Technical field

The invention relates to a computing device for relative positioning of wireless communications nodes, a method of relative positioning of wireless communications nodes, a corresponding computer program, a corresponding computer-readable data carrier, and a corresponding data carrier signal.

Background

A known way to localize a mobile node capable of wireless communications, e.g., a radio-based technology such as Bluetooth, a cellular technology, WiFi, or the like, is to rely on a few stationary nodes (aka anchor nodes) with known positions which receive a radio signal from the mobile node and measure the time between transmission and reception. The time differences can be converted into a distance between the mobile node and each anchor node. If there is a sufficient number of anchor nodes (three anchor nodes are sufficient to localize a mobile node in a two- dimensional (2D) plane) one can solve for the relative position of the mobile node, i.e. , the position of the mobile node relative to the anchor nodes. This approach, which is known as Time of Arrival (ToA) positioning, requires that the clocks of all the nodes are synchronized, which increases complexity.

Another known technique is called Time Difference of Arrival (TDoA), and relies on anchor nodes which have synchronized clocks (synchronization is typically achieved over a wired connection), whereas the mobile node does not need to have a synchronized clock. The relative times of arrival of the signal transmitted by the mobile node and received by the anchor nodes allow solving for both the transmission time and the respective distances between the mobile node and the anchor nodes. In addition to requiring time-synchronized anchor nodes, an additional anchor node is required.

To avoid the need for clock synchronization, a technique which may be referred to as Asynchronous TDoA (ATDoA) (see, e.g., “TDOA localization in asynchronous WSNs”, by F. Bandiera, A. Coluccia, G. Ricci, F. Ricciato, and D. Spano, 12th IEEE International Conference on Embedded and Ubiquitous Computing, IEEE, 2014) may be used. ATDoA is based on transmitting a signal, by each node (both the mobile node and the anchor nodes), at some unknown transmission time. All the other nodes record the reception times of the signal according to their local (not synchronized) clocks for all the signals received from the other nodes. Based on time differences between these local reception times obtained from all nodes, one can solve for the respective distances between the nodes as well as the time offsets between the local clocks of each node, which allows expressing the local times in a global time frame. This avoids the need to for synchronized clocks. A significant error source for ATDoA is the drift of the local clock in each node, since the method is based on the time interval between reception of signals. As an example, a good quartz crystal may drift 20 ppm, which amounts to 20 ns/ms, i.e., a distance error of 6 m per each ms between the received signals.

It is an object of the invention to provide an improved alternative to the above techniques and prior art.

More specifically, it is an object of the invention to provide an improved solution for relative positioning of wireless communications nodes. In particular, it is an object of the invention to provide an improved solution for TDoA-based positioning asynchronous wireless communications nodes.

These and other objects of the invention are achieved by means of different aspects of the invention, as defined by the independent claims. Embodiments of the invention are characterized by the dependent claims.

According to a first aspect of the invention, a computing device for relative positioning of wireless communications nodes is provided. The computing device comprises processing circuitry which causes the computing device to become operative to calculate pairwise distances between the at least four wireless communications nodes. The pairwise distances are calculated based on time differences between reception times of wireless signals transmitted by each of at least four wireless communications nodes and received by the other wireless communications nodes of the at least four wireless communications nodes as part of a signaling sequence. The computing device is further operative to select a transmission time of a first wireless signal of a subsequent signaling sequence for transmission by a first one of the at least four wireless communications nodes. The computing device is further operative to select transmission times of subsequent wireless signals of the subsequent signaling sequence by the other wireless communications nodes of the at least four wireless communications nodes. The selected transmission times of the subsequent wireless signals reduce a sum of squared time intervals between reception of a first wireless signal and a last wireless signal of the subsequent signaling sequence by each of the at least four wireless communications nodes.

According to a second aspect of the invention, a method of relative positioning of wireless communications nodes is provided. The method is performed by a computing device and comprises calculating pairwise distances between the at least four wireless communications nodes. The pairwise distances are calculated based on time differences between reception times of wireless signals transmitted by each of at least four wireless communications nodes and received by the other wireless communications nodes of the at least four wireless communications nodes as part of a signaling sequence. The method further comprises selecting a transmission time of a first wireless signal of a subsequent signaling sequence for transmission by a first one of the at least four wireless communications nodes. The method further comprises selecting transmission times of subsequent wireless signals of the subsequent signaling sequence by the other wireless communications nodes of the at least four wireless communications nodes. The selected transmission times of subsequent wireless signals reduce a sum of squared time intervals between reception of a first wireless signal and a last wireless signal of the subsequent signaling sequence by each of the at least four wireless communications nodes.

According to a third aspect of the invention, a computer program is provided. The computer program comprises instructions which, when the computer program is executed by a processor comprised in the computing device, cause the computing device to carry out the method according to an embodiment of the second aspect of the invention. According to a fourth aspect of the invention, a computer-readable storage medium is provided. The computer-readable storage medium has stored thereon the computer program according to the third aspect of the invention.

According to a fifth aspect of the invention, a data carrier signal is provided. The data carrier signal carries the computer program according to the third aspect of the invention.

In the present context, wireless communications nodes may, e.g., be autonomous vehicles, drones, robots, stationary sensors, mobile sensors (e.g., worn by people or animals, or floating in water), and the like. The invention makes use of an understanding that an error in TDoA-based positioning, which stems from drift of the local clocks in the wireless communications nodes, can be reduced by reducing the duration of a signaling sequence in time. Advantageously, this leads to a smaller error in the resulting positions of the wireless communications nodes.

Even though advantages of the invention have in some cases been described with reference to embodiments of the first aspect of the invention, corresponding reasoning applies to embodiments of other aspects of the invention.

Further objectives of, features of, and advantages with, the invention will become apparent when studying the following detailed disclosure, the drawings and the appended claims. Those skilled in the art realize that different features of the invention can be combined to create embodiments other than those described in the following.

Brief description of the drawings

The above, as well as additional objects, features and advantages of the invention, will be better understood through the following illustrative and non-limiting detailed description of embodiments of the invention, with reference to the appended drawings, in which:

Fig. 1 illustrates four wireless communications nodes in a 2D plane, with respective positions and distances between the wireless communications nodes, in accordance with embodiments of the invention.

Fig. 2 schematically shows a computing device for relative positioning of wireless communications nodes, in accordance with embodiments of the invention. Fig. 3 illustrates signaling sequences for relative positioning of wireless communications nodes, in accordance with embodiments of the invention.

Fig. 4 shows a method of relative positioning of wireless communications, in accordance with embodiments of the invention.

All the figures are schematic, not necessarily to scale, and generally only show parts which are necessary in order to elucidate the invention, wherein other parts may be omitted or merely suggested.

Detailed description

The invention will now be described more fully herein after with reference to the accompanying drawings, in which certain embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided by way of example so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

In the following, embodiments of a computing device for relative positioning of wireless communications nodes are described. Embodiments of the invention do not require the wireless communications nodes to have access to synchronized (internal) clocks, i.e. , the wireless communications nodes may be asynchronous.

A typical scenario is illustrated in Fig. 1, which shows four wireless communications nodes 100:1 to 100:4 (“1” to “4”). Throughout this disclosure, a reference to a/the wireless communications node 100 is understood to denote any one, or all, of the wireless communications nodes 100:1 to 100:4. Even though embodiments of the invention are described in relation to relative positioning of four wireless communications nodes 100, embodiments for relative positioning of more than four wireless communications nodes may easily be envisaged. It will also be appreciated that one or more of the four wireless communications nodes 100 may be stationary. The wireless communications nodes 100 may, e.g., be autonomous vehicles, drones, robots, stationary sensors, mobile sensors (e.g., worn by people or animals, or floating in water), or the like. Each wireless communications node 100 i i,j e {1,2, 3, 4}) is characterized by its position (x^yi) (for sake of simplicity, only the position (%i,yi) of the first wireless communications node 100:1 is shown in Fig.1 ). The pairwise distance between two wireless communications nodes i and j is:

It will be appreciated that the choice of coordinate system is arbitrary, as the position of one of the wireless communications nodes, e.g., wireless communications node 100:1 , is determined relative to the three or more other wireless communications nodes 100:2 to 100:4.

Fig. 2 schematically illustrates an embodiment of the computing device 200 for relative positioning of wireless communications nodes. The computing device 200 may, e.g., be a central node, which selects transmission times of wireless signals of a subsequent signaling sequence as is described further below, based on time differences between reception times it has received from the wireless communications nodes 100. The central node may, e.g., deployed as an edge node or in a local network close to the wireless communications nodes 100. As an alternative, the computing device 200 may be comprised in one of the at least four wireless communications nodes 100. For instance, one of the wireless communications nodes 100 (e.g., node 100:1) may assume the role of a coordinating node and select the transmission times of wireless signals of a subsequent signaling sequence as is described further below, based on time differences between reception times it has received from the other wireless communications nodes 100 (nodes 100:2 to 100:4). As yet another alternative, several, or even all, of the wireless communications nodes 100 may select the transmission times of wireless signals of a subsequent signaling sequence autonomously, i.e., independently of each other, based on time differences between reception times they have received from the other wireless communications nodes 100. This is advantageous in that there is no single point of failure.

The computing node 200 comprises a processing circuitry 210, which may comprise one or more processors 211 , such as Central Processing Units (CPUs), microprocessors, application processors, application-specific processors, Graphics Processing Units (GPUs), and Digital Signal Processors (DSPs) including image processors, or a combination thereof, and a memory 212 comprising a computer program 213 comprising instructions. When executed by the processor(s) 211 , the instructions cause the computing device 200 to become operative in accordance with embodiments of the invention described herein. The memory 212 may, e.g., be a Random-Access Memory (RAM), a Read-Only Memory (ROM), a Flash memory, or the like. The computer program 213 may be downloaded to the memory 212 by means of a communications interface circuitry 201, as a data carrier signal carrying the computer program 213. The processing circuitry 210 may alternatively or additionally comprise one or more Application-Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or the like, which are operative to cause the computing device 200 to become operative in accordance with embodiments of the invention described herein.

The communications interface circuitry 201 supports communications with the wireless communications nodes 100, directly or indirectly (via a communications network such as a Local Area Network, or the Internet) via a wired or wireless technology, such as Ethernet, Bluetooth, Near-Field Communication (NFC), ZigBee, visible or infrared coded light, or the like, for receiving and/or transmitting data between the computing device 200 and the wireless communications nodes 100.

More specifically, the processing circuitry 210 causes the computing device 200 to be operative to calculate pairwise distances d _if j between the at least four wireless communications nodes 100, as is known from “TDOA localization in asynchronous WSNs” (by F. Bandiera, A. Coluccia, G. Ricci, F. Ricciato, and D. Spano, 12th IEEE International Conference on Embedded and Ubiquitous Computing, IEEE, 2014). The pairwise distances d _if j are calculated based on time differences between local reception times of wireless signals which are transmitted by each one of the at least four wireless communications nodes 100 and received by the other wireless communications nodes of the at least four wireless communications nodes 100 as part of a signaling sequence. The local reception times are expressed in the respective local time frames of the (asynchronous) wireless communications nodes 100. By relying on time differences rather than absolute times, ATDoA alleviates the need for synchronized clocks to establish a global time frame common to all wireless communications nodes 100. Once the pairwise distances are established, the time offsets between the local times of the wireless communications nodes 100 can be established and a global time frame can be defined. The reception times of wireless signals received by the wireless communications nodes 100 are transmitted to the computing device 200, either over the same wireless technology used for exchanging (transmitting and receiving) the wireless signals between the wireless communications nodes 100, or a different technology. Each of the wireless communications nodes 100 reports the reception times relative to its own internal clock, where the internal clocks of the wireless communications nodes 100 may be asynchronous. As an alternative to transmitting the reception times to the computing device 200, which may be operative to calculate the time differences between the reception times for each of the wireless communications nodes 100, the wireless communications nodes 100 may be operative to calculate the time differences between their respective reception times and transmit the time differences to the computing device 200.

Throughout this disclosure, a signaling sequence is understood to comprise the transmission of one wireless signal by each one of the at least four wireless communications nodes 100 and reception by the transmitted wireless signals by each of the other of the at least four wireless communications nodes 100. For example, and with reference to Fig. 3 which illustrates signaling sequences for relative positioning of the four wireless communications nodes 100, during an example signaling sequence 310 the first wireless communications node 100:1 (“1”) transmits a (first) signal at a time t _± . The first signal is received by the second wireless communications node 100:2 (“2”) at a time t _{1 2} (herein, the time t _ifj denotes the time a signal transmitted by the wireless communications node i is received by the wireless communications node j), by the third wireless communications node 100:3 (“3”) at a time t _{1 3} , and by the fourth wireless communications node 100:4 (“4”) at a time t ₁₄ (for simplicity, only reception times t _{1 3} and t _4;2 are illustrated in Fig. 3). Subsequently, the second wireless communications node 100:2 transmits a (second) signal at a time t ₂ , which is received by the first 100:1 , the third 100:3., and the fourth 100:4, wireless communications node at times t _{2 1} , t _{2 3} , and t _{2 4} , respectively, and correspondingly for signals transmitted by the third and fourth wireless communications nodes 100:3 and 100:4. In other words, the example signaling sequence 310 illustrated in Fig. 3 starts with transmission of the first signal by the first wireless communications node at and commences until the reception of the last signal, in this case at time t _4;2 .

Embodiments of the invention may be based on any type of wireless signals, such as electromagnetic signals (e.g., radio signals, visible or invisible light), or acoustic signals (e.g., ultrasonic sound). In practice, the wireless signals are transmitted by a transmitter comprised in the wireless communications node 100, e.g., a radio transmitter, a Light Emitting Diode (LED), or an ultrasonic actuator, and received by a receiver comprised in the wireless communications node 100, e.g., a radio receiver, a light sensor, or an ultrasonic sensor. The pairwise distance d _if j between two wireless communications nodes i and j is related to the transmission time tt at the wireless communications node i, the reception time t _ifj at the wireless communications nodes j, and the propagation speed c of the wireless signals (in the case of radio signals, the speed of light), by:

In order to be able to calculate the pairwise distances between the wireless communications nodes 100, the wireless signals which are received must be distinguishable. In other words, it must be possible to identify the wireless communications node 100 which has transmitted the wireless signal. In practice, this may be achieved by including an identifier of the wireless communications node 100 which has transmitted the wireless signal in each wireless signal, or by utilizing distinct frequencies or other modulation schemes which enable a unique identification of the transmitting wireless communications node 100. The identifiers of the at least four wireless communications nodes 100 may comprise any of: MAC addresses, network addresses (e.g., IP address), and configurable identifiers. In practice, configurable identifiers may be assigned by a manufacturer of the wireless communications nodes 100, by a user, or by a service or software application which is used in connection with the wireless communications nodes 100. It will also be appreciated that the wireless communications nods 100 may establish the origin of a received wireless signal based on the selected transmission times and the pairwise distances.

The computing device 200 is further operative to select a transmission time of a first wireless signal of a subsequent signaling sequence for transmission by a first one of the at least four wireless communications nodes 100. The transmission of the first wireless signal marks the start of the next, subsequent signaling sequence and can be selected arbitrarily. For instance, the next signaling sequence may be initiated if positioning needs to be updated, e.g., if one or more of the wireless communications nodes have moved by more than a threshold distance. Alternatively, new signaling sequences may be initiated regularly or periodically. The wireless communications node 100 which transmits the first wireless signal and thereby starts the next signaling sequence may be selected randomly. Alternatively, the wireless communications node 100 which transmits the first wireless signal may be selected based on the identifiers of the wireless communications node 100, e.g., the lowest or highest identifier of an ordered sequence of the identifiers. For the example signaling sequence 310 illustrated in Fig.3, the first wireless signal is transmitted by the wireless communications node 100:1 (“1”) at time t . For an alternative signaling sequence 320 which is illustrated in Fig. 3, the first wireless signal of a subsequent signaling sequence is transmitted by the wireless communications node 100:4 (“4”) at time t ₄ . As yet a further alternative, the wireless communications node 100 which transmits the first wireless signal may be selected based on a current or preceding signaling sequence.

The computing device 200 is further operative to select the transmission times of subsequent wireless signals of the subsequent signaling sequence by the other wireless communications nodes of the at least four wireless communications nodes 100. For the example signaling sequence 310 illustrated in Fig. 3, the other wireless communications nodes are 100:2, 100:3, and 100:4, with transmission times t ₂ , t ₃ , and t ₄ , respectively. Further, for the example signaling sequence 320, the ordered subsequent transmission times are t ₃ , t ₂ , and t _± .

The transmission times of the subsequent wireless signals which are selected by the computing device 200 reduce a sum of squared time intervals between reception of a first wireless signal and a last wireless signal of the subsequent signaling sequence by each of the at least four wireless communications nodes 100. That is, the sum of squared time intervals between reception of a first wireless signal and a last wireless signal of the subsequent signaling sequence is reduced as compared to the sum of squared time intervals between reception of a first and a last of the wireless signals by each of the at least four wireless communications nodes 100 during a current or preceding signaling sequence. Optionally, the computing device 200 may be operative to minimize the sum of squared time intervals between reception of a first wireless signal and a last wireless signal of the subsequent signaling sequence by each of the at least four wireless communications nodes 100. More specifically, if t™ ⁿ denote the time of reception of the first (transmitted by the wireless communications node j) and last (transmitted by the wireless communications node j) wireless signal by the wireless communications node n, respectively, the transmission times tj can be determined by solving

The thereby obtained transmission times t ₂ , can then be used for the subsequent signaling sequence. For this purpose, the computing device 200 may be operative to send the selected transmission times of the wireless signals of the subsequent signaling sequence to the wireless communications nodes 100. An example of a signaling sequence with a reduced or minimized sum of squared time intervals between reception of a first wireless signal and a last wireless signal of the subsequent signaling sequence is signaling sequence 320 illustrated in Fig. 3.

Advantageously, by reducing, or minimizing, the duration of a signaling sequence in accordance with embodiments of the invention, the error in the determined pairwise distances, and accordingly in the relative positions, can be reduced. This is the case since the impact of the drift of the internal clocks of the wireless communications nodes 100 on the pairwise distances is reduced or minimized. Embodiments of the invention are further advantageous in that a new signaling sequence can be initiated earlier. In other words, the frequency of signaling sequences can be increased, and the relative positions of the wireless communications nodes 100 can accordingly be determined more often.

The computing device 200 may optionally be operative to select the transmission times of the subsequent wireless signals of the subsequent signaling sequence under the constraint that a minimum time interval between reception or transmission of any two wireless signals by each of the at least four wireless communications nodes 100 is equal to, or longer than, a time interval required to receive and process a received wireless signal, or transmit a wireless signal by the wireless communications nodes 100, and to become operational for receiving or transmitting a next wireless signal. This time interval may also be referred to as a collision margin and aims to avoiding collisions between transmission of wireless signals and receptions of wireless signals by a wireless communications node 100. In practice, the collision margin is selected to reflect the time required by a wireless communications node 100 to switch between reception and transmission of wireless signals and/or to register or process a received wireless signal before the wireless communications node 100 is ready for receiving the next wireless signal.

Optionally, the minimum time interval (the collision margin) between reception or transmission of any two wireless signals by each of the at least four wireless communications nodes 100 is equal to, or longer than, a sum of the time interval required to receive or transmit a wireless signal and to become operational for receiving or transmitting a next wireless signal, and a time interval required for a wireless signal to travel an expected maximum change in pairwise distance between the at least four wireless communications nodes 100 between two subsequent signaling sequences. Thereby, collisions which are caused by changes in positions of the wireless communications nodes, e.g., if two or more of the wireless communications nodes have moved closer to each other between two subsequent signaling sequences, can be avoided.

The expected maximum change in pairwise distance between the at least four wireless communications nodes 100 between two subsequent signaling sequences may, e.g., be calculated based on an expected maximum relative speed between the at least four wireless communications nodes 100. In practice, this means that a time T * v _max /c is added to the collision margin, where v _max is the expected maximum relative speed of the at least four wireless communications nodes 100 and T is the time interval between subsequent signaling sequences.

The expected maximum relative speed may be calculated based on a maximum speed at which the wireless communications nodes 100 can travel, and may optionally be further based on an environment through which the wireless communications nodes 100 move (potentially limiting the maximum speed of travel due to obstacles or other conditions impeding movement of the wireless communications nodes 100) and/or a frequency of changes in the direction of travel (potentially limiting the maximum speed of travel). Alternatively, the expected maximum change in pairwise distance between the at least four wireless communications nodes 100 between two subsequent signaling sequences may be calculated based on route information for the at least four wireless communications nodes 100. For instance, the expected maximum change of pairwise distances may be calculated based on route information which defines trajectories along which the at least four wireless communications nodes 100 travel between subsequent signaling sequences, and optionally further based on constraints for the movement of the wireless communications nodes 100 which are dictated by route information.

The computing device 200 may be operative to select the transmission times of the subsequent wireless signals of the subsequent signaling sequence in accordance with an ordered sequence of reception of the wireless signals of the subsequent signaling sequence by each of the at least four wireless communications nodes 100. The ordered sequence may be ordered according to identifiers of the at least four wireless communications nodes 100, i.e., t ₂ ,i < < ,3 < t ₂ , ₄ for the wireless communications node 100:2 (“2”). More generally, this requirement may be formulated such that for a wireless communications node n, tt,n < tj,n if i < /■ Alternatively, the ordered sequence may be ordered according to a sequence of reception of wireless signals during a current or preceding signaling sequence between the at least four wireless communications nodes 100.

For instance, and with reference to signaling sequence 330 in Fig. 3, this means that the wireless communications node 100:1 (“1”) first receives the wireless signal transmitted by the wireless communications node 100:2 (“2”), then the wireless signal transmitted by the wireless communications node 100:3 (“3”), and finally the wireless signal transmitted by the wireless communications node 100:4 (“4”). Further, the wireless communications node 100:2 (“2”) first receives the wireless signal transmitted by the wireless communications node 100:1 (“1”), then the wireless signal transmitted by the wireless communications node 100:3 (“3”), and finally the wireless signal transmitted by the wireless communications node 100:4 (“4”), and correspondingly for the wireless communications node 100:3 (“3”) and the wireless communications node 100:4 (“4”). Different from what is illustrated in the signaling sequence 310 of Fig. 3, the wireless communications nodes 100 are not required to transmit the wireless signals in accordance with the ordered sequence. For example, as is shown in signaling sequence 330, the wireless communications node 100:4 (“4”) may transmit its wireless signal before the wireless communications node 100:3 (“3”) has transmitted its wireless signal, i.e., t ₄ < t ₃ .

Optionally, the computing device 200 may be operative to select the transmission times of the subsequent wireless signals of the subsequent signaling sequence in accordance with an ordered sequence of transmission and reception of the wireless signals of the subsequent signaling sequence by each of the at least four wireless communications nodes 100. That is, not only the receptions of the wireless signals transmitted by the wireless communications nodes 100 are ordered, but also the transmissions of the wireless signals by the wireless communications nodes 100. As is illustrated by the signaling sequence 340 of Fig. 3, this means that the wireless signals are transmitted first by the wireless communications node 100:1 (“1”), then by the wireless communications node 100:2 (“2”), then by the wireless communications node 100:3 (“3”), and finally by the wireless communications node 100:4 (“4”), < t ₂ < t ₃ < t ₄ . In practice, a signaling sequence with an ordered sequence of both transmission and reception of wireless signals, such as signaling sequence 340, can be optimized so as to reduce the duration of the subsequent signaling sequence by minimizing the shortest time interval for any of the wireless communications nodes 100 between receiving or transmitting a wireless signal and the same wireless communications node 100 receiving or transmitting the subsequent wireless signal in the signaling sequence 340. In Fig. 3, each such shortest time interval in the signaling sequence 340 is illustrated as a thick line, and the resulting shortened signaling sequence is illustrated as signaling sequence 350. Embodiments of the invention which rely on selecting transmission times of the subsequent wireless signals of the subsequent signaling sequence in accordance with an ordered sequence for reception and optionally also transmission are advantageous in that the cardinality of the set of possible combinations of transmission and receptions times at the different wireless communications nodes 100 is reduced.

In the following, embodiments of a method 400 of relative positioning of wireless communications nodes 100 are described with reference to Fig. 4. The wireless communications nodes 100 may be asynchronous. The method 400 is performed by a computing device 200 and comprises calculating 402 pairwise distances between the at least four wireless communications nodes. The pairwise distances are calculated based on time differences between reception times of wireless signals transmitted by each of at least four wireless communications nodes and received by the other wireless communications nodes of the at least four wireless communications nodes 100 as part of a signaling sequence. The method 400 optionally comprises receiving 401 the reception times, or time difference between reception times, from the at least four wireless communications nodes 100. A signaling sequence comprises transmission of one wireless signal by each one of the at least four wireless communications nodes 100 and reception of the transmitted wireless signals by each of the other of the at least four wireless communications nodes 100.

The method 400 further comprises selecting 403 a transmission time of a first wireless signal of a subsequent signaling sequence for transmission by a first one of the at least four wireless communications nodes 100.

The method 400 further comprises selecting 404 transmission times of subsequent wireless signals of the subsequent signaling sequence by the other wireless communications nodes of the at least four wireless communications nodes 100. The selected transmission times of subsequent wireless signals reduce a sum of squared time intervals between reception of a first wireless signal and a last wireless signal of the subsequent signaling sequence by each of the at least four wireless communications nodes 100. Preferably, the sum of squared time intervals between reception of a first wireless signal and a last wireless signal of the subsequent signaling sequence by each of the at least four wireless communications nodes 100 is minimized.

Preferably, the transmission times of the subsequent wireless signals of the subsequent signaling sequence are selected 404 under the constraint that a minimum time interval between reception or transmission of any two wireless signals by each of the at least four wireless communications nodes 100 is equal to, or longer than, a time interval required to receive or transmit a wireless signal and to become operational for receiving or transmitting a next wireless signal. Optionally, the minimum time interval between reception or transmission of any two wireless signals by each of the at least four wireless communications nodes 100 is equal to, or longer than, a sum of the time interval required to receive or transmit a wireless signal and to become operational for receiving or transmitting a next wireless signal, and a time interval required for a wireless signal to travel an expected maximum change in pairwise distance between the at least four wireless communications nodes 100 between two subsequent signaling sequences.

The expected maximum change in pairwise distance between the at least four wireless communications nodes 100 between two subsequent signaling sequences may be calculated based on an expected maximum relative speed between the at least four wireless communications nodes 100.

Alternatively, the expected maximum change in pairwise distance between the at least four wireless communications nodes 100 between two subsequent signaling sequences may be calculated based on route information for the at least four wireless communications nodes 100.

The transmission times of the subsequent wireless signals of the subsequent signaling sequence may be selected 404 in accordance with an ordered sequence of reception of the wireless signals of the subsequent signaling sequence by each of the at least four wireless communications nodes 100. Optionally, the transmission times of the subsequent wireless signals of the subsequent signaling sequence are selected in accordance with an ordered sequence of transmission and reception of the wireless signals of the subsequent signaling sequence by each of the at least four wireless communications nodes 100.

The ordered sequence may be ordered according to identifiers of the at least four wireless communications nodes 100. The identifiers of the at least four wireless communications nodes 100 may comprise any of: MAC addresses, network addresses, and configurable identifiers.

Alternatively, the ordered sequence is ordered according to a sequence of reception of the wireless signals during a current or preceding signaling sequence between the at least four wireless communications nodes 100.

The method 400 may further comprise sending 405 the selected transmission times of the wireless signals of the subsequent signaling sequence to the wireless communications nodes 100.

It will be appreciated that the method 400 may comprise additional, alternative, or modified, steps in accordance with what is described throughout this disclosure. An embodiment of the method 400 may be implemented as the computer program 213 comprising instructions which, when the computer program 213 is executed by the processor 211 comprised in a computing device 200, cause the computing device 200 to carry out the method 400 and become operative in accordance with embodiments of the invention described herein. The computer program 213 may be stored in a computer-readable data carrier, such as the memory 212. Alternatively, the computer program 213 may be carried by a data carrier signal, e.g., downloaded to the memory 212 via the communications interface circuitry 201.

The person skilled in the art realizes that the invention by no means is limited to the embodiments described above. On the contrary, many modifications and variations are possible within the scope of the appended claims.