Mobile Information Systems

Volume 2017 (2017), Article ID 9170746, 18 pages

https://doi.org/10.1155/2017/9170746

## Positioning Using Terrestrial Multipath Signals and Inertial Sensors

German Aerospace Center (DLR), Institute of Communications and Navigation, Oberpfaffenhofen, 82234 Weßling, Germany

Correspondence should be addressed to Christian Gentner

Received 24 February 2017; Revised 15 June 2017; Accepted 20 July 2017; Published 2 October 2017

Academic Editor: Ruizhi Chen

Copyright © 2017 Christian Gentner et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper extends an algorithm that exploits multipath propagation for position estimation of mobile receivers named Channel-SLAM. Channel-SLAM treats multipath components (MPCs) as signals from virtual transmitters (VTs) and estimates the positions of the VTs simultaneously with the mobile receiver positions. For Channel-SLAM it is essential to obtain angle of arrival (AoA) measurements for each MPC in order to estimate the VT positions. In this paper, we propose a novel Channel-SLAM implementation based on particle filtering which fuses heading information of an inertial measurement unit (IMU) to omit AoA measurements and to improve the position accuracy. Interpreting all MPCs as signals originated from VTs, Channel-SLAM enables positioning also in non-line-of-sight situations. Furthermore, we propose a method to dynamically adapt the number of particles which significantly reduces the computational complexity. A posterior Cramér-Rao lower bound for Channel-SLAM is derived which incorporates the heading information of the inertial measurement unit (IMU). We evaluate the proposed algorithm based on measurements with a single fixed transmitter and a moving pedestrian carrying the receiver and the IMU. The evaluations show that accurate position estimation is possible without the knowledge of the physical transmitter position by exploiting MPCs and the heading information of an IMU.

#### 1. Introduction

Today, most smartphones are equipped with global navigation satellite systems (GNSSs) receivers which allow using applications on the smartphones for navigation [1]. GNSSs provide sufficient position accuracies for mass market application in open sky conditions. However, indoors or in urban canyons the GNSS positioning accuracy could be drastically reduced. In these situations, the GNSS signals might be blocked, degraded by multipath effects, or received with low power. To enhance the positioning performance indoors, different methods and sensor systems can provide position information rather than relying on GNSSs [2–4]. Most of the indoor positioning systems use local infrastructure like positioning with Radio Frequency Identification (RFID) [5], mobile communication base-stations [6, 7], wireless local area network (WLAN) [8], or ultra-wideband (UWB) [9–11]. However, also these wireless radio technologies experience multipath and non-line-of-sight (NLoS) propagation. Multipath propagation is experienced when the transmitted signal arrives at the receiver via several propagation paths. These propagation paths with different delays are caused by reflections, diffractions, and scattering of the electromagnetic wave. Hence, the signal at the receiving antenna consists of a superposition of multiple replicas of the transmitted signal, where each version is called multipath component (MPC) traveling along an individual propagation path. The delay estimate of standard algorithms like the delay locked loop (DLL) is biased in multipath propagation environments [12]. Algorithms like [13–15] reduce the multipath error by modifying the DLL structure. Other algorithms estimate the channel impulse response (CIR) in order to mitigate the influence of multipath propagation on the delay estimate, for example, [16–20]. To retrieve the required delay from the CIR, the path with the smallest delay is treated as the line-of-sight (LoS) path. However, treating the smallest delay as the LoS path may result in weak positioning performance in NLoS situations. Furthermore, even advanced multipath mitigation algorithms reduce the multipath effects only to a certain degree due to limited signal bandwidth and measurement noise [18].

Nowadays, multipath exploitation instead of mitigation is attracting more and more interest. The authors of [21, 22] exploit multipath propagation for positioning of mobile terminals using multipath fingerprinting algorithms. Other algorithms, for example, [23, 24], interpret reflected signals as signals emitted from virtual transmitters (VTs), where the VT positions are precalculated based on the knowledge of the reflecting surface and physical transmitter positions. Furthermore, the authors of [25] estimate and track the phase information of MPCs using an extended Kalman filter (EKF) and estimate the user position using a time difference of arrival (TDOA) positioning approach. Other algorithms like [26] use a nonlinear least squares algorithm combining UWB measurements at several receiver positions to estimate the positions of the VTs and the receiver simultaneously within small scale scenarios.

This paper describes and extends the multipath assisted positioning algorithm referred to as Channel-SLAM; see [27–31]. Channel-SLAM considers a moving receiver and is suitable for GNSS denied areas like indoor areas. Similarly to other multipath assisted positioning approaches, Channel-SLAM interprets MPCs as LoS signals emitted from VTs. In addition to reflected signals, Channel-SLAM considers also paths occurring due to multiple number of reflections, diffractions, or scattering as well as combinations of these effects. As a consequence, the reception of several MPCs allows position estimation even if only one physical transmitter is present. Interpreting MPCs as directly propagated signals originated from VTs, Channel-SLAM enables positioning also in NLoS situations. Additionally, Channel-SLAM does not require any prior knowledge on locations of reflecting surfaces as Channel-SLAM estimates the receiver position, velocity, clock bias, and the VT positions simultaneously which can be interpreted as simultaneous localization and mapping (SLAM) with radio signals. In [27, 28, 31], we showed that positioning is possible in NLoS scenarios using MPCs without the knowledge of the room geometry by using Channel-SLAM. We investigated in [27] TDOA positioning and especially TDOA between MPCs such that time synchronization between physical transmitters is not essential. In [31], we derived Channel-SLAM based on a Rao-Blackwellized particle filter (RBPF) and compared the accuracy of Channel-SLAM to a derived posterior Cramér-Rao lower bound (PCRLB). However, the Channel-SLAM algorithms in [27, 28, 31] use linear antenna arrays and assume the knowledge of the physical transmitter position.

In this paper, we propose an implementation of Channel-SLAM that uses only a single receiving antenna and fuses similarly to [29, 30] additional information obtained from an inertial measurement unit (IMU). Today many smartphones feature Microelectromechanical System (MEMS) IMUs, which can provide short term relative orientation and position information. Theoretically, the measurements of the IMU can be directly used in an inertial navigation system. However, the position calculation involves double integrations; hence, even small measurement errors quickly cause a drift in the position solution [32]. To avoid that, we only fuse heading measurements from the IMU which solely requires an alignment of the coordinate systems. The heading information of the IMU allows improving the performance of Channel-SLAM by resolving ambiguities and angle of arrival (AoA) measurements are not mandatory anymore. Being a relative positioning system, Channel-SLAM requires an initial prior knowledge of the receiver position and moving direction to define the coordinate system. The positioning algorithm derived in this paper is based on a RBPF where we employ a new transition model for pedestrians. In [29, 30], we showed that positioning with only one physical transmitter is possible if MPCs and heading information from an IMU are used. Compared to [29, 30], the novel transition model enables a performance gain in the position accuracy. In addition to [27–31], we propose a method to dynamically adapt the number of particles which significantly reduces the computational complexity. Furthermore, a PCRLB for Channel-SLAM is derived which incorporates heading information obtained by using an IMU. The developed positioning algorithm is evaluated based on measurement data obtained in an outdoor scenario, where the position of the physical transmitter is unknown. Based on these measurements, we compare the accuracy of Channel-SLAM to that of the derived PCRLB.

The paper is structured as follows: Section 2 describes the signal model; afterwards, Section 3 describes the proposed algorithm which is split into four subsections: Section 3.1 addresses Channel-SLAM; Section 3.2 describes two different transition models using the heading information from an IMU; Section 3.3 summarizes the RBPF; Section 3.4 describes the implementation of the RBPF; afterwards, we derive in Section 4 the PCRLB for Channel-SLAM incorporating the heading changes of the IMU. Thereafter, Section 5 evaluates the algorithm based on measurement data. The last section, Section 6, concludes the paper.

Throughout the paper, we will use the following notations:(i) stands for the vector transpose.(ii)All vectors are interpreted as column vectors.(iii)Vectors are denoted by bold small letters.(iv) denotes the th element of vector .(v) represents the square of the Frobenius norm of .(vi) denotes a Gaussian distributed random variable with mean and variance .(vii) stands for expectation or sample mean of .(viii) stands for all integer numbers starting from to , thus .(ix) denotes the probability density function of .(x) is the speed of light.(xi) denotes the estimation of .(xii) stands for proportional.(xiii) defines the set for with .(xiv) denotes the uniform distribution on the interval .

#### 2. Concept of Virtual Transmitters

Mathematically, the behavior of the multipath channel can be described by the time variant CIR , where indicates the discrete time instants and the delay [33]. According to [33], the CIR can be assumed to be constant for a short time interval at discrete time with index ,for , where is the number of MPCs, is the delay, the complex amplitude of the th MPC, and stands for the Dirac distribution [34] (please note that the CIR is generally a summation of an infinite number of MPCs; however, a practical receiver is only capable of capturing signals whose powers are above a certain sensitivity level). For notational conveniences, the LoS propagation path is considered also as a MPC in this paper. Assuming that the transmitted signal is band-limited with bandwidth and time-limited with a length smaller than , the signal received at time sampled with rate , bin indices , and the delay can be expressed aswhere denotes the white circular symmetric normal distributed receiver noise with variance . Using vector notation we obtain from (2)

In order to obtain the sparse structure of the CIR from the measurements , super resolution multipath estimation algorithms are necessary. The received signal is geometrically dependent on the transmitter and receiver positions as well as on the environment. Thus, the channel is spatially correlated as long as the spatial sampling is small enough. Hence, we use in this paper the dynamic multipath estimator named Kalman enhanced super resolution tracking (KEST) [20, 35–37] for estimating and tracking multipath parameters. KEST allows estimating the evolution of the CIR over time which is essential for Channel-SLAM as shown in the following section. KEST consists of a Kalman filter (KF) to estimate the complex amplitude and delay for each MPC utilizing maximum likelihood (ML) estimates as measurements. In the used implementation, KEST uses a standard model for the CIR which comprises a sum of weighted Dirac impulses as in (1). This model describes distinct paths sufficiently well. However, dense multipath components (DMC) lead to a model mismatch in the used KEST implementation. This model mismatch results in an increased variance of the estimated MPC parameters used as measurement noise in Channel-SLAM. For further details about KEST, see [20, 35–37].

To use the delay measurements of the tracked MPCs for positioning, a model describing the delays depending on the current user position is necessary. For developing such a model, we consider a static environment with a fixed transmitter and a receiver moving along an arbitrary trajectory. Figure 1 summarizes four propagation scenarios; for a detailed description see [31]. In the first scenario, the transmitted signal is reflected on a reflecting surface indicated by the blue lines. For reflection, we consider the effect of an electromagnetic wave reflected by a reflecting surface. When the receiver is moving, the reflection point on the reflecting surface is moving as well. If we mirror the physical transmitter position on the reflecting surface, we obtain the position of which is static during the receiver movement. The distance between and the receiver is equivalent to the propagation time of the reflected signal multiplied by the speed of light. Hence, the reflected signal can be interpreted as a direct signal from to the receiver.