Patent Description:
For example, one parameter in providing good performance and capacity for a given communications protocol in a communications network is the ability to correctly determine the position of wireless devices served by the communications network. As a non-limiting and illustrative example, positioning determination of wireless devices in indoor scenarios might utilize estimates of either the time of flight (ToF) measurements or angle-of-arrival (AoA) measurements of signals received at antenna arrays of network nodes from the wireless device in order to determine the position of the wireless device. One advantage of using angle-of-arrival measurements over ToF measurements is that there is no requirement on accurate time synchronization between the network nodes. Positioning methods based on angle-of-arrival measurements do thus not require network synchronization. Positioning methods based on angle-of-arrival measurements can therefore be used in scenarios where accurate network synchronization is difficult to achieve.

Using the angle-of-arrival measurements (both azimuth and elevation; thus requiring the use of a two-dimensional (2D) antenna array) from at least two antenna arrays, the location of the wireless device can be estimated using triangulation. An accurate estimate of the angle-of-arrival can be realized in the uplink provided that the amplitude and phase of an uplink signal, for example a sounding reference signal (SRS), is available for each antenna element or group of antenna elements, at the antenna array of the network node. At each network node, three channel measurements are needed from antenna elements in two directions.

The angle-of-arrival can be obtained by exploiting the fact that the phase difference of the received signal between two antenna elements in an antenna array is equal to the dot product of the vectors describing the relative position of the antenna elements and the unit vector pointing from the antenna array towards the wireless device. The angle-of-arrival can also be determined in the beam domain by taking the 2D Fourier transform of the amplitude and phase of the received signal at each antenna element. In case of multipath, multiple beams will be present and it is often possible (with the use of additional signal processing) to discriminate between the line-of-sight (LoS) beam and the multipath beams, assuming that a LoS beam exists. The accuracy of the angle-of-arrival estimate will depend primarily on the electrical size (expressed in terms of wavelength) of the antenna array and the number of antenna elements per antenna array.

One-dimensional (1D) antenna arrays are antenna arrays where all antenna elements are located along one and the same line. One example of a 1D antenna array is a uniform linear array (ULA). 1D antenna arrays are smaller and more cost effective than 2D antenna arrays. Positioning methods based on angle-of-arrival measurements require both azimuth and elevation angles. They will therefore not work in cases where 1D antenna arrays are used since the angle representing a rotation around the antenna array cannot be measured.

Hence, there is still a need for positioning methods where 1D antenna arrays are used.

<CIT> discloses a system for identifying a real-world geographic location of an emission source emitting electromagnetic energy includes a platform configured for movement and an apparatus disposed on the platform and configured to collect and process, in a passive manner and during movement of the platform, at least a pair of successive samples of the electromagnetic energy emission and define angular and spatial coordinates of the emission source. The apparatus includes at least a pair of antennas, a receiver coupled to antennas and a processor executing a predetermined logic.

<CIT> discloses a tracking computer system that may track a target using a single linear array. The system may receive first sensor measurements and one or more additional sensor measurements from the linear array. The system may determine whether a location of the target can be identified based on a cone intersection algorithm. When the target location can be identified based on the cone intersection algorithm, the first and the one or more additional sensor measurements may be applied to the cone intersection algorithm to identify the target location. When target location cannot be identified based on the cone intersection algorithm, the first and the one or more additional sensor measurements may be applied to an angular motion model to determine a best fit arc path corresponding to the target. A true target angle estimate and a target angular velocity may be determined based on the determined best fit arc path.

An object of embodiments herein is to enable positioning determination using 1D antenna arrays.

According to a first aspect there is presented method for position determination of a wireless device as in claim <NUM>.

The method comprises determining the position of the wireless device by combining the angle-of-arrival values from the at least three 1D antenna arrays.

According to a second aspect there is presented a network node for position determination of a wireless device as in claim <NUM>.

According to a third aspect there is presented a computer program for position determination of a wireless device, the computer program comprising computer program code which, when run on a network node, causes the network node to perform a method according to the first aspect.

According to a fourth aspect there is presented a computer program product comprising a computer program according to the fourth aspect and a computer readable storage medium on which the computer program is stored. The computer readable storage medium could be a non-transitory computer readable storage medium.

Advantageously, these aspects enable positioning determination using 1D antenna arrays.

Advantageously, in turn, this enables angle-of-arrival positioning methods to be implemented using simpler equipment, i.e., 1D antenna arrays, than in traditional angle-of-arrival based positioning methods, which are based on the use of 2D antenna arrays.

Advantageously, these aspects are applicable to any communications networks where angle-of-arrival measurements can be obtained using 1D antenna arrays, for example cellular communications networks (such as Long-Term Evolution (LTE) or New Radio (NR) based cellular communications networks), wireless local area networks (such as WiFi networks), ultra-wide band (UWB) cellular communications networks, Bluetooth networks, etc..

As noted above there is still a need for positioning methods where 1D antenna arrays are used.

The embodiments disclosed herein therefore relate to mechanisms for position determination of a wireless device. In order to obtain such mechanisms there is provided a network node, a method performed by the network node, a computer program product comprising code, for example in the form of a computer program, that when run on a network node, causes the network node to perform the method.

<FIG> is a schematic diagram illustrating a communications network <NUM> where embodiments presented herein can be applied. The communications network <NUM> could be any of: a cellular communications network (such as Long-Term Evolution (LTE) or New Radio (NR) based cellular communications networks), a wireless local area network (such as WiFi networks), an ultra-wide band (UWB) cellular communications network, a Bluetooth network. The communications network <NUM> comprises a network node <NUM> operatively connected to three 1D antenna arrays 120a, 120b, 120c. The 1D antenna arrays 120a, 120b are placed on one and the same line 140a whereas the 1D antenna array 120c is placed on line 140b which thus does not coincide with line 140a. The network node <NUM> might be any of: a (radio) access network node, a radio base station, a base transceiver station, a node B (NB), an evolved node B (eNB), a gNB, or a dedicated positioning server. The 1D antenna arrays 120a, 120b, 120c are configured to provide network access to wireless devices, one of which is identified at reference numeral <NUM>. The wireless device <NUM> might be any of: a portable wireless device, a mobile station, a mobile phone, a handset, a wireless local loop phone, a user equipment (UE), a smartphone, a wearable communication device, a laptop computer, a tablet computer, a wireless sensor, an Internet-of-Things (IoT) device, a network equipped vehicle. Wireless device <NUM> is assumed to, in an x, y, z-coordinate system, be located at a position (rx, ry, rz). According to embodiments disclosed herein, this position is to be determined by the network node <NUM> based on angle-of-arrival values θ<NUM>, θ<NUM>, θ<NUM> of the 1D antenna arrays 120a, 120b, 120c, where θn is the angle-of-arrival value of the n:th 1D antenna array.

<FIG> schematically illustrates how an angle-of-arrival value can be obtained at antenna array 120a having two antenna elements 130a, 130b. However, each of the antenna arrays 120a, 120b, 120c might have a plurality of antenna elements 130a, 130b. In this respect, in <FIG> is shown the calculation of the zenith angle θ', i.e., the angle to a surface perpendicular to the 1D antenna array 120a. The angle-of-arrival, θ, as expressed in degrees can then be found as θ = <NUM>° - θ'. In this respect, -<NUM>° ≤ θ' ≤ +-<NUM>°. Thus, if l is the distance between the two antenna elements 130a, 130b, and λ is the wavelength of the incoming signal from wireless device <NUM>, and Δφ denotes the phase difference of the signal received by the two antenna elements 130a, 130b, then (expressed in radians): <MAT> from which θ can be solved.

<FIG> is a flowchart illustrating embodiments of methods for position determination of a wireless device <NUM>. The methods are performed by the network node <NUM>. The methods are advantageously provided as computer programs <NUM>.

The herein disclosed embodiments are based on estimating the angle-of-arrival for the 1D antenna arrays 120a, 120b, 120c, given the measured phase differences from the antenna elements in the 1D antenna arrays 120a, 120b, 120c. In particular, the network node <NUM> is configured to perform step S102:
S102: The network node <NUM> estimates a respective angle-of-arrival value for each of at least three 1D antenna arrays 120a, 120b, 120c. The respective angle-of-arrival values are estimated from measured phase differences between antenna elements 130a, 130b per 1D antenna array 120a, 120b, 120c for a signal communicated between the wireless device <NUM> and the at least three 1D antenna arrays 120a, 120b, 120c. The antenna elements 130a, 130b of each 1D antenna array 120a, 120b, 120c are arranged along a respective line. At least two of the lines are non-coincident with respect to each other.

At each individual 1D antenna array 120a, 120b, 120c the phase of a signal communicated with the wireless device <NUM> is thus collected at all antenna elements 130a, 130b. The collected phase measurements are the relative phase differences between the antenna elements 130a, 130b within an antenna array 120a, 120b, 120c, as illustrated in <FIG>.

Using angle-of-arrival estimates from at least three different 1D antenna array locations, the position of the wireless device <NUM> can be determined. Hence, the network node <NUM> is configured to perform step S104:
S104: The network node <NUM> determines the position of the wireless device <NUM> by combining the angle-of-arrival values from the at least three 1D antenna arrays 120a, 120b, 120c.

This method thus enables the position of the wireless device <NUM> to be determined if the different 1D antenna arrays 120a, 120b, 120c used for the position estimation are placed on lines where at least two of the lines are non-coincident with respect to each other.

Embodiments relating to further details of position determination of a wireless device <NUM> as performed by the network node <NUM> will now be disclosed.

In some aspects, each angle-of-arrival estimate gives rise to a cone on which the position of the wireless device <NUM> is located. Such a cone will hereinafter be referred to as an angle-of-arrival-cone. In this respect, the angle-of-arrival cone for a given 1D antenna array can be defined using the orientation of that given 1D antenna array as the symmetry axis and the angle-of-arrival as half of the apex angle. Each of the estimated angle-of-arrival values might thus define a half-apex angle of a respective cone, where each cone has its apex centred at a respective one of the 1D antenna arrays 120a, 120b, 120c. In some embodiments, determining the position of the wireless device <NUM> in step S104 then equals identifying a position where all the cones intersect. Since the angle-of-arrival values define the half-apex angle of the cones, it is the lateral surfaces of the cones that intersect.

The angle-of-arrival cone can thus be defined using the orientation of the antenna array as symmetry axis and the angle-of-arrival as half of the apex angle. Hence, in some embodiments, the line along which the antenna elements 130a, 130b of one of the 1D antenna arrays 120a, 120b, 120c are arranged defines a symmetry axis for this one of the 1D antenna arrays 120a, 120b, 120c, and half of an apex angle of the symmetry axis defines the cone for this one of the 1D antenna arrays 120a, 120b, 120c.

The position of the wireless device <NUM> can be determined using the intersection of at least three angle-of-arrival cones, one for each of the 1D antenna arrays 120a, 120b, 120c. As illustrated in <FIG>, this is equivalent to, for at least one of the 1D antenna arrays 120a, 120b, 120c, finding an unknown angle ϕ around the axis of rotation of the antenna array and the distance from the antenna array to the wireless device <NUM>, given that the angle θ for this at least one of the 1D antenna arrays is already known. <FIG> schematically illustrates the angle-of-arrival cone <NUM> seen from an antenna array 120a comprising two antenna elements 130a, 130b. The angle-of-arrival cone <NUM> defines possible positions of the wireless device <NUM>. The angle-of-arrival θ is calculated using the phase difference of the signal received by antenna elements 130a and 130b. ϕ is the unknown angle of rotation around the axis connecting the two antenna elements 130a and 130b. In this respect, in some embodiments, determining the position of the wireless device <NUM> in step S104 involves, for at least one of the 1D antenna arrays 120a, 120b, 120c, determining an angle ϕ around the symmetry axis and determining the distance between the wireless device <NUM> and this at least one of the 1D antenna arrays 120a, 120b, 120c.

As illustrated in <FIG>, the intersection of two angle-of-arrival cones <NUM>, <NUM>, one for a respective 1D antenna array, will give a circle, or ellipsis, <NUM> on which the wireless device <NUM> is located. In <FIG> the position and orientation of two 1D antenna arrays are shown with arrows P<NUM> and P<NUM> and the true position of the wireless device <NUM> is marked by a cross. All possible positions of the wireless device <NUM> are on the ellipsis <NUM> defined by the intersection of the two angle-of-arrival cones <NUM>, <NUM>. A third measurement is thus needed to determine where on the ellipsis the true position of the wireless device <NUM> can be found.

<FIG> illustrates, according to a first example, the intersection of three angle-of-arrival cones, one for each pair of 1D antenna arrays 120a, 120b, 120c, in terms of a lines, on which the position of the wireless device <NUM> is located. The position and orientation of each 1D antenna array are shown with arrows P<NUM>, P<NUM> and P<NUM> in the figure and the true position of the wireless device <NUM> is marked by a cross. The orientation of the 1D antenna array at position P<NUM> is perpendicular to the 1D antenna arrays at positions P<NUM> and P<NUM>. In <FIG> only the angle-of-arrival cone for the 1D antenna array located at position P<NUM> is shown to avoid cluttering. Ellipsis <NUM> marks the intersection between the angle-of-arrival cones for the 1D antenna arrays located at positions P<NUM> and P<NUM>. Line <NUM> marks the intersection between the angle-of-arrival cones for the 1D antenna arrays located at positions P<NUM> and P<NUM>. Line <NUM> marks the intersection between the angle-of-arrival cones for the 1D antenna arrays located at positions P<NUM> and P<NUM>.

<FIG> illustrates, according to a second example, the intersection of three angle-of-arrival cones, one for each pair of 1D antenna arrays 120a, 120b, 120c, in terms of lines <NUM>, <NUM>, on which the position of the wireless device <NUM> is located. The position and orientation of each 1D antenna array are shown with arrows P<NUM>, P<NUM> and P<NUM> in the figure and the true position of the wireless device <NUM> is marked by a cross. The 1D antenna arrays at positions P<NUM> and P<NUM> are on one and the same lines whereas the 1D antenna array at position P<NUM> is not on the same line as the 1D antenna arrays at positions P<NUM> and P<NUM>. In <FIG> only the angle-of-arrival cone <NUM> for the 1D antenna array located at position P<NUM> is shown to avoid cluttering. Lines <NUM>, <NUM>, <NUM> marks the intersection between the angle-of-arrival cones for the 1D antenna arrays.

In general terms, for three 1D antenna arrays 120a, 120b, 120c, yielding three angle-of-arrival cones, two distinct possible positions of the wireless device <NUM> can be determined. That is, in some embodiments there are two positions at which all the cones intersect, and the position of the wireless device <NUM> is determined by selecting one of the two positions. One of the two possible positions might be highly improbable in a practical implementation and can thus be disregarded. In particular, each of the two positions might be associated with a respective probability value for being the position of the wireless device <NUM>, and the position with highest probability value is selected. This could be the case where the 1D antenna arrays 120a, 120b, 120c are arranged to provide network access to wireless devices in a confined, or in other ways well-defined, region or space. One such example could be where the 1D antenna arrays 120a, 120b, 120c are arranged to provide network access to wireless devices in an indoor location and where the position of a wireless device corresponding to an outdoor location thus could be disregarded. Additional angle-of-arrival information from a fourth 1D antenna array may also be utilized to resolve this ambiguity.

In general terms, the problem of determining the position of a wireless device <NUM> using angle-of-arrival measurements from 1D antenna arrays 120a, 120b, 120c can be formulated as <MAT>.

Here, r = (rx, ry, rz) defines the position of the wireless device <NUM>, pn is the position of the n:th 1D antenna array, p̂n is the unit vector describing the orientation of the n:th 1D antenna array and θn is the angle-of-arrival measurement from the n:th 1D antenna array. This is a nonlinear system of equations (one for each value of n) which can be solved using a number of different approaches. Hence, in some embodiments, determining the position of the wireless device <NUM> in step S104 involves solving a nonlinear system of equations. Different ways in which the nonlinear system of equations can be solved will be disclosed next.

In some embodiments, the nonlinear system of equations is analytically solved.

Further in this respect, the system of equations might be reduced to a simpler problem which can be solved analytically. One example is when all three 1D antenna arrays are located on the x-axis in an x, y, z-coordinate system, where two of these 1D antenna arrays are also oriented along the x-axis whereas the third 1D antenna array is oriented along the y-axis. That is, in this example there are exactly three 1D antenna arrays 120a, 120b, 120c at positions (x<NUM>, <NUM>, <NUM>), (x<NUM>, <NUM>, <NUM>), and (x<NUM>, <NUM>, <NUM>) in an x, y, z-coordinate system, where the antenna elements 130a, 130b of the first and second of the 1D antenna arrays 120a, 120b, 120c are arranged along the x-axis and the antenna elements 130a, 130b of the third of the 1D antenna arrays 120a, 120b, 120c are arranged along the y-axis in this x, y, z-coordinate system. If the positions of the three antenna arrays are given by (x<NUM>, <NUM>, <NUM>), (x<NUM>, <NUM>, <NUM>), and (x<NUM>, <NUM>, <NUM>), respectively, and θ<NUM>, θ<NUM> and θ<NUM> are the estimated angle-of-arrival values of the three 1D antenna arrays, the position (rx, ry, rz) of the wireless device <NUM> is given by a nonlinear system of equations defined as: <MAT> <MAT> <MAT>.

In some embodiments, the nonlinear system of equations is numerically and iteratively solved.

In this respect, the position of the wireless device <NUM> can be determined based on an initial guess of the position of the wireless device <NUM>, and where the position is updated by calculating the direction and distance from one position guess to the next guess which minimizes the error of the position estimate.

In particular, in some embodiments, the position of the wireless device <NUM> is iteratively determined using gradient descent by, for each of the 1D antenna arrays 120a, 120b, 120c and for each current iteratively determined position of the wireless device <NUM>, determining an angle error as difference between an angle-of-arrival value calculated for the current iteratively determined position and the estimated angle-of-arrival value. That is, for each 1D antenna array, based on an initial position estimate, the error Δθn of the angle-of-arrival value can be calculated as the difference between the measured angle θn and the angle corresponding to the current position estimate. The shortest vector which eliminates Δθn (that is, taking the shortest step to the surface of the cone corresponding to antenna array n) is then calculated. A new position estimate is calculated by adding these vectors corresponding to all the 1D antenna arrays to the previous position estimate. The process is then repeated until convergence is reached, or a fixed number of iterations have been made.

<FIG> shows an example where the position of the wireless device <NUM> is iteratively determined using gradient descent. The position and orientation of the 1D antenna arrays are marked with arrows, the true position of the wireless device <NUM> is marked with a cross and the estimated position at each iteration is marked with dots (starting at the origin as the initial guess) connected by lines.

In some embodiments, the nonlinear system of equations is solved using brute force. For example, the nonlinear system of equations might be solved by testing a set of solutions, each corresponding to a respective position of the wireless device <NUM>, and selecting one of the solutions according to a minimum error criterion. When using brute force, different possible positions of the wireless device <NUM> are tested and the one with the smallest error, according to some metric, is assumed to be the correct position. As a non-limiting illustrative example, the root mean square of the angle errors can be used as metric. The angle error is the difference between the (theoretical) angle θ* that would have been observed by the 1D antenna arrays if the wireless device <NUM> had been located in the tested positions and the estimated angle at the different 1D antenna arrays. That is, in some embodiments, each respective position of the wireless device <NUM> yields a calculated angle-of-arrival value for each of the at least three 1D antenna arrays 120a, 120b, 120c, and the minimum error criterion pertains to a difference between the calculated angle-of-arrival values and the estimated angle-of-arrival values.

<FIG> illustrates, as a contour plot, an example of the root mean square of the angle errors for different tested positions of the wireless device <NUM> and where the true position of the wireless device <NUM> is marked with a cross. The numbers on each height curve in the contour plot correspond to the root mean square of the angle errors to three antenna arrays in degrees. The result in <FIG> assumes knowledge of the height of the wireless device. If the height is not known, the brute force process can be repeated for different values of the height.

<FIG> schematically illustrates, in terms of a number of functional units, the components of a network node <NUM> according to an embodiment. Processing circuitry <NUM> is provided using any combination of one or more of a suitable central processing unit (CPU), multiprocessor, microcontroller, digital signal processor (DSP), etc., capable of executing software instructions stored in a computer program product <NUM> (as in <FIG>), e.g. in the form of a storage medium <NUM>. The processing circuitry <NUM> may further be provided as at least one application specific integrated circuit (ASIC), or field programmable gate array (FPGA).

Particularly, the processing circuitry <NUM> is configured to cause the network node <NUM> to perform a set of operations, or steps, as disclosed above. For example, the storage medium <NUM> may store the set of operations, and the processing circuitry <NUM> may be configured to retrieve the set of operations from the storage medium <NUM> to cause the network node <NUM> to perform the set of operations.

Thus the processing circuitry <NUM> is thereby arranged to execute methods as herein disclosed. The network node <NUM> may further comprise a communications interface <NUM> at least configured for communications with other entities, functions, nodes, and devices of the communications network <NUM>, such as the 1D antenna arrays 120a, 120b, 120c. As such the communications interface <NUM> may comprise one or more transmitters and receivers, comprising analogue and digital components. The processing circuitry <NUM> controls the general operation of the network node <NUM> e.g. by sending data and control signals to the communications interface <NUM> and the storage medium <NUM>, by receiving data and reports from the communications interface <NUM>, and by retrieving data and instructions from the storage medium <NUM>. Other components, as well as the related functionality, of the network node <NUM> are omitted in order not to obscure the concepts presented herein.

<FIG> schematically illustrates, in terms of a number of functional modules, the components of a network node <NUM> according to an embodiment. The network node <NUM> of <FIG> comprises a number of functional modules; an estimate module 210a configured to perform step S102, and a determine module 210b configured to perform step S104. The network node <NUM> of <FIG> may further comprise a number of optional functional modules, such as represented by functional module 210c. In general terms, each functional module 210a-210c may in one embodiment be implemented only in hardware and in another embodiment with the help of software, i.e., the latter embodiment having computer program instructions stored on the storage medium <NUM> which when run on the processing circuitry makes the network node <NUM> perform the corresponding steps mentioned above in conjunction with <FIG>. It should also be mentioned that even though the modules correspond to parts of a computer program, they do not need to be separate modules therein, but the way in which they are implemented in software is dependent on the programming language used. Preferably, one or more or all functional modules 210a-210c may be implemented by the processing circuitry <NUM>, possibly in cooperation with the communications interface <NUM> and/or the storage medium <NUM>. The processing circuitry <NUM> may thus be configured to from the storage medium <NUM> fetch instructions as provided by a functional module 210a-210c and to execute these instructions, thereby performing any steps as disclosed herein.

In some examples, the network node <NUM> is collocated with at least one of the 1D antenna arrays 120a, 120b, 120c. In some examples, at least one of the 1D antenna arrays 120a, 120b, 120c is collocated with another network node, and the measured phase difference for this at least one of the 1D antenna arrays 120a, 120b, 120c is obtained from this another network node. In some examples, the network node <NUM> is implemented in, or acts as, a positioning server.

Further, the network node <NUM> may be provided as a standalone device or as a part of at least one further device. For example, the network node <NUM> may be provided in a node of the radio access network or in a node of the core network. Alternatively, functionality of the network node <NUM> may be distributed between at least two devices, or nodes. These at least two nodes, or devices, may either be part of the same network part (such as the radio access network or the core network) or may be spread between at least two such network parts. In general terms, instructions that are required to be performed in real time may be performed in a device, or node, operatively closer to the cell than instructions that are not required to be performed in real time.

Thus, a first portion of the instructions performed by the network node <NUM> may be executed in a first device, and a second portion of the of the instructions performed by the network node <NUM> may be executed in a second device; the herein disclosed embodiments are not limited to any particular number of devices on which the instructions performed by the network node <NUM> may be executed. Hence, the methods according to the herein disclosed embodiments are suitable to be performed by a network node <NUM> residing in a cloud computational environment. Therefore, although a single processing circuitry <NUM> is illustrated in <FIG> the processing circuitry <NUM> may be distributed among a plurality of devices, or nodes. The same applies to the functional modules 210a-210c of <FIG> and the computer program <NUM> of <FIG>.

Claim 1:
A method for position determination of a wireless device (<NUM>), the method being performed by a network node (<NUM>), the method comprising:
estimating (S102) a respective angle-of-arrival value for each of three 1D antenna arrays (120a, 120b, 120c) at positions (x_1,<NUM>,<NUM>), (x_2,<NUM>,<NUM>), and (x_3,<NUM>,<NUM>) in an (x,y,z)-coordinate system, from measured phase differences between antenna elements (130a, 130b) per 1D antenna array (120a, 120b, 120c) for a signal communicated between the wireless device (<NUM>) and the three 1D antenna arrays (120a, 120b, 120c), wherein the antenna elements of a first and a second of the 1D antenna arrays are arranged along the x-axis and the antenna elements of a third of the 1D antenna arrays are arranged along the y-axis in said (x, y, z)-coordinate system; and
determining (S104) the position of the wireless device (<NUM>) by combining the angle-of-arrival values from the three 1D antenna arrays (120a, 120b, 120c) and where in the determining involves the solving of a nonlinear system of equations defined as: <MAT> <MAT> <MAT>
wherein (rx, ry, rz) is the position of the wireless device, and θ<NUM>, θ<NUM> and θ<NUM> are the estimated angle-of-arrival values of the three 1D antenna arrays.