TECHNICAL FIELD OF THE INVENTION

The invention relates to measuring distance in general. More specifically, the invention relates to evaluating at least one distance by at least measurement of radio link phase and determination of an integer ambiguity in a distance between a first antenna unit and second antenna unit.

BACKGROUND OF THE INVENTION

Methods for measuring distances where phase measurements between transmitter and receiver are carried out are burdened by the integer ambiguity (IA) problem. For instance, a measurement between a transmitter device and responder device can comprise measurement of a phase difference between a transmitted signal and response signal and this can be used to calculate a part (the length of a fractional part of a wavelength used) of the distance between the transmitter and responder. The determination of uncertainty in the number of full wavelengths - the integer ambiguity - between the transmitter and responder is also required in order to determine the total distance.

The prior art discloses different methods for resolving the above discussed integer ambiguity problem. Carrier phase techniques with Global Navigation Satellite Systems (GNSS) solve the integer ambiguity problem by utilizing tens of simultaneous measurements of phase over radio links (pairs of radio units of which at least one transmits a signal and one receives a transmitted signal). The simultaneous phase measurements allow a joint solution for the integer ambiguities. In terrestrial systems this would require tens of access points / base stations to be visible in line-of-sight simultaneously. This is not practically possible. Also, strong radio reflections make this technique unreliable.

To solve the I A problem in terrestrial positioning or distance determination systems, the IA for each radio link (or a very small number of radio links) has to be solved. One solution is to measure the distance of each link with a radio pulse, but this suffers from poor accuracy with respect to the radio signal wavelength unless the instantaneous measurement bandwidth is very large. In addition, such a delay measurement suffers from radio reflections, making this technique impractical. There is a need fora method of accurate determination of a radio link distance enabled through phase measurement and reliable and simple determination of integer ambiguity in the link distance.

SUMMARY OF THE INVENTION

An object of the invention is to alleviate at least some of the problems in the prior art. In accordance with one aspect of the present invention, a method is provided for evaluating at least one distance between at least a first antenna unit and a second antenna unit, the method comprising at least resolving an integer ambiguity by: sending, as a broadcast and consecutively with each signal in its own time slot, primary signals comprising frequencies in a first frequency range, and determining at least one set of one or more possible distance values being indicative of possible distances between at least one pair of antenna units, each pair of antenna units comprising antenna units that mutually transmit and receive at least one signal among each other, at least one of said pairs comprising the first antenna unit and second antenna unit through:

- sending at least first primary signals having a first primary frequency and second primary signals having a second frequency via at least a first antenna unit and a second antenna unit,

- receiving the first primary signals and second primary signals at at least one non-transmitting antenna unit to obtain the at least one pair of antenna units,

- determining at least first primary phase information and second primary phase information related to each of the received first primary signals and second primary signals, said first and second primary phase information being indicative of a phase of the received first and second primary signal with respect to a local oscillator of a radio unit with which the receiving antenna unit is associated with,

- determining, for the at least one pair of antenna units, at least a first primary phase sum being indicative of a sum of the first primary phase information regarding a first primary signal received at one of the antenna units in a pair of antenna units and the first primary phase information regarding a first primary signal received at the other antenna unit in the pair of antenna units,

- determining, for at least one pair of antenna units, at least a second primary phase sum being indicative of a sum of the second primary phase information regarding a second primary signal received at one of the antenna units in a pair of antenna units and the second primary phase information regarding a second primary signal received at the other antenna unit in the pair of antenna units,

- determining the at least one set of one or more possible distance values, respectively for each pair of antenna unit, by determining a first distance variable, said distance variable being indicative of a first approximated distance between the antenna units in the pair of antenna units, based on at least a difference between the first primary phase sum and second primary phase sum, wherein the set of possible distance values is based on a set of possible distance values obtained through variation of the integer ambiguity corresponding to distance variations of integer numbers of half wavelengths at the first primary frequency, said set of possible distance values being limited by the estimated maximum error in the first distance variable, said maximum error being determined based at least on a maximum error of the first primary phase sum, a maximum error of the second primary phase sum, and the frequency difference between the first and second primary signals, and sending, as a broadcast and consecutively with each signal in its own time slot, one or more auxiliary signals comprising frequencies in at least one second frequency range, and determining the distance between the at least one pair of antenna units by:

- sending at least first auxiliary signals having a first auxiliary frequency via at least the first antenna unit and second antenna unit,

- receiving the first auxiliary signals at at least one non transmitting antenna unit,

- determining at least first auxiliary phase information related to each of the received first auxiliary signals, said first auxiliary phase information being indicative of a phase of the received first auxiliary signal with respect to a local oscillator of a radio unit with which the receiving antenna unit is associated with,

- determining, for at least one pair of antenna units, at least a first auxiliary phase sum being indicative of a sum of the first auxiliary phase information regarding a first auxiliary signal received at one of the antenna units in a pair of antenna units and the first auxiliary phase information regarding a first auxiliary signal received at the other antenna unit in the pair of antenna units, and evaluating the distance between the at least one pair of antenna units based on a selected likely distance value from the previously determined set of possible distance values for each pair, by determining a second distance variable corresponding to a second approximate but more accurate distance than the first distance variable between the pair of antenna units based on a difference between the first primary phase sum and first auxiliary phase sum divided by the frequency difference of the first primary and first auxiliary signal, and selecting (826) as the likely distance value the distance value from the set of possible distance values fitting the smaller error margin in the second distance variable, said error margin being determined by the estimated maximum error in the first primary phase sum, the estimated maximum error in the first auxiliary phase sum, and the frequency difference between the first primary signal and first auxiliary signal.

The invention also relates to an arrangement according to independent claim 13 and a computer program product according to independent claim 14.

The present invention may provide a method of determining an absolute distance for a single link between transceivers (a radio link between the first antenna unit and the second antenna unit or other possible pair of antenna units) without the need for further transmitters or receivers in the determination of the distance between the two transceivers in each pair. Phase techniques in the prior art (e.g. Real Time Kinematic GNSS) require a high number of satellites transmitting signals to at least two receivers to resolve the IA problem.

The present invention may be used in terrestrial systems, optionally also indoors to enable indoor positioning. This is because only one radio link between two antenna units in a pair of antenna units may be required for accurate determination of a distance between the units.

The arrangement may be utilized for accurate determination of a plurality of distances between different pairs of antenna units, and the distances may advantageously be determined for each link/distance separately. Here, the first primary signals, second primary signals, and first auxiliary signals may be transmitted via a plurality of antenna units and a plurality of distances between pairs of antenna units may be evaluated. The plurality of distances may be determined using a limited number of transmissions, as the signals are transmitted as broadcasts. The present invention may allow determination or evaluation of distance between antenna units with narrow instantaneous bandwidth of used frequencies in the transmitted signals (e.g. a bandwidth of 40 MHz). This is opposed to other existing systems such as Ultra-Wide-Band (UWB) systems, where a much larger instantaneous bandwidth must be used. The present invention provides a method and arrangement which may be inexpensive to implement, whereby inexpensive narrow band receivers may be utilized.

Due to the narrow operating bandwidth of the present invention, the system may operate at frequency bands/ranges where high transmission powers are allowed, enabling better range and accuracy than e.g. UWB and Bluetooth- based positioning systems, which operate at frequency bands where lower transmission powers must be used. Bands that are feasible with the present invention may be e.g. 5GHz RLAN (enabling transmission power of 100 mW or even 1W) or WIA band (enabling transmission power of 400 mW). Therefore, the power used for transmission of one or more signals (e.g. primary and/or auxiliary signals) may be over tens of mW, such as over 20 mW, over 50 mW, or over 80 mW. In e.g. UWB techniques, the transmission powers are limited to levels that are several orders of magnitude smaller than with the present invention.

With the present invention, it may also be easier to fit the utilized narrow bands between e.g. wifi network channels.

The method may additionally comprise sending a plurality of auxiliary signals.

The frequency of consecutive or simultaneous primary signals and/or frequency of consecutive or simultaneous auxiliary signals may in an embodiment preferably be separated from each other by under 20 MHz, more preferably under 10 MHz, such as 5 MHz.

Advantageously a difference between the first frequency range and the second frequency range is at least 150 MHz, preferably at least 200 MHz, most preferably at least 500 MHz. The frequency ranges may also be in completely different radio bands: for example, the higher range could be in the 5 GHz RLAN band whereas the lower range could be in 2.4 GHz ISM band, allowing a frequency difference over 3 GHz. Thus, the first frequency range and second frequency range could be separated by e.g. 500 MHz- In an embodiment of the invention, the second (or any subsequent) frequency range may be selected based on the estimated maximum error in the determined distance variable so that the difference between the first and second frequency range ensures that unaccounted phase rotations are avoided, optionally by determining a possible range for the distance variable based on its maximum error and selecting the second frequency range such that the expected minimum and maximum values of the first auxiliary phase sum corresponding to the minimum and maximum values of the first distance variable do not differ more than a threshold value, such as 2TT. Using 2p or smaller value for the threshold prevents phase ambiguity when the first auxiliary (or any subsequent) phase sum is used to further limit the set of possible distance values.

The first frequency range and/or the second frequency range may encompass a maximum bandwidth of 100 Hz-100 kHz, preferably 10-100 kHz in the case of only one signal transmitted in said range or 5-100 MHz, preferably 10-50 MHz, such as e.g. 40 MHz at least in the case of a plurality of simultaneous signals being transmitted in said range. When referring to simultaneous transmissions, it should be understood that two or more signals that are configured to be transmitted by one antenna unit are transmitted simultaneously, yet preferably with the different antenna units still transmitting in their own separate time slots.

A first and/or second frequency range may in some embodiments of the invention be considered as having a selected bandwidth, yet it should be understood that one or more signals in said ranges do not necessarily have to span said bandwidths, but can exhibit separate frequencies which may be comprised in said ranges.

All of the primary and/or auxiliary signals that are to be transmitted by an antenna unit may be transmitted simultaneously, yet in one embodiment of the invention all signals may be transmitted consecutively, by at least one or even all of the antenna units. In this embodiment, simpler and/or cheaper antenna units capable of transmitting only at one frequency at a given time, that may be e.g. coin battery operated, may be utilized in an arrangement.

It is also possible to use any number of auxiliary signals in various different frequency ranges (such as third, fourth etc. frequency ranges). For simplicity, the detailed description below focuses mainly on the case where only one frequency range (the second frequency range) for auxiliary signals is used. First and subsequent primary signals may be transmitted to determine respective phase information to obtain a plurality of phase sums, while the difference between phase sums (such as difference between first and each subsequent phase sum) may be used to determine a distance variable that is indicative of an approximate distance between the pair of antenna units, such as first and second antenna unit.

The maximum error in the distance variable may be determined based on at least the estimated maximum error in each of the determined phase information. A maximum error in one or more determined phase sums may be determined based on one or more maximum errors in determined phase information.

A maximum error in the distance variable may in some embodiments be determined based on other information or may e.g. be obtained as a previously determined parameter.

When the (estimated) maximum error of the first distance variable is known, this may limit the possible distance values to ones which are within the maximum error values of the distance variable. This may then be used to determine the set of possible distance values, which gives the possible distances between the antenna units in terms of distances that differ from each other in integer ambiguity.

The maximum error of the second distance variable may then further limit the possible distance values. Advantageously, when determining the second distance variable based on the first primary phase sum and first auxiliary phase sum, the maximum error of the second distance variable is significantly smaller than that of the first distance variable and leaves only one possible distance value. The likely distance value may then be selected as the distance value from the set of possible distance values fitting an error margin in the second distance variable, said error margin being determined by the estimated maximum error in the first primary phase sum, the estimated maximum error in the first auxiliary phase sum and the frequency difference of the first primary signal and the first auxiliary signal.

The likely distance value may be or correspond to the actual distance between the first antenna unit and the second antenna unit or be indicative of said distance. The determining of a distance between the first antenna unit and the second antenna unit may herein refer to determining a value of distance that is an approximation of the actual distance between the first antenna unit and the second antenna unit based on the measurements carried out.

In one embodiment of the invention, one or more auxiliary signals comprising frequencies in a plurality of frequency ranges may be sent, said plurality of frequency ranges comprising at least the second frequency range, wherein auxiliary signals are sent in a subsequent frequency range if it is determined that the likely distance value cannot be uniquely selected based on the determined first or subsequent, previously determined auxiliary phase sum.

If it is determined, for instance after determining an auxiliary phase sum and a second distance variable, that possible distance values (corresponding to distance values within an error margin of the second distance variable corresponding to distance differences of integer half wavelengths at the first primary frequency) are not only limited to one possible value, and therefore that the likely distance value cannot be unambiguously selected, then a third frequency range may be selected, and subsequent auxiliary signals may be transmitted and respective phase information determined, whereby the possible distance values are further limited, and it may be feasible to uniquely select the likely distance value.

Some embodiments of the method additionally comprise tracking the distance between the first and second antenna unit by resolving the integer ambiguity at least once and subsequently repeatedly sending subsequent primary signals, determining subsequent primary phase information, and determining primary phase sums to repeatedly determine distance information being indicative of a change in distance between the first and second antenna unit.

Embodiments of the invention may thus provide an arrangement and method for continuous distance tracking or provision of location information, where integer ambiguity may be resolved/determined e.g. once or at predetermined intervals, while otherwise operating in a tracking mode, where only primary signals are sent (and received) to repeatedly determine a primary phase sum which may be used to repeatedly determine the distance between the antenna units without re-determination of an integer ambiguity.

In continuous distance tracking or tracking mode, the subsequent primary signals could be transmitted at predetermined adequately short time intervals such that it may be assumed that the integer ambiguity problem does not reappear, i.e. that the distance uncertainty between antenna units between times of sending subsequent signals increases less than an amount that would lead to a cycle slip that cannot be accounted for.

Distance tracking may be used to track a position of a physical object, where e.g. a first or second antenna unit is associated with the physical object, such as coupled to the object.

A maximum time interval between subsequent primary signals for tracking a physical object may be determined e.g. through a maximum uncertainty in the speed and/or acceleration of the physical object.

In tracking of an object, the object’s approximate location, speed and/or acceleration may be estimated or an approximate (maximum) uncertainty in these may be determined. In some embodiments, an estimator may be used for tracking/estimating the object's location. The object’s location may be tracked using e.g. simple interpolators, Kalman filters, extended Kalman filters, or particle filters. The use of such estimators may make it possible to measure the link phase (such as determined phase sums) with lower repetition rate (i.e. with using less and/or less frequent e.g. primary signals) without a risk of uncounted 2p phase slips in the phase sum.

The arrangement could be used for distance tracking such that most of the time, the transmitted signals only need to be in one narrow frequency band, e.g. a first frequency range.

In one embodiment, at least the first primary signal and the first auxiliary signal may be sent in succession.

In one other embodiment, at least the first primary signal and the first auxiliary signal may be sent at least partially simultaneously. Also a plurality of e.g. primary signals and/or a plurality of auxiliary signals may be sent simultaneously.

The novel features which are considered as characteristic of the invention are set forth in particular in the appended claims. The invention itself, however, both as to its construction and its method of operation, together with additional objects and advantages thereof, will be best understood from the following description of specific example embodiments when read in connection with the accompanying drawings.

The previously presented considerations concerning the various embodiments of the method may be flexibly applied to the embodiments of the arrangement mutatis mutandis, and vice versa, as being appreciated by a skilled person.

BRIEF DESCRIPTION OF THE DRAWINGS

Next the invention will be described in greater detail with reference to exemplary embodiments in accordance with the accompanying drawings, in which:

Figure 1 depicts one exemplary arrangement according to an embodiment of the invention,

Figure 2 shows one more exemplary arrangement according to an embodiment of the invention,

Figure 3 shows exemplary first and second antenna units and radio units that may be used in an arrangement,

Figure 4 shows other exemplary first and second antenna units and radio units that may be used in an arrangement,

Figure 5 shows, on a graph of determined phase sum as a function of transmitted signal frequency, possible determined primary phase sums, auxiliary phase sums, and integer ambiguity lines corresponding to a set of determined distance values in one use case scenario according to one embodiment of the invention,

Figure 6 illustrates one possible radio unit that may be used in an arrangement,

Figure 7 depicts allocation of time slots in measurement cycles,

Figure 8 portrays a flow chart of a method according to one embodiment of the invention, and

Figure 9 shows a flow chart of a method of selecting frequency ranges to be utilized in embodiments of the invention.

DETAILED DESCRIPTION

Figure 1 shows an arrangement 100 according to one embodiment of the invention. The arrangement comprises at least a first antenna unit (AU) 104 and a second antenna unit 106. An arrangement 100 may also comprise some other number of antenna units, such as a third antenna unit and a fourth antenna unit etc. The number of antenna units may determine how many distances the arrangement 100 may possibly evaluate. Any number of distances between antenna units, such as the distance D between the fist antenna unit 104 and second antenna unit 106 may be evaluated.

The first antenna unit 104 may be associated with a first radio unit 108 and the second antenna unit 106 may be associated with a second radio unit 110. One radio unit 108, 110 could also be associated with two or more antenna units 104, 106. An antenna unit 104, 106 may be comprised in a radio unit 108, 110 or be coupled to a radio unit via e.g. cables.

The radio units 108, 110 are coupled to at least one processor 102. The processor 102 may be a controller unit that is external to the radio units 108, 110, and may be implemented as a microprocessor unit or provided as a part of a larger computing unit such as a personal computer. Yet in some embodiments, the processor 102 may be comprised in or be considered to be part of a radio unit 108, 110

The processor 102 may be configured to control the radio units and/or antenna units comprised in an arrangement 100. The processor 102 may additionally receive data from the antenna units 104, 106 or radio units 108, 110.

The processor 102 may additionally or alternatively be configured to receive data from the antenna units and/or radio units comprised in an arrangement 100 in a wired (e.g. Ethernet) or wireless (e.g. WLAN) manner. Figure 2 shows an embodiment of an arrangement 100 where the processor 102 is wirelessly coupled to the radio units 108, 110. A processor 102 may be associated with a processor antenna unit 112.

The processor 102 and radio units 108, 110 may be powered using for instance power-over-Ethernet (PoE), direct mains supply, batteries, solar panels, or mechanical generators (e.g. in wind turbine blades).

In some embodiments, also a remote processor may be utilized in an arrangement 100, e.g. in addition to the processor 102 which may be a local processor or the processor 102 may be realized as a remote processor with no need for a local processor. A remote processor may receive any of the data obtained and could e.g. perform at least a portion of the determination of data that is carried out by the arrangement 100. A remote processor may refer to a processor which may be accessed through cloud computing or the remote processor may e.g. refer to a virtual processor comprised in a plurality of locations which may be configured to execute procedures presented herein through parallel processing means.

The antenna units 104, 106 of the arrangement are configured to send signals, with each antenna unit transmitting its respective signal in a dedicated time slot as a broadcast, while the other non-transmitting antenna units of the arrangement may receive the transmitted signals. Preferably all antenna units transmit the same or corresponding signal (i.e. a signal at the same frequency), such that each antenna unit of the arrangement has preferably sent at least primary signals and at least one auxiliary signal as will be described further below. Pairs of antenna units (comprising at least the first antenna unit and second antenna unit) are then obtained, where each pair of antenna units comprises one antenna unit that has transmitted a signal that is received at the other antenna unit and the one antenna unit receives a corresponding signal that is transmitted by the other antenna unit.

In the following example, the arrangement 100 and its functionality is described in connection with the first antenna unit 104 and second antenna unit 106, where at least a first primary signal and first auxiliary signal is transmitted by both antenna units.

The first antenna unit 104 is configured to send at least a first primary signal having a first primary frequency, which may be a radiofrequency (RF) signal. The primary signal is preferably a sine wave, but can be any signal with a known modulation. The first antenna unit 104 may also transmit subsequent primary signals, which will be discussed further below.

The first primary frequency (and possible subsequent primary signals) may be comprised in a first frequency range. The first frequency range may for instance encompass a maximum bandwidth of 100 Hz-100 kHz, preferably 10-100 kHz in the case of only one signal transmitted in said range or 5-100 MHz, preferably 10-50 MHz, such as e.g. 40 MHz in the case of a plurality of signals being transmitted in said range.

The duration of the first primary signal (and any subsequent signals transmitted/sent by any of the antenna units of the arrangement) may for instance be between 10 and 10 000 ps depending on e.g. the length of the distances that are to be evaluated, the time intervals between measurement cycles, and/or the quality of local oscillators comprised in the radio units 108, 110. A duration of a signal may for instance be about 100 ps.

The first primary signal is then received at the second antenna unit 106. Based on the received first primary signal, at least first primary phase information related to the first primary signal is determined, said first primary phase information being indicative of a phase of the received first primary signal with respect to a local oscillator of the radio unit with which the at least one second antenna unit is associated, here the second radio unit 110.

To be precise, typically the signal frequency is higher than the local oscillator frequency and the phase measurement often occurs in digital baseband using e.g. fast fourier transform. Essentially, this is equivalent to measuring the phase against the local oscillator that can, for simplicity, be understood to operate at the signal frequency.

If an arrangement 100 comprises further antenna units such as e.g. a third antenna unit, then the (first) primary signal may also be received at the third antenna unit and (first) primary phase information could be determined also at the third (and subsequent) antenna units. Generally, the signals may be transmitted as broadcasts, such that the remaining non-transmitting antenna units of the arrangement receive the signals.

The determination of phase information, such as the first primary phase information, may be carried out at the radio unit with which the receiving antenna unit is associated, such as the second radio unit 110 in the case of the second antenna unit 106 receiving the first primary signal.

The second antenna unit 106 is configured to transmit at least a signal corresponding to the first primary signal. The second antenna unit 106 may be configured to transmit subsequent primary signals.

The first primary signal transmitted by the second antenna unit is received at the first antenna unit 104. Based on the received first primary signal, at least first primary phase information is determined, said first primary phase information being indicative of a phase of the received first primary signal with respect to a local oscillator of the radio unit with which the at least one first antenna unit is associated, here the first radio unit 108.

If an arrangement 100 comprises a plurality of antenna units 104, 106, each of the antenna units of the arrangement may be configured to send the e.g. first primary signal (as a broadcast after a preceding antenna unit in the sequence or at least the first antenna unit 104 has sent the first primary signal), which may be received at the other antenna units of the arrangement. Corresponding phase information may be determined regarding each of the received signals.

In addition to determining phase information, also amplitude information may be determined in some embodiments. For example, both phase information and amplitude information may be determined at a receiving radio unit upon receiving a signal.

The determined phase information may be received by the processor 102.

In some embodiments where amplitude information is determined, the amplitude information may be used to estimate the reliability of the determined data (e.g. a determined distance). For example, a temporary obstruction in the line of sight between the antenna units may be detected and any data marked invalid for the affected time period.

The first primary phase information is then used to determine (by the processor 102) at least a first primary phase sum being indicative of a sum of the first primary phase information regarding the first primary signal received at the second antenna unit 106 and the first primary phase information regarding the first primary signal received at the first antenna unit 104.

The first antenna unit 104 and second antenna unit 106 may be configured to send subsequent primary signals, e.g. at least a second primary signal, which differs in frequency from the first primary signal. The first and subsequent primary signals are yet preferably within the first frequency range and may be transmitted simultaneously or sequentially.

The subsequent primary signal(s) may be received by the non-transmitting antenna unit(s) of the arrangement, and subsequent primary phase information (e.g. at least second primary phase information) may be determined.

From subsequent primary phase information, subsequent primary phase sums, e.g. at least a second primary phase sum may be determined.

If an arrangement 100 comprises more than two antenna units 104, 106, any one of them may transmit and receive the discussed signals, such that a distance between any two antenna units that have among themselves sent and received at least one signal can be evaluated. Pairs of antenna units that have performed two-way transmissions may be obtained, where two-way phase information is determined.

A set of possible distance values is then determined based at least on the first primary phase sum, a determined first distance variable that is indicative of a first approximated distance between the antenna units, and an estimated maximum error in the determined first distance variable. The distance variable could in some embodiments be based on an approximate distance between the antenna units. Possible ways of determining the set of possible distance values will be discussed in more detail further below. A set of possible distance values may be determined regarding each pair of antenna units.

The first antenna unit 104 is also configured to send at least a first auxiliary signal having an auxiliary frequency. Except for the frequency, the first auxiliary signal may essentially correspond to the first primary signal. The first auxiliary frequency may exhibit a frequency that is in a second frequency range. The second frequency range may encompass a maximum bandwidth of 100 Hz-100 kHz, preferably 10-100 kHz in the case of only one signal transmitted in said range or 5-100 MHz, preferably 10-50 MHz, such as e.g. 40 MHz in the case of a plurality of signals being transmitted in said range.

A difference between the first frequency range (a range of the first and possible subsequent primary signals) and the second frequency range may be at least 150 MHz, preferably at least 200 MHz, most preferably at least 500 MHz. The difference could even be over 3 GHz, for example, where the two frequency ranges lie in completely different radio bands, such as the 2.4 GHz ISM and 5 GHz RLAN/ISM bands.

The frequency values of the first, second and/or any subsequent frequency range may essentially comprise any frequency values. More significant than the frequency values comprised in the frequency ranges may be a selected separation/distance or difference in frequency between the separate ranges or between the frequencies of at least the first primary signal and the first auxiliary signal.

The second antenna unit 106 receives the first auxiliary signal and first auxiliary phase information may be determined regarding the second antenna unit 106, where the first auxiliary phase information is indicative of a phase of the received first auxiliary signal with respect to a local oscillator of the second radio unit 110.

The second antenna unit 106 then transmits a signal essentially corresponding to the first auxiliary signal.

The first auxiliary signal transmitted by the second antenna unit 106 is received at the first antenna unit 104, and respective first auxiliary phase information is determined, where the first auxiliary phase information is indicative of a phase of the received first auxiliary signal with respect to a local oscillator of the first radio unit 108.

The first auxiliary phase information is then used to determine at least a first auxiliary phase sum being indicative of a sum of the first auxiliary phase information regarding the first auxiliary signal received at the second antenna unit 106 and the first auxiliary phase information regarding the first auxiliary signal received at the first antenna unit 104.

If the arrangement 100 comprises a plurality of antenna units 104, 106, then each antenna unit may be configured to send a signal corresponding to the first auxiliary signal, preferably consecutively and each in their own time slot. Each signal may be received by the remaining non-transmitting antenna units of the arrangement and corresponding first auxiliary phase information may be determined. First auxiliary phase sums may be determined in connection with each pair of antenna units that has transmitted a two-way signal corresponding to the first auxiliary signal.

Processing of information may be conducted in different order than that which is proposed here. For instance, the aforementioned determination of a set of possible distance values may also be done e.g. after sending (and receiving) auxiliary signals.

Subsequent auxiliary signals may also be transmitted to determine subsequent auxiliary phase information and subsequent auxiliary phase sums.

Subsequent auxiliary signals may comprise frequencies in the second frequency range.

If a plurality of auxiliary signals are transmitted, they may be transmitted simultaneously or sequentially. Simultaneous transmission refers to transmission of signals that are sent by the same antenna unit, while the sending of signals that is executed via different antenna units preferably occurs at different times in dedicated time slots.

Based at least on the determined first primary and first auxiliary phase sums, a likely distance value is determined/selected from the set of possible distance values (assuming that the difference between the first and second frequency range is sufficient for being able to carry out the selection unambiguously). The selection of the likely distance value will be discussed in more detail further below.

The likely distance values may be determined regarding each pair of antenna units for which the set of possible distance values is determined.

Figure 3 illustrates exemplary first and second antenna units 104, 106 and radio units 108, 110 that may be used in an arrangement. In the example of Fig. 3, the antenna units 104, 106 are provided separately from the radio units 108, 110. Fig. 3 exhibits schematically how phase information related to signals that are transmitted and received between two antenna units 104, 106 in a pair of antenna units that mutually transmit and receive at least one signal among each other may be used to evaluate a distance D between them. Corresponding considerations will apply to further pairs of antenna units that may be obtained in various embodiments of the arrangement.

As may be easily understood by the skilled person, distances may be defined in terms of phase lengths, i.e. , phase shifts that occur in a signal (e.g. sine wave) as it traverses a certain length.

Assuming that the transmitting first antenna unit 104 transmits the at least one first primary signal with zero phase with respect to its local clock/oscillator (LO), the measured/determined phase q>i2 (or first primary phase information) of the primary signal received at the second antenna unit 106 may be determined by (as also seen from Figure 3): yΐ2 ⁼ 0C,1 - 0T,1 QA,1 - F12 - QA,2 - 0R,2 - 0c,2. (1)

0c,i and 0c are the phases of the local oscillators of the first and second radio units 108, 110, respectively (at the time of transmission for the first radio unit 108). F12 is the geometric phase corresponding to the distance or baseline or connecting geometric line between the first antenna unit 104 and the second antenna unit 106. qt,i and 0R, ₂ are the transmit and receive branch phase lengths corresponding to the first antenna unit 104 and second antenna unit 106, respectively (with phase length referring here to the phase shift that occurs in a signal traversing along a certain distance). 0A, i and 0A, 2 are the phase lengths of the antenna feed cables of the first antenna unit 104 and second antenna unit 106, respectively. The transmit and receive branch phase lengths, e.g. qt,i and 0R, _2, comprise the phase lengths that are due to the physical lengths of the transmit and receive branches of the associated radio units, comprising e.g. amplifiers and also possible cables in the radio units. For instance, the phase length qt,i corresponds to the length of transmission branch from the digital-analog converter (DAC) to the antenna port of the first radio unit 108.

Accordingly, the second antenna unit 106 may then also transmit at least a first primary signal (possibly after determining that the corresponding signal from the first antenna unit 104 has been transmitted), and the first primary signal may be received at at least the first antenna unit 104.

Yet, assuming that the second antenna unit 106 transmits the first primary signal with zero phase with respect to its local clock/oscillator (LO), the measured/determined phase 9 ₂₁ (or first primary phase information) of the primary signal received at the first antenna unit 104 may be determined by: f21 = 0c, 2 - 0T,2 - 0A,1 - F2I - 0A,2 - 0R,1 " 0C,1. (2)

0c,2 and 0c, 1 are the phases of the local oscillators of the second and first radio units 110, 108, respectively (at the time of transmission for the second radio unit 110). F21 is the geometric phase corresponding to the distance or baseline or connecting geometric line between the second antenna unit 106 and the first antenna unit 104. qt,2 and 0RI are the transmit and receive branch phase lengths corresponding to the first antenna unit 104 and second antenna unit 106, respectively.

The radio units may send the determined phase information (and possibly also other information, such as amplitude information) to a processor 102 (which may e.g. be incorporated with one of the radio units). The processor 102 may then determine at least a first primary phase sum.

A phase sum may be determined as a sum of the phase information relating to a signal that has been sent by one antenna unit and received at one other antenna unit and a corresponding signal that has been sent by the one other antenna unit (e.g. second antenna unit 106) and received at the one antenna unit (e.g. first antenna unit 104). In the example of Fig. 3 with a first 104 and second antenna unit 106, a phase sum (e.g. first primary phase sum) Foΐ may be determined as:

Od - yΐ2 + f21 - - Qϊ,1 - 0A,1 - Fΐ2 " 0A,2 " 0R,2 " 0T,2 " 0A,2 " F21 " 0A,1 " 0R,1

(3) The LO terms 0c,i and 0c, 2 cancel out, assuming that the LO phases have not drifted between the two transmissions (the signal sent by the first antenna unit and the signal sent by the second antenna unit).

The phase sum determined as described herein is thus advantageously not dependent on the phase of the local oscillators of the radio units involved.

Possible frequency offset between local oscillators of radio units 108 and 110 can be easily measured from the determined phase information. The linear phase drift in Od from such frequency offset can therefore be compensated for.

If the instrumental terms in Equation 3 cannot be assumed to be stable, and their omission would lead to erroneous or inexact distance variables (which may be determined based on the phase sums, e.g. as demonstrated hereinlater), in one advantageous embodiment of the invention, calibration data may be determined in addition to the phase information for a pair of antenna units to perform self-calibration via self-measurements and subsequently essentially eliminate at least some of the instrumental terms in the phase sums. The calibration data may comprise calibration phase information being indicative of a phase of a self-measurement signal received at a transmitting antenna unit during transmission of a signal. Determining of calibration data according to an exemplary embodiment shown in Fig. 3 will be given below.

An (attenuated) sample of for instance a first primary signal (or e.g. any subsequent primary signal or auxiliary signal) may be received at the first antenna unit 104 as a self-measurement signal and the phase cpn of the received (first primary) signal as it reaches the antenna unit 104 may be determined by the first radio unit 108. The phase of the received signal may be determined/measured in the radio unit 108 with respect to the radio unit sampling clock or local oscillator of the radio unit 108.

According to Figure 3 it may be determined that first calibration phase information indicative of the phase of the self-measurement signal may be given by fi 1 — Qt,i - 0R,I , (4).

Accordingly, a sample of the e.g. first primary signal transmitted by the second antenna unit 106 may be received at the second antenna unit 106 as a self measurement signal and the phase f 2 of the received first primary signal as it reaches the second antenna unit 106 may be determined by the second radio unit 110. The phase of the received signal may be determined/measured in the second radio unit 110 with respect to the radio unit sampling clock or local oscillator of the second radio unit 110.

Calibration phase information indicative of the phase of the self-measurement signal at the second antenna unit 106 may be given by f22 = - 0T,2 - 0R,2. (5)

The radio units 108, 110 may send the determined calibration data (comprising the calibration phase information) to the processor 102, and the processor 102 may in some embodiments determine a phase sum as being indicative of a difference between a sum of the phase information relating to a signal that has been sent by one antenna unit and received at one other antenna unit and a corresponding signal that has been sent by the one other antenna unit (e.g. second antenna unit 106) and received at the one antenna unit (e.g. first antenna unit 104) and the sum of the calibration data. Alternatively, the radio units may pre-compensate for the instrumental terms by subtracting the calibration phase information before sending the e.g. primary phase information to the processor.

A phase sum may then be determined as (from Equations 3, 4, and 5):

Od - F12 + f21 - fΐ 1 — f22

= - Qt,1 - QA,1 - Fΐ2 - QA,2 - 0R,2 " ©T,2 " 0A,2 " F21 " 0A,1 " 0R,1 + ©T,1 + 0R,1 +

0T,2 + 0R,2

=- F12 - 20A, 2 - F21 - 20A, 1. (6)

In embodiments where calibration phase information is determined, an arrangement 100 may employ antenna units 104, 106 which have a switch implemented in the antenna unit 104, 106 (and not the radio unit 108, 110). Here, possible changes in the active transmit or receive lines and components in the radio units 108 and 110 are essentially eliminated by the calibration. Only the antenna cable lengths remain as instrumental terms in the determined phase sum. However, these are rather constant and can be separately calibrated simply by doing one calibration measurement with a known distance between the first antenna unit 104 and second antenna unit 106. The above considerations may apply also to any possible auxiliary signals, subsequent primary signals, and subsequent primary auxiliary signals.

Figure 4 exhibits other exemplary first and second antenna units 104 and 106 and radio units 108 and 110 that may be used in an arrangement 100. In this embodiment, the antenna units 104, 106 are comprised in the radio units 108, 110, or advantageously connected only with a single antenna cable.

Figure 5 shows, on a graph of determined phase sum as a function of transmitted signal frequency, possible determined primary phase sums, auxiliary phase sums, and integer ambiguity lines corresponding to a set of determined distance values in one use case scenario according to one embodiment of the invention. The e.g. numbers, lines, and calculated values of Fig. 5 are merely exemplary and are intended as visual aids in describing the invention. The exact depicted values might be possible e.g. in a case where a distance D between antenna units is only about 25 mm. However, the principle remains the same for much larger distances.

Depicted points 302 and 304 may correspond to a first primary phase sum and second primary phase sum, respectively. In this example, first and second primary signals (having frequencies of fi and h) have therefore been transmitted. The primary signals are in a first frequency range f _a . The exemplary first frequency range f _a spans a frequency range of about 40 MHz. E.g. the number of transmitted signals and the frequencies that the first frequency range f _a spans, along with the width of first band (range of spanned frequencies) may of course differ between use cases.

The primary signals may be sent in one transmission (regarding one antenna unit transmitting in its respective time slot) where a plurality of e.g. sine waves may be transmitted simultaneously. The difference in frequency between consecutive signals may be e.g. between 1 and 40 MHz, between 5 and 20 MHz, such as about 10 MHz.

Points 308 and 310 may correspond to a first auxiliary phase sum and second auxiliary phase sum respectively. In this example, first and second auxiliary signals (with frequencies of f3 and U) have therefore been transmitted. The auxiliary signals are in a second frequency range fb. The exemplary second frequency range fb spans a frequency range of about 40 MHz. Again, the number of transmitted signals and the frequencies that the second frequency range fb spans (which could be e.g. only one frequency), and with the width of the second band may also differ. First and second frequency ranges f _a , fb may be equivalent in bandwidth or they may differ from each other. Yet, the first and second frequency ranges are advantageously both narrow enough to enable the use of narrow band receivers (cf. WiFi receivers) or even Internet-of-Things receivers operating on a coin battery.

The difference Dί between the first frequency range f _a and second frequency range fb is about 550 MHz in the example of Fig. 5. The frequencies of the primary signals can be larger than the frequencies of the auxiliary signals or the frequencies of the primary signals can be smaller than the frequencies of the auxiliary signals, yet there is advantageously a difference Dί between the frequencies/frequency ranges that is sufficiently large that a likely distance value can be determined.

In some embodiments of the invention, signals may be transmitted also in third and possibly fourth and subsequent narrow bands in addition to the first band or first frequency range f _a and second band or second frequency range fb.

A number of frequency ranges that should preferably be utilized in order to be able to determine or select a likely distance value from the set of determined possible distance values may vary depending on the environment, use case or embodiment.

When at least two signals, e.g. a first primary signal and second primary signal having carrier frequencies fi and h are utilized (it may be assumed herein that in the case of transmitting a primary or auxiliary signal, said signal is transmitted by the at least first and second antenna units 104, 106, preferably by all antenna units comprised in an arrangement 100), a difference between respective phase sums (difference between a first (primary) phase sum and second (primary) phase sum) may be expressed in terms of the distance between the first and second antenna units as:

AOd,i = Od,fi - Od,f ₂ = 2p ^* (fr f ₂ ) ^* (2 ^* D) / c, (7) where c is the speed of light.

From equation (7), a first approximation of the distance D between the antenna units in the at least one pair of antenna units may be considered as a distance variable Di that is indicative of an approximate distance D and may be determined as Di = (AOd,i ^* c) / [4 p (fi- f ₂ )] (8).

The inaccuracy of the distance D determined through equation (8) may however, be relatively high due to measurement error or estimated possible error d in measurements of phase sums Od, _fi and Od, _f 2. Of course, an error d could theoretically also be zero, in which case the distance D could be determined precisely, and integer ambiguity could be resolved.

The measurement error d in e.g . Od,fi is typically caused by signal components reflected from nearby objects that sum up with the direct signal component. If the reflected components are summed and their total signal voltage is marked in the receiver as e and the direct signal component is marked as z, the maximum phase error bmax in O _d , may be given approximately as

Sm _a x = 2 arctan (| J |) (9), where the factor of 2 arises from the fact that bmax is the sum of two phase measurements.

A reflection level may be known or estimated for the environment.

Through the estimated maximum error value bmax, limits for any errors in values determined using the determined phase information may be determined. An estimate for a maximum error bmax may be sufficient for the procedure described herein to be feasible. In what follows, bmax should be understood as the maximum value that the phase measurement error can take.

The maximum measurement error bmax may be determined for a specific use case or arrangement 100. The maximum measurement error may be known a priori or may be received by an arrangement 100. For instance, the maximum measurement error bmax may be determined based on a known phase measurement/determination accuracy of the arrangement 100.

In some embodiments, the maximum measurement error bmax, which could be considered an error variable, may be determined based on e.g. the environment. A maximum measurement error bmax may be e.g. 5-20 degrees, such as around 10 degrees bmax may be a value that is selected such that it is known that a true error in phase measurements will likely always be below this value.

The maximum measurement error bmax may be utilized to determine a maximum error in the distance variable Di. Because the phase sum measurements may be used to determine distances, it may be understood that a maximum error in a phase measurement may be used to define a maximum error in any distance or distance value derived from said phase measurement.

It should be noted that using a value bmaxthat is too large does not in any way make the following procedure invalid. Too small a value, however, can lead to unaccounted for phase rotations between the frequency ranges and can lead to incorrect distance determination. Therefore, 6max should preferably be selected conservatively.

For instance, if fi and differ from each other by 40 MHz and considering a measurement error 6max of 10 degrees, the maximum error in the determined distance variable Di may be about 10 cm. This may be seen from equations (7) and (8) by varying the measured phase values Od,fi and Od,f2 by 6max.

A determined approximate distance between the at least one pair of antenna units, comprising at least the first antenna unit and second antenna unit may in some embodiments alternatively (instead of through phase measurements such as described above) be obtained e.g. through previous knowledge or a measured approximate distance (measured e.g. using a radio, optical, or sound-based method). This approximate distance may be used as the distance variable. A maximum error for an e.g. otherwise measured approximate distance (variable) may then also be determined or obtained. A maximum error for the approximate distance (variable) may for instance be determined in some cases as a maximum dimension of a contained space where the method, such as positioning, occurs.

In addition to ambiguity arising from the measurement error 6max, there may also be an ambiguity of 2p in the determined AOd,i but this would already mean an ambiguity of about 3.75 m considering the above example scenario. In this case if there is preliminary information regarding the distance D that is more accurate than the 3.75 m, the 2p inaccuracy could be eliminated.

This problem of 2p uncertainty may also be reduced by transmitting consecutive primary signals that differ in frequency by less than a threshold value. The consecutive primary signals (such as fi and f2) may e.g. be separated by under 20 MHz, under 15 MHz, or e.g. by 10 MHz or 5 MHz or under. In the case of 5 MHz signal frequency difference (difference between e.g. fi and f2), a 2p uncertainty / measurement error in the distance D determined through equation (8) would be about 30 m. Upon having a priori knowledge about the distance that has accuracy better than 30m, the 2p uncertainty can be eliminated in this particular case. Yet, it is advantageous to have the transmitted primary signals cover a frequency range that in total spans e.g. at least 40 MHz in order to limit the inaccuracy of the approximate distance determination.

Upon considering that the distance D must be the sum of N + IA half wavelengths and a fractional component D _frac (always smaller than quarter of a wavelength in magnitude), equations (7) and (8) may be utilized to determine the integer ambiguity through:

D = (N + IA) ^* (li / 2) + D _f rac = (AO _d,i ^* c) / [4 p (fr f ₂ )], (10) where li is the wavelength of the first primary signal and AO _d , is given in radians.

The possible values of N + IA correspond to those which satisfy equation (10), taking into account the maximum error in the measurement of AO _d,i which is 26max (the factor of 2 following from the fact that AOd,i is the difference of two phase sums). 6max therefore defines a range which integer ambiguity values IA or N + IA may take, giving a set of possible integer ambiguity values. The set of possible integer ambiguity values corresponds to or defines a set of possible distances D, or set of possible distance values if D _frac can be determined.

N, which is the best estimate of the number of half wavelengths between the antennas, can be derived as the closest match to equation (10) by setting IA=0.

The possible range of IA (-DIA < IA < DIA) is limited by this maximum phase estimation error 6max as follows (as can be derived from the previous equation):

By setting f ₂ (and correspondingly also Od, _f 2) in equation (7) to zero and noting that Od, _fi must correspond to the fractional component of D _frac , it follows that the phase sum fulfills the following equation:

This is assuming that the phase error (the instrumental component that cannot be canceled out with the basic measurement, for example - 2QA,2 - 2QA,I in equation (6)) of the arrangement is zero (or is known and may be eliminated from the phase sum determination). From this, the distance D may be determined as from which D may be determined with higher accuracy than with equation (8), because fi is much larger in magnitude than fi - f _å.

The problem with equation (13) is then the integer ambiguity (not knowing the value of N+IA, or, if N is determined from equation 10, the value of IA). For example, with a signal frequency fi of 6 GHz, the ambiguity in D is IA ^* 25 mm. Equation (13) may however be used to determine all possible distance values, from which the set of possible distance values and the likely distance value may be determined, based on the obtained phase information, approximate distance D, and estimated maximum errors therein.

Yet, as given before, through determining the phase sum difference AOd = Od, _fi - Od, _f 2, the distance D may be known (through the distance variable Di) roughly to an accuracy of ±100 mm if fi and f2 are separated by 40 MHz and if the maximum measurement error 6max in the phase sums is 10 degrees. In this case, the integer ambiguity is limited to about 13 different possible values (a set of determined possible integer ambiguity values).

The set of possible integer ambiguity values may be graphically understood to correspond to integer ambiguity lines, when considering phase sum as a function of transmission frequency, where the integer ambiguity lines have slopes determined by the distance given by equation (13) (with a scaling factor of 4TT/C). This is illustrated in Fig. 5. The set of possible IA values or set of possible distance values are shown as integer ambiguity lines that cross the first primary phase sum 302. The line corresponding to slope determined from (13) with IA=0 (the best preliminary match), which also determines the value for N, is shown as 316. The neighboring possibilities are IA=+1 (318) and IA=-1 (314), corresponding to distance differences of D of half a wavelength larger or smaller, respectively. All of these fit the error margins 26max of the primary phase sum measurements shown as error bars in the phase sum measurement and are therefore part of the set of possible IA values or possible distance values.

In terms of a determined first distance variable when considering a first and second primary signal, the error margins to be considered upon determining the set of possible distance values may be limited by the maximum error in the phase sums and the frequency difference between the first and second primary signals, as may be understood from equation (8). The maximum error of the first distance variable may thus be given by (26max ^* c) / [4 p (f1- f2)], which may be used to give the error margins for the first distance variable, which limit the set of possible distance values.

In embodiments where subsequent primary or auxiliary phase sums are determined, the integer ambiguity line IA=0 may be determined as the line that crosses two of the determined primary phase sums or a line that has the best least-squares fit to the primary phase sum points.

In the case of utilizing more than two primary signals, the first distance variable may be determined as a least-squares fit and to determine the maximum error for the first distance variable, one may for instance use statistical estimation methods to derive the boundaries for the first distance variable for given probability values. If more than two primary signals are utilized, the discussed first primary signal and second primary signal should be understood as referring to the primary signals that are spaced furthest apart in frequency, with third and possible subsequent primary signals having frequencies between the first primary signal and second primary signal.

Upon transmission of at least one auxiliary signal between antenna units, preferably where the auxiliary signal frequency f3 differs from fi or f ₂ by at least e.g. 400 MHz, at least a first auxiliary phase sum Od, _f 3 may then be determined. With a determined second phase sum difference AOd, ₂ = Od, - Od, _f 3 and fr f3 and utilizing equation (8), a second, better approximation of distance D may be determined, in which the inaccuracy may be e.g. ±10 mm instead of the ±100 mm for the first approximation obtained from equation (8) using AOd,i and fr f ₂ . It should be noted that the values are here estimated for the considered frequencies and may vary between use cases. Numerical values are given here to illustrate differences in error magnitudes of determined approximate distances D.

Through equation (8), but utilizing the first primary phase sum and the first auxiliary phase sum to obtain a second phase sum difference AOd, ₂ , a second distance variable D ₂ being indicative of a second approximate distance D may be determined as:

D ₂ = (AOd,2 ^* c) / [4 p (fr f ₃ )] (14).

Using the estimated maximum error 6max in the first primary phase sum and/or an estimated maximum error in the first auxiliary phase sum, which may also be e.g. 6 _max, an estimated maximum error for AOd, 2 may be obtained (possibly amounting to 26max). This may also give a maximum error for the second distance variable (giving error margins for the second distance variable), which may be determined utilizing the frequency difference between the first primary and first auxiliary signals, as may be seen from equation (14), i.e. as (26max ^* c) / [4 p (f1- f3)].

The second distance variable D2 may be used to determine possible distance values for the distance D which correspond to distance variations of integer numbers of half wavelengths at the first primary frequency. The maximum error of the second distance variable may give error limits/margins in which the likely distance value should fit.

Through the above, there may only be one possible distance value or, in other words, only one possible value of IA left, giving the likely IA value or likely distance value which may be obtained from the likely IA value, and the integer ambiguity may thereby be resolved.

Through the determined likely integer ambiguity value IA, the distance D may be calculated/determined using equation (13), and the distance D between the first antenna unit 104 and the second antenna unit 106 may be determined to an accuracy of e.g. under 1 mm.

In embodiments of the invention, the possible distance values may be determined directly as distances or the distance values may e.g. be determined as IA values or other parameters (such as slopes of integer ambiguity lines) that are indicative of the possible distance between the first and second antenna unit.

If it is observed that the likely distance values are not limited to one possible distance value, a third frequency range may be selected that differs from the second frequency range by a selected frequency difference and auxiliary signals may be transmitted in the third frequency range to further limit the set of possible distance values.

In Fig. 5, it is seen that the likely integer ambiguity value is one which corresponds to an integer ambiguity line that fits the measurement error 26max, which in this example would be IA=0, corresponding to line 316.

In cases where a plurality of primary and/or auxiliary phase sums are determined, e.g. least squares fitting or some other fitting technique may be used to determine integer ambiguity lines or possible distance values, through slopes of integer ambiguity lines, that are fit taking into account preferably all of the measured phase sums.

In one embodiment, an arrangement 100 may be configured to perform the above discussed integer ambiguity determination protocol at least once and thereafter operate in a tracking mode, where the arrangement 100 may be configured to track the distance between the antenna units in the pairs of antenna units, comprising at least the first and second antenna unit 104 and 106 by repeatedly sending subsequent primary signals (in an e.g. first frequency range, spanning a narrow range of frequencies f _a ), determining subsequent primary phase information, and determining primary phase sums to repeatedly determine distance information being indicative of a change in distance between the first and second antenna unit. By summing up such distance changes the true distance D can be continuously tracked in this mode.

After the integer ambiguity has been determined at least once, it may be assumed (e.g. based on a known or approximated velocity or a change in distance between the first antenna unit 104 and the second antenna unit 106) that the integer ambiguity does not change between subsequent measurements in the tracking mode. An integer ambiguity could also be determined e.g. between predetermined time intervals to ensure that the integer ambiguity value determined previously is still valid, i.e. no phase slips have occurred.

The tracking mode is advantageously used in position tracking as only one narrow frequency band (e.g. a first frequency range f _a comprising primary signals) may be required for transmission of signals during regular operation. Transmissions in a different (narrow) frequency range (e.g. second frequency range fb) may only be needed once before transitioning into the tracking mode or at predetermined time intervals which may still be only rare compared to the signals transmitted in the tracking mode. For example, the phase tracking (through transmission of (primary) signals in a first narrow band) could be repeated between time intervals ranging between for instance 0.1 and 50 ms or 1 and 20 ms, e.g. every 10 ms. A new IA determination (through additional transmission of at least one (auxiliary) signal via the antenna units in a second narrow band) could be only done between time intervals ranging between for instance 0.1 s and 10s s or 0.5 s and 5 s, e.g. once per second.

Figure 6 shows one possible embodiment of a radio unit 108, 110 that may be used in an arrangement 100, where an antenna unit 104, 106 is comprised in the radio unit 108, 110. The radio unit 108, 110 of Fig. 6 comprises two receivers and transmitters, the frequency of which can be set separately.

Utilizing a radio unit 108, 110 with a plurality of receivers, simultaneous measurement of multiple bands, such as a first band comprising primary frequencies and at least a second band comprising auxiliary frequencies may be possible. At least a portion of primary signals that are to be transmitted and at least a portion of auxiliary signals that are to be transmitted can be transmitted at least partially simultaneously.

In some embodiments, a radio unit 108, 110 may comprise more than two receivers, and more than two primary or auxiliary signals may be transmitted (and received) simultaneously. In addition to a first band comprising primary frequencies a second band comprising auxiliary frequencies, e.g. a third band comprising further frequencies could be transmitted and received at least partially simultaneously.

In still another embodiment, the primary and auxiliary signals in a plurality of frequency ranges can be sent in a succession (only one signal at a time). Such a system could operate with extremely narrow bandwidth (e.g. 100 Hz- 100 kHz) and use extremely low-cost hardware and small batteries.

Figures 7A and 7B illustrate how time slots may be allocated in measurement cycles for transmission and receiving of signals and possibly also communication of data in an arrangement 100. A measurement cycle may refer to a set of transmitted signals or a time duration within which signals are sent one after another such that the time between subsequent transmissions is below a threshold value. For instance, a first measurement cycle could comprise the transmission (and receiving) of primary signals and auxiliary signals. In some embodiments, a second measurement cycle may be carried out. The second measurement cycle could e.g. be equivalent to the first measurement cycle or a second measurement cycle could e.g. comprise only transmission (and receiving) of primary signals in embodiments where a tracking mode is utilized.

One measurement cycle may comprise at least one measurement frame (with N measurement slots). During the measurement frame, the at least first antenna unit 104 and second antenna unit 106 may transmit their respective signals separately, each in their own time slot which is allocated to them. One measurement frame may comprise the transmission of signals having one frequency. For example, primary signals could be transmitted in a first measurement frame, while auxiliary signals are transmitted in a second measurement frame. The measurement cycle of Fig. 7 A is applicable to an arrangement 100 comprising N antenna units, where the distance between each antenna unit may be evaluated. Each antenna unit may transmit their respective signals in their own time slot.

Transmissions may be carried out so that transmissions occur in subsequent time slots so that no empty time slots are left between the transmissions. The transmissions and time slots may also be proportioned such that there a time interval between the end of a transmission and the start of a subsequent time slot where a subsequent antenna unit will start its transmission is below a selected maximum time interval. A time interval between the end of a transmission and the start of a subsequent transmission may be less than less than 50 ps, preferably less than 20 ps, such as less than 16 ps.

The subsequent provision of a compact transmission signal may be advantageously used in combination with e.g. WiFi networks. With the present invention, a wireless channel for the transmissions only needs to be reserved once per measurement cycle. This feature may enable compatibility of the present invention with networks such as WiFi.

Without transmissions occurring in subsequent time slots a, a measurement cycle could take longer and an unknown time duration to complete. This is because one measurement cycle could not be carried out effectually as a single transmission in a wireless channel that only needs to compete for the channel once as defined e.g. in ETSI EN 301 893 (the standard specification regulating 5GHz WiFi transmissions). The channel would have to be competed for by each transmitting antenna unit separately during transmission, which could cause arbitrarily long measurement sequences if the channel gets occupied by other users between the transmissions.

Figure 7B shows how time slots may be allocated in measurement cycles where at least one communication frame (with one or more communication slots) is also employed. During a communication frame, signals, measured/determined data, or any other data may be transmitted to a processor 102. At least one data communication may be transmitted and multiplexed with the measurement signals transmitted by the antenna units in time or frequency domain. The at least one data communication may comprise at least the determined phase information. A data communication may additionally or alternatively comprise any other information. An arrangement 100 may thus serve as a measurement arrangement and a communication network simultaneously.

The required time synchronization accuracy should preferably be better than one tenth of the duration of a possible guard time between subsequent signals) in order to prevent overlapping transmissions.

Figure 8 illustrates a flow chart of a method according to one embodiment of the invention. At least one primary signal with a frequency in a first frequency range f _a is sent 802 via a first antenna unit 104, which is received 804 at a second antenna unit 106, through which primary phase information is determined.

At least one primary signal is also sent 806 by the second AU 106, which is received 808 at the first AU, through which corresponding primary phase information is determined.

Based on the determined two-way phase information regarding the at least one air of antenna units, at least one primary phase sum is determined 810. An approximate distance between the first and second antenna unit and a maximum error in the approximate distance may be obtained at 812, while a set of possible distance values being indicative of the distance between the AUs is determined 814, preferably being based at least on the approximate distance and its error and the first primary phase sum.

At least one auxiliary signal with a frequency in a second frequency range fb is then sent 816 via the first antenna unit 104, which is received 818 at a second antenna unit 106, through which auxiliary phase information is determined.

At least one auxiliary signal is also sent 820 by the second AU 106, which is received 822 at the first AU, through which corresponding auxiliary phase information is determined.

Based on the determined two-way auxiliary phase information regarding the at least one pair of antenna units, at least a first auxiliary phase sum and its maximum error is determined 824.

At 826, the likely distance value is selected from the set of possible distance values preferably based at least on the first primary phase sum, first auxiliary phase sum, and the maximum error in the first primary and/or auxiliary phase sums. A corresponding procedure may be carried out regarding each pair of antenna units of an arrangement 100. It should be noted that all possible pairs that may be made regarding the antenna units of an arrangement are not required. For example, an arrangement may comprise a plurality of antenna units, while line of sight may not be available regarding at least one theoretical pair of antenna units that could be made, and therefore the method may comprise evaluation of only distances regarding the other pairs of antenna units of the arrangement that may be obtained through the performed transmissions.

Figure 9 shows a flow chart of a method of selecting frequency ranges to be utilized in embodiments of the invention. A first frequency range f _a is selected 902, with a first bandwidth. At least a first primary frequency is then set, while possible second and subsequent primary frequencies may also be set.

A maximum error in the phase information that is determined may be estimated or obtained at 904.

At 906 a maximum error in a determined or obtained approximate distance between the first and second antenna unit is determined. The maximum error in the approximate distance may be based on maximum errors in phase sums (if at least two primary frequencies are used), being based on the determined maximum error in phase information at step 904. Alternatively, any other means to determine the maximum error in the approximate distance may be used, e.g. a maximum error in another measurement method that may be used to determine the approximate distance.

A maximum frequency difference Afmax between the first frequency range f _a and the second frequency range fb may be determined 908, such that unaccounted phase rotations are avoided. It may be advantageous to set the frequency difference Af as large as possible, i.e. to the maximum value Afmax to reduce the set of possible distance values most efficiently, preferably to be able to unambiguously select the likely distance value from the set of possible distance values.

The first frequency range f _a may comprise frequencies that are larger than those comprised in the second frequency range fb or vice versa.

In determining the maximum frequency difference Afmax, to ensure that unaccounted phase rotations, i.e. phase slips of 2p do not occur, minimum and maximum possible values of at least the first distance variable (or approximated distance) could in one embodiment be used to determine a possible range for at least the first distance variable. If an obtained range for the first distance variable D1 is between [Dimin, Dmax] (range between the minimum and maximum values for D1 ) and a determined primary phase sum at a first primary frequency fi is F1 then it is known that a first auxiliary frequency f3 should be in a range limited by expected minimum and maximum values of the first auxiliary phases sums and determined by [03min,03max] = Fi + (fi-f3) ^* phase slope range = F1 + (f-i -f ₃ ) ^* 4p ^* [Dimin, Di _max ] / c, where f ₃ is the first auxiliary phase sum and the phase slope range refers to a range of possible slopes for integer ambiguity lines, which could also be expressed in terms of an error in distance values. If the difference between the expected minimum and maximum values of the at least first auxiliary phase sum, |F3h _3c - F3hί _h |, is larger than 2TT, then the first primary frequency f3 is too far from the first primary frequency fi, in other words, the frequency difference exceeds a maximum frequency difference Afmax which is the largest value that still realizes this condition. The difference between the expected minimum and maximum values of the at least first auxiliary phase sum F3 could be selected to be under a threshold value, such as 2TT. This may give a possible range for the at least one first auxiliary frequency f3, giving a possible second frequency range fb, which differs from the first frequency range f _a by Afmax at most.

A second frequency range fb may then be determined and at least a first auxiliary frequency may be set 910. After determining at least a first auxiliary phase sum and its error, the size of the set of possible distance values may be determined 912. Advantageously, the set has only one possible distance value left, which can be determined as the likely distance value. Yet, if at 914 it is determined that there is ambiguity in the distance value, i.e. the size of the set of possible distance values is larger than 1 , the process may be continued at 908, and a maximum frequency difference Af _max ,2 between the second frequency range fb or the first frequency range f _a and new, third frequency range may be determined. Signals in the third frequency range may be set and subsequent phase information may be determined to determine a new, third set of possible distance values.

Selection of a new auxiliary frequency range may be carried out any number of times, if it is determined that there is ambiguity in the distance value, i.e. the likely distance value cannot be selected uniquely. The process is ended 916 when there is only one possible distance value left, this being the likely distance value from which the distance between the first and second antenna unit may be determined with an accuracy that is higher than the approximate distance. The invention has been explained above with reference to the aforementioned embodiments, and several advantages of the invention have been demonstrated. It is clear that the invention is not only restricted to these embodiments, but comprises all possible embodiments within the spirit and scope of inventive thought and the following patent claims.

The features recited in dependent claims are mutually freely combinable unless otherwise explicitly stated.