^{1}

^{2}

^{1}

^{1}

^{2}

^{1}

^{2}

^{3}

^{1}

^{2}

^{3}

Geomagnetic indoor positioning is an attractive indoor positioning technology due to its infrastructure-free feature. In the matching algorithm for geomagnetic indoor localization, the particle filter has been the most widely used. The algorithm however often suffers filtering divergence when there is continuous variation of the indoor magnetic distribution. The resampling step in the process of implementation would make the situation even worse, which directly lead to the loss of indoor positioning solution. Aiming at this problem, we have proposed an improved particle filter algorithm based on initial positioning error constraint, inspired by the Hausdorff distance measurement point set matching theory. Since the operating range of the particle filter cannot exceed the magnitude of the initial positioning error, it avoids the adverse effect of sampling particles with the same magnetic intensity but away from the target during the iteration process on the positioning system. The effectiveness and reliability of the improved algorithm are verified by experiments.

With the rapid development of location-based services, indoor positioning is receiving increased attention. Indoor positioning technology can be applied to public security, location tracking, intelligent transportation, and so forth. For example, a hospital can locate and monitor patients using indoor positioning technology. Indoor positioning can solve the problem of finding cars in large complexes and underground parking lots; it can also quickly find an optimal shopping route in large shopping malls. Indoor positioning is currently based on technologies such as Wi-Fi, RFID, Bluetooth, UMB, and geomagnetism. Among different technologies for indoor positioning, the geomagnetic indoor positioning approach has broad application prospects because it is infrastructure-free and has geomagnetic signal stability [

As early as the 1950s, the geomagnetic positioning technology based on geomagnetic field vector matching was applied to large-scale outdoor environment navigation, including those of surface ships, submarines, and missiles. In the past, the geomagnetic positioning techniques typically used the correlation matching algorithms [

At present, the particle filter algorithm,

The use of particle filters requires the carrier to complete a continuous recursive filter location over a period of time, and it suffers the problem of filtering divergence [

In response to this challenge, this paper proposes the use of point set matching in the Hausdorff distance measurement method to improve the particle filter algorithm as well as the method of positioning error constraints. In the new particle filter algorithm, the initial positioning error is used as the distance constraint, only allowing particles that meet the constraints to iterate, and resampling. Coupled with the convergence characteristics of the resampling step, we can suppress the effect of persistent divergence. The main contributions of this work include (1) the development of a geomagnetic data acquisition platform, (2) an improved particle filter algorithm to prevent filter divergence, and (3) the design of an offline test system to estimate the location of mobile robots carrying magnetic sensors.

The paper is organized as follows. The classical particle filter algorithm is described in Section

The particle filter algorithm is an optimal Bayesian estimation method based on Monte Carlo’s idea [

The particle filter algorithm follows the general framework of a sequential importance sampling (SIS) algorithm, and it adds the sampling importance resampling (SIR) to solve the sample impoverishment caused by the iterative process. It first generates a set of samples with

In (

For geomagnetic indoor positioning based on the particle filter, the particle weight is determined by (

Increasing the characteristic elements of the geomagnetic matching can effectively solve the divergence problem in the particle filter algorithm, but it will also greatly increase the complexity of the original algorithm and the time required for positioning. Inspired by the Hausdorff distance matching, an improved particle filter algorithm based on the Hausdorff distance is proposed and described in the following.

We know that the magnetic field at any point is stable in the static environment and it is unique within a certain range. If the particle filter starts within a reasonable range, the deviation of estimated position will be reduced. The Hausdorff distance can then be applied to determine this reasonable range for the particle filter. The Hausdorff distance is the maximum value of the distance between the two sets of points in space which is defined as follows [_{i}_{i}

In general, in the geomagnetic feature matching based on classical particle filtering, we can control the weight of the particles that participate in calculating the estimated position in (

The position

For time steps

For particle numbers

IF

The particle state is shifted:

Get mobile vector online observations:

Weight update:

END IF

END FOR

Make CDF of

For particle numbers

Draw

Resample

END FOR

Flowchart of improved particle filter algorithm.

The construction of a geomagnetic fingerprint model is a prerequisite for geomagnetic indoor positioning technology. In order to quickly and effectively establish a fingerprint model, a data acquisition robot has been developed by Urban Surveying and Mapping Institute which includes data acquisition module and control module as shown in Figure

Geomagnetic data acquisition robot platform. (a) Front view. (b) Bottom view.

Comparison of magnetic field values after magnetic sensor compensation.

The method to correct the value

The experimental data acquisition was conducted in the 2nd floor of the Institute of Surveying and Mapping at Beijing University of Civil Engineering and Architecture (BUCEA). The frames of the building are reinforced concrete. Figure

Floor map of the Institute of Surveying and Mapping.

In order to prove the defect of particle filter algorithm, we randomly collected a row of data in the corridor. Figure

Distribution of the magnitude of the magnetic field in a row of the corridor. Blue spots indicate points with the same magnetic field intensity.

According to (

In the corridor, we collected geomagnetic data along four lines of 60 cm apart. For building the fingerprint model, we control the acquisition robot along the planned route to move forward which the step length of robot is 0.2 m with geomagnetic data measurement at a sampling rate of 5 Hz. To perform localization, we use the norm of the magnetic field

The final fingerprint model is created by applying a linear interpolation to the magnetic field intensity using a 0.02 m step size in the computer, as shown in Figure

Geomagnetic fingerprint model. Straight-line AB is any one row of the corridors.

The acquisition robot used to take measurements was controlled to travel straight along the corridor, with a step length of 0.6 m. It recorded data every second, iteration times

The burr in Figure

Positioning error based on SIS algorithm.

As shown in Figure

Positioning error based on particle filter algorithm with the SIR.

The idea of the positioning error constraint method is shown in Figures

Initial positioning of

Positioning error constraint.

Figure

Initial positioning errors. Maximum value: 8.81 m, average value: 7.30 m, and minimum value: 5.10 m.

Positioning errors based on improved algorithm.

Indoor geomagnetic disturbance prevents the classical particle filter algorithm from stably finding the location in real time. Although the particle filter algorithm has a strong convergence in the matching accuracy, the particle iteration process is accompanied by the loss of positioning. In this paper, we add the position error constraint to the particle filter algorithm and compare and analyze the advantages and disadvantages of the classical particle filter algorithm with the improved algorithm in matching accuracy, running time, and other aspects by real-field test. The results show that the improved algorithm can solve the persistent divergence problem in the particle filter and avoid the loss of positioning. Under the premise of the single variable feature, it can improve the indoor positioning speed and effectively solve the technical defect in geomagnetic matching. In the future work we will try to combine WLAN and other technologies to achieve effective initial positioning accuracy better than 5 meters.

The authors declare that they have no conflicts of interest.

This study was supported by National Key Research and Development Program of China (no. 2017YFB0503702).