This work presents a radio based localization approach that is capable of accurately positioning radio emitters even when no direct line-of-sight signal is available. A dual polarized array is employed along with the space alternating generalized expectation maximization (SAGE) algorithm. To lighten the computational load and improve the accuracy of the proposed method, Global Navigation Satellite Systems (GNSS) positioning is used to initialize and limit the search area of SAGE. A set of numerical simulations is presented, highlighting the performance of the proposed method.
This work presents a geometric localization approach that leverages a dual-polarization antenna array for positioning even under NLOS only conditions (blocked LOS component). The method presented relies employs DOA, TDOA, and the reflection angle estimates of several NLOS components to accurately position a radio transmitter. Furthermore, in order to improve the accuracy and reduce the computational load of the space alternating generalized expectation maximization (SAGE) algorithm, employed to acquire the parameter estimates, a position provided by a GNSS receiver on the transmitter is used to initialize the algorithm. The proposed method requires that the orientation of both transmitter and receiver antennas are known.
This work assumes a polarized electromagnetic transmitter that is transmitting a broadband
signal and a dual-polarization antenna array receiver composed of M antenna elements, and
we consider N impinging wavefronts. The polarized wavefront of the nth path is propagating
in direction ⃗dn. Assuming a signal path that impinges onto a reflective surface with angle ϕ the
horizontal and vertical components of the polarized wave are reflected with relative amplitude
and phase given by
where Eh,i and Ev,i refer to the complex amplitudes of the incident electric field and Eh,r and
Ev,r refer to the complex amplitudes of the reflected electric field. For a smooth, plane surface,
κ h and κ v can be written as [4]
(
The received multi-carrier signal’s space-frequency response of the kth subcarrier received by antenna m with polarization z at time snapshot t can be written as
L xm,z,k[t] = ∑︂ κ l,zsl,kejw(xm cos θ l+ym sin θ l) · ej2πk ∆ f τ l Ev,r ,
Ev,i κ h κ v = = µµ pr η r2 cos ϕ − η p√︂η r2 − η p2 sin ϕ 2 µµ pr η r2 cos ϕ + η p√︂η r2 − η p2 sin ϕ 2
µ p √︂η r2 − η p2 sin ϕ 2 η p cos ϕ − µ r η p cos ϕ + µµ pr √︂η r2 − η p2 sin ϕ 2 (a) Depiction of NLOS localization scenario (b) Example of search areas for transmitter and
reflectors
+ nm,z,k[t],
(
To estimate the position of a transmitter, this work applies a dual polarized antenna array A LOS path is not required, as the present of two distinct NLOS paths is suficient for obtaining a position estimate of a transmitter. A graphical description of the scenario considered in this work is presented in Figure 1a. The figure presents two NLOS paths impinging over an antenna array whose center serves as the origin for a two-dimensional coordinate system. The parameters show in the figure are the angle of arrival θ , and angle of reflection ϕ of the two diferent paths.
The parameters τ l, θ l, and ϕ l of the lth signal are related to the position of the transmitter tl and reflector rl according to
Π θ l = 2 − arctan ︃( yrl )︃
xrl
ϕ l = ⃓⃓⃓⃓ xyttll −− yxrrll ⃓⃓⃓⃓ + (Π − | θ l|)
(
Equations (
This work extends the work in [5] by employing the space alternating generalized expectation maximization (SAGE) algorithm [6] to directly solve the multidimensional problem over the transmitter and reflector positions. Directly searching over the position will yield a more robust estimation, by eliminating nonlinear error relationships that arise when a position is estimated geometrically with respected to angles of arrival and reflection.
However, directly searching over the possible positions greatly increases the computational load required to obtain a position estimate for the transmitter. In order to mitigate this problem, two steps are proposed.
The first step consists of using a position estimate provided by the transmitter itself. This work considers that this estimate is obtained by a GNSS system. The estimate can than be sent to the receiver in order to minimize the search area with respect to the transmitter location. The average horizontal position accuracy of a GPS receiver in a smartphone in urban environments ranges from 7 to 13 meters [7]. Whiles this accuracy may be insuficient for safety of life applications, such as autonomous vehicles, it is suficient to greatly reduce to computational complexity of the proposed method.
To reduce the search area with respect to the reflector locations an initial angle of arrival estimate can be used. This estimate can be obtained by applying SAGE itself over only one of the polarization’s of the received signal, preferably the one with a higher signal to noise ratio (SNR). Once the DOA estimates have been obtained it is possible to restrict the search area to a given region around the line created by the DOA line crossing the receiving antenna array. The area around the DOA line can be defined by defining a tolerance or sensitivity parameter α such that the search area is contained within the lines that cross the center of the receiving array with angles θ l + α and θ l − α . Figure 1b presents an example of the search areas for the transmitter and for the possible reflectors.
Figure 2 presents the results for a set of numerical simulations performed to access the performance of the proposed method, refereed to as direct positioning, in comparison to the method proposed in [5], refereed to as geometric positioning. For this set of simulations, a transmitter is placed 30 meters in front of the receiver at coordinates (0, 30). Three reflectors are placed at coordinates (− 30, 20), (25, 10), and (15, 16). For this set of simulations it is assumed that no LOS signal reaches the receiving antenna array. The antenna array is composed of M = 10 dual-polarized antenna elements, and T = 100 snapshots are used to estimate the position of the transmitter. The permittivity and permeability of the reflectors are assumed to be known in this case.
The results show that the method proposed in this paper outperforms the one presented [5], especially at low SNRs. Furthermore, the accuracy of the proposed method is superior to that of a commercial GPS receiver present in a modern smartphone, making it a more suitable method for safety of life applications.
Geometric positioning
Direct positioning 5.0 7.5
This work presented a radio localization method based on a dual polarization antenna array. The proposed approach utilizes a GNSS based position to reduce the search area of a SAGE based search in order to directly estimate the position of the receiver. When compared to a geometric based positioning approach the accuracy obtained by the proposed method is vastly superior at low SNRs as it avoids errors caused by highly nonlinear relationships between parameters such as angle of arrival and angle of reflection with the position of the transmitter. Future research should focus on estimating the permittivity and permeability of the reflectors. This would allow for a more flexible implementation of the proposed algorithm as it would be able to respond to changes in the physical parameters of the material around the receiver that might be caused by phenomena such as rain or rust.
The research leading to the results reported in this work has received funding from the Knowledge Foundation in the framework of SafeSmart” Safety of Connected Intelligent Vehicles in Smart Cities” Synergy project (2019– 2023), Swedish Foundation for Strategic Research (SSF) in the framework of Strategic Mobility Program (2019-2020) and the ELLIIT Strategic Research Network.