at which the samples were collected (morning, afternoon and evening). • At each location indoors, there is a small variation in the signatures as we change the height of the sensors, see Fig. 4.
The collected data at both outdoor and indoor environments is processed to obtain the mean magnitudes – plotted as a heat maps in Fig. 5(a), 5(b) and 5(c) – at every individual cell in the defined grid. The data is then normalised over all the cells, for a better representation of the heat maps. Observe from Fig. 6 (for outdoor environment), the oscillations/non-uniformity in the normalized magnitude values as we move among various cells on the grid.
In our paper, we employ classifiers such as Random Forest(RF) and XG-Boost, since these are purely tree-based ensemble algorithms. Comparatively, in RF classifier, more number of Decision Trees (DT) are applied to multiple sub-samples, so as to increase the prediction performance, to prevent over fitting while training, and also to enhance the stability and accuracy. RF classifier is a bootstrap ensemble for decision trees. Usually, Hyper parameters namely, number of trees and depth etc, are tuned for better prediction performances.
Where in, D denotes number of data points in node. m,n denotes number of labels (label m and n correspond to row and column information of room, in our case). P(m,n) denotes probability of data belonging to a label.
Average entropy of a split D: {︀ }︀ =1 and Information gain() can be calculated using below equations, = [︃ ∑︁ || H() =1 ||
]︃ = H() − = H() − [︃ ]︃ ∑︁ || H() . =1 ||
XG-Boost(Xgb) classifier was found efective over of-the-shelf ML classifiers with categorical data. In simple words, Xgb is an algorithm which is an implementation of Gradient Boosted DT’s. It is being very dominant in applied machine learning now a days. One of the objectives of Xgb is to minimize the error of cost function ℓ(, ()), via applying gradient descent algorithm. In this algorithm, DT’s are created in a sequential order. Weights, which play an important role in XGBoost, are assigned to all the independent variables, which are then fed into the DT which predicts the outputs. The weight of the variables that is predicted wrong by the DT, is increased and then the variables are fed to the next DT. These individual DT’s are then ensemble to give a concrete and more eficient (in terms of accuracy) model. It can work on both the regression and classification problems. (1) (2) (3) (a) (b) (c) altitude at Indoor environment; (c) Magnetic field at 4 feet altitude at indoor environment.
The training data set is D = {︀ (, )︀} =1, where and corresponding to the input and output attributes (a total of 8 attributes) of data set, = {︀ [, ] ︀} ,,=1, Note that the lengths of and are same. Let the diferential loss function for our model be ℓ(, ()), where () is the prediction corresponding to the input of classifier. We begin by initializing the model with some constant value: compute the entries of the Gradient and Hessian iteratively (using a for loop) as follows: Let be a positive integer. For each ∈ {1, . . . , } and for each ∈ {1, . . . , }, we 0() = arg min ∑︁ ℓ (, ) =1 = − = − ︂[ ℓ (, ()) ]︂
() ︂[ 2ℓ (, ()) ]︂ () 2 ()=-1() ()=(− 1)() (4) (5) (6) ( is the learning rate.) ():
After finding and thereby () as above, we now update (in the for loop) the parameter (7) (8) (9) (10) = arg min ∑︁ 1 =1
︂[ 2 − − () () = − 1() + () () = ()() = ∑︁ () =0
We fit a base learner (Decision tree) for the training set {︁ optimization problem: }︁ , − =1 , solving the following
To begin with, we have collected data inside as well as outside our research laboratory building. Next, we captured the real time data from both the Wi-Fi module and Magnetic sensor, and then stored all of this data in an SD card for further processing. The data extracted from the Magnetic sensor are composed of an individual reading for each Cartesian axis (x, y and z). In real time, the data from the magnetic sensors are anomalous due to sudden changes in the magnetic field, or erroneous sensor readings. The data stored in SD cards has been transferred to a laptop for further data processing, that includes training and testing of ML models.
We have then classified the target attributes into two outputs. The first output corresponds to the row information of the cell in the grid, while the second to the column information. The lfoor map of outdoor environment can be found in Fig. 5(a). The values 0–12 on the x-axis (as in this figure) represent individual columns of the grid, while the values 0–6 on the y-axis represent individual rows. Similarly, for indoor environment, we considered the total area into a 5x9 grid, and the same can be seen clearly from both Fig. 5(b) and 5(c). Next, the values 0–8 on the x-axis (in both the figures in the previous line) represent individual columns of the grid, while 0–4 on the y-axis represent individual rows.
Now, we present our experimental results, comparing the performances of various ML models used in this paper for the position estimation.
We observed very good testing accuracy running a series of experiments on the collected data set, with varying test sizes.
As can be seen in Fig. 8, the results obtained after training and testing the classifiers with both magnetic field data and Wi-Fi data are depicted (collected from the embedded test bed developed presently). Observe in the same figure that the RF classifier has a very good accuracy of around > 95%. Because we are working with a fixed number of samples, the test size increases as the size of the training data set decreases. Our accuracy results immediately show that we are able to predict with high appreciable accuracy, and more importantly (perhaps remarkably) with only few samples.
The following example is for a quick grasp: • At 95% test sample size, the number of samples used for training is 2730 (which amounts to the leftover 5%). • All of these 2730 samples are uniformly distributed across 91 classes, i.e., 30 samples per each class.
• Our prediction accuracy (with only 5% of training data set) is > 95%.
∑︀ (︀ Prediction(m) == Original label(m))︀ = =1
Total no. of samples used for testing where, m is a element in a array.
Motivated by the outdoor results, we considered a small number of samples at each cell in an indoor environment at two diferent altitudes. The results shown in Fig. 9 are the result of applying ML classifiers to two separate data sets collected at two diferent altitudes within the room. It is clear that all of the classifiers we used performs very well.
In this paper, we presented a novel approach for estimating the user’s position indoors with high accuracy (around 98%). The motivation for using statistical approaches is that deep learningbased models are computationally expensive and require a large amount of memory for real-time deployment. We created a machine learning-based multi-label and multi-output strategy for indoor localization and demonstrated it using our own embedded test bed. However, the motivation for this work is to predict the position of the user indoors as well. In our experiment, we used industry standard sensors on our test bed to evaluate the performance of ML classifiers with very good resolution (in terms of accuracy) for indoor localization. Changes in the size of the training data set were also used to evaluate performance.
We achieved best accuracy of around 98.6% and 97.6% with RF and XGB classifiers, respectively, by training the models with 5% of the original data set. Furthermore, we evaluated the efectiveness of our approach for interior location detection at various altitudes. Our method is simple to implement, and the time required for data collection and prediction is minimal. We mapped a small area within a large building, but given the promising accuracy, this approach can be scaled up to larger infrastructures such as large ofice buildings and shopping malls, among other things.
Note that this paper does not focus on: materials, configurations of material, and other properties of buildings cause our observations. Indeed, if we can understand the elements playing a role in our observations – such as before – then we can make some predictions on the possible magnetic field variations that might occur in future, in the same buildings worked inside/ others. Such predictions would allow for improvements in evaluation of scientific grounding in localization techniques. To begin with, for studying possible links between variables, one can investigate using a building information model to predict the magnetic fields inside it. This approach could help in associating magnetic field variations with specific building elements for instance: steel beams, heating and cooling systems such as Air coolers. In parallel, one can extend the study of the performance of any machine learning model, via conducting the same experiments in diferent environments in large areas like: a multi-story building constructed by brick and concrete, a warehouse/factory building, a high-rise building made of steel. We would like to explore the above avenues in future, in the light of a reasonable thinking that, there is no guarantee that the results shown in this paper would hold the same for every building, with may be similar structure etc. [20] H. J. Bae, L. Choi, Large-scale indoor positioning using geomagnetic field with deep neural networks, in: ICC 2019 - 2019 IEEE International Conference on Communications (ICC), 2019, pp. 1–6. [21] G. M. Mendoza-Silva, J. Torres-Sospedra, F. Potortì, A. Moreira, S. Knauth, R. Berkvens, J. Huerta, Beyond euclidean distance for error measurement in pedestrian indoor location, IEEE Transactions on Instrumentation and Measurement 70 (2021) 1–11. [22] C. Feng, W. S. A. Au, S. Valaee, Z. Tan, Received-signal-strength-based indoor positioning using compressive sensing, IEEE Transactions on Mobile Computing 11 (2012) 1983–1993. [23] K. Cengiz, Comprehensive analysis on least-squares lateration for indoor positioning systems, IEEE Internet of Things Journal 8 (2021) 2842–2856. [24] J. Palacios, G. Bielsa, P. Casari, J. Widmer, Single- and multiple-access point indoor localization for millimeter-wave networks, IEEE Transactions on Wireless Communications 18 (2019) 1927–1942. [25] R. Shirai, M. Hashimoto, Dc magnetic field based 3d localization with single anchor coil,
IEEE Sensors Journal 20 (2020) 3902–3913. [26] D. Hanley, A. S. D. d. Oliveira, X. Zhang, D. H. Kim, Y. Wei, T. Bretl, The impact of height on indoor positioning with magnetic fields, IEEE Transactions on Instrumentation and Measurement 70 (2021) 1–19. [27] M. T. Hoang, B. Yuen, X. Dong, T. Lu, R. Westendorp, K. Reddy, Recurrent neural networks for accurate rssi indoor localization, IEEE Internet of Things Journal 6 (2019) 10639–10651. [28] S. Knauth, M. Storz, H. Dastageeri, A. Koukofikis, N. A. Mähser-Hipp, Fingerprint calibrated centroid and scalar product correlation rssi positioning in large environments, in: 2015 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2015, pp. 1–6. [29] M. Kwak, C. Hamm, S. Park, T. T. Kwon, Magnetic field based indoor localization system: A crowdsourcing approach, in: 2019 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 2019, pp. 1–8. [30] I. Ashraf, S. Hur, Y. Park, Enhancing performance of magnetic field based indoor localization using magnetic patterns from multiple smartphones, Sensors 20 (2020).