DE102008034567A1 - Method for locating wirelessly communicating radio subscriber in e.g. parking area, involves correcting averaged phase difference of channels around estimated error, and determining position of transmitter from corrected phase difference - Google Patents

Abstract

The method involves estimating an error between an averaged phase difference and an actual phase difference of a set of channels by a combination of measured phases and/or averaged phase differences of the set of channels and/or another set of channels of a sequence. The averaged phase difference of the latter set of channels around the estimated error is corrected. A position of a transmitter (T1) is determined from the corrected phase difference of the latter set of channels, where the transmitter is used to transmit a sequence of signals to the former set of channels. An independent claim is also included for a system for locating a wirelessly communicating a radio subscriber, comprising a transmitter.

Description

The The invention relates to a method and a system for locating wireless communicating radio subscribers.

Methods are known from the prior art in which radio subscribers send and receive unsynchronized signals, wherein based on these signals, the position of a radio subscriber can be located. The publication WO 2008/025713 A1 describes such a method wherein at least two transmitters and at least two receivers are used to provide a position estimate for a transmitter. In this case, the receiver and at least one reference transmitter must have a known location, while the other stations are to locate. The number of recipients determines in how many dimensions the location can be performed. Due to the reference transmitter synchronization of the participants of the system is unnecessary.

In the German patent application DE 10 2007 043 649.3 as well as in the relevant publication S. Schwarzer, M. Vossiek, M. Pichler and A. Stelzer, "Precise Distance Measurement with IEEE 802.15.4 (ZigBee) Devices", IEEE Radio and Wireless Symposium, Orlando, Florida, USA, January 2008, pages 779-782 , a further method for locating unsynchronized radio subscribers is described, in which method a high positioning accuracy is achieved by using predetermined hopping schemes. In this case, a hopping scheme specifies at which times in a sequence of transmission times in which radio channels the transmitters of the radio subscribers emit signals. In this method, a transit time difference of the signal of a respective channel between two transmitters of the radio subscribers is determined on the basis of averaged phase differences of the respective channels used, and from this the position of one of the transmitters is determined. The averaged phase difference of a respective channel results from the arithmetic mean of the phases of the signals measured in the receivers, which are transmitted in a sequence of the hopping scheme in the respective channel.

In the process of the German patent application DE 10 2007 043 649.3 and the related publication arises by the averaging of the phase differences, where appropriate, an error that falsifies a precise position determination or impossible under certain conditions.

task The invention is therefore a method for locating unsynchronized To create radio subscribers, which is a reliable and exact position determination of a radio subscriber to be located guaranteed.

These Task is by the independent claims solved. Further developments of the invention are in the dependent Claims defined.

In the method according to the invention, the position of at least one transmitter is determined by means of a further transmitter and at least two receivers, wherein the transmitter each emit a sequence of a plurality of signals on channels. A channel is a radio channel that transmits data at a predetermined frequency. The sequence is defined by a hopping scheme, which defines the channel (s) in which one or more of the transmitters emit a signal for predefined transmission times. The hopping scheme can be, for example, one of the schemes described in the German patent application DE 10 2007 043 649.3 are defined. The entire disclosure content of this patent application is incorporated by reference into the content of the present application.

The according to the hopping scheme emitted signals are received by the receivers and their phases the recipients are measured. It is from the measured Phases of a respective channel an average phase difference of respective channel determined which of the position of at least a transmitter in relation to the other transmitter depends.

According to the invention an error between the averaged phase difference and the actual phase difference of the respective channel by a combination of the measured phases and / or the averaged phase differences of the respective channel and / or other channels of the sequence of the hopping scheme. Finally, the average phase difference of each channel corrected by the estimated error, and corrected from the Phase differences of the channels of the sequence eventually become determines the position of the at least one transmitter.

The method according to the invention is based on the knowledge that by a suitable Kom bination of the measured phases or the averaged phase differences in the channels of the sequence of the originally unknown error, which results from the averaging of the phase differences of the respective channel can be estimated, so that by a corresponding correction with the estimated error reliable and accurate position determination can be achieved. The averaged phase difference is in particular the arithmetic mean of the phase differences of a respective channel, wherein the number of channel uses in the sequence of the hopping scheme is averaged.

• – Sei I die Anzahl der Sender, wobei I ganzzahlig und größer oder gleich 2 ist.
• – Sei N die Anzahl der Hops/Sendezeitpunkte (d. h. N bestimmt die Länge des Hoppingschemas), wobei N ganzzahlig, gerade und größer oder gleich 4 ist.
• – Der in Hop n vom Sender Ti zu benutzende Kanal sei c Ti / n für alle i = 0, ... I – 1 und n = 0, ... N – 1.
• – Der Sendezeitpunkt für Hop n des Senders Ti sei t Ti / n für alle i = 0, ... I – 1 und n = 0, ... N – 1.
• – Die Differenz zwischen der Phase des Datenstroms und der Phase des Trägersignals in Kanal c_n des Senders Ti sei φ^Ti(c_n) für alle i = 0, ... I – 1 und n = 0, ... N – 1.

As already stated above, one of the hopping schemes which are described in the German patent application can be used in the method according to the invention DE 10 2007 043 649.3 to be discribed. The hopping scheme is characterized in particular by a special education law, which can be established by the following definitions:

• Let I be the number of transmitters where I is integer and greater than or equal to 2.
• Let N be the number of hops / send times (ie N determines the length of the hopping scheme), where N is integer, even and greater than or equal to 4.
• Let the channel to be used in Hop n from the transmitter Ti be c Ti / n for all i = 0,... I-1 and n = 0,... N-1.
• - The transmission time for Hop n of the transmitter Ti is t Ti / n for all i = 0, ... I - 1 and n = 0, ... N - 1.
• Let the difference between the phase of the data stream and the phase of the carrier signal in channel c _{n of} the transmitter Ti be φ ^Ti (c _n ) for all i = 0, ... I-1 and n = 0, ... N-1 ,

• a) Die Hoppingschemata sind für alle Sender Ti symmetrisch um ihren Mittelpunkt: cTin = cTiN-n-1 ∀ i = 0, ... I – 1 ∧ n = 0, ... N/2 – 1
• b) Zwei oder mehr Sender dürfen nie zeitgleich denselben Kanal c_n benutzen: cTin ≠ cTjn ∀ i, j = 0, ... I – 1 ∧ i ≠ j ∧ n = 0, ... N – 1 Für den Fall, dass zwei oder mehr Sender unterschiedliche, orthogonale Codes verwenden (z. B. DSSS, Spreizcode), um ihre Datenströme spektral zu spreizen (vgl. CDMA), kann Regel b) entfallen und mehrere Sender können auch zeitgleich einen Kanal belegen, um die spektrale Breite zu minimieren. Hierbei wäre jedoch mit Nachteilen zu rechnen (near-far-Problem, unzureichende Kreuzkorrelationseigenschaften der Codes).
• c) Die Mengen aller im Hoppingschema benutzten Kanäle c_n müssen für alle Sender Ti identisch sein, d. h. alle Sender müssen im Laufe des Hoppings dieselben Kanäle c_n benutzen, kein Sender darf einen oder mehrere Kanäle c_n gegenüber den anderen Sendern auslassen: {cTin |n = 0, ... N – 1} = {cTjn |n = 0, ... N – 1} ∀ i, j = 0, ... I – 1 Diese Forderung darf verletzt werden, falls einzelne Sender mit schlechterer Genauigkeit geortet werden sollen. Dann genügt auch eine Teilmenge der Kanäle c_n, die der ortsfeste Sender verwendet. Die Anzahl der übereinstimmenden Kanäle c_n darf jedoch nie kleiner als 2 sein.
• d) Die Menge aller im Hoppingschema verwendeten Kanäle c_n bildet eine lineare Frequenzrampe mit konstantem Frequenzabstand f_d zwischen den Kanälen c_n (evtl. nach einer Umsortierung und der Entfernung mehrfach angesprungener Kanäle): f(kn) = f0 + n·fd ∀ n = 0, ... N – 1f₀ ist hierbei die niedrigste zu verwendende Frequenz, z. B. f₀ = 2405 MHz bei IEEE 802.15.4. Diese Regel ist evtl. nicht zwingend. Es kann auch ein Kanal ausgelassen werden, ohne die Theorie zu verletzen. Jedoch erschwert dies die anschließende Auswertung in nicht unerheblichem Maße.
• e) Die Sendezeitpunkte eines Senders Ti müssen über alle Hops eines Hoppingschemas einen konstanten Abstand aufweisen: tTin+1 – tTin = tTin – tTin-1 ∀ i = 0, ... I – 1 ∧ n = 1, ... N – 2 Dieser für einen Sender konstante Abstand kann von Sender zu Sender verschieden sein. Die Sendezeitpunkte müssen keine weiteren Anforderungen erfüllen, also auch nicht die nach einer Synchronisation zwischen den Sendern.
• f) Die Beziehung zwischen der Phase des Datenstroms und der Phase des Trägersignals eines jeden Kanals (k_n) muss konstant sein für einen Sender Ti: φTi(kTin ) = φTi(kTim ) ∀ i = 0, ... I – 1 ∧ n = 0, ... N – 1 ∧ {m|cTjn = cTjn } Diese Forderung kann in den Sendern mit geeigneten Vorrichtungen zur Signalerzeugung (z. B. Integer-PLL) erfüllt werden.

Based on this, the hopping scheme is created according to the following rules:

• a) The hopping schemes are symmetrical about their center for all transmitters Ti: c Ti n = c Ti Nn-1 ∀ i = 0, ... I - 1 ∧ n = 0, ... N / 2 - 1
• b) Two or more transmitters may never use the same channel c _{n at the} same time: c Ti n C tj n ∀ i, j = 0, ... I - 1 ∧ i ≠ j ∧ n = 0, ... N - 1 In the event that two or more transmitters use different orthogonal codes (eg DSSS, spreading code) to spectrally spread their data streams (see CDMA), rule b) can be omitted and several transmitters can occupy a channel at the same time to minimize the spectral width. However, disadvantages would have to be expected (near-far problem, insufficient cross-correlation properties of the codes).
• c) The quantities of all the channels c _n used in the hopping scheme must be identical for all transmitters Ti, ie all transmitters must use the same channels c _n during the hopping, and no transmitter may omit one or more channels c _n from the other transmitters: {c Ti n | n = 0, ... N - 1} = {c tj n | n = 0, ... N - 1} ∀ i, j = 0, ... I - 1 This requirement may be violated if individual transmitters are to be located with less accuracy. Then also a subset of the channels c _n , which uses the stationary transmitter is sufficient. However, the number of matching channels c _n must never be less than 2.
• d) The set of all channels c _n used in the hopping scheme forms a linear frequency ramp with a constant frequency spacing f _d between the channels c _n (possibly after a resorting and the removal of multiply branched channels): f (k n ) = f 0 + n · f d ∀ n = 0, ... N - 1 f ₀ is the lowest frequency to be used, z. B. f ₀ = 2405 MHz in IEEE 802.15.4. This rule may not be mandatory. It is also possible to omit a channel without violating the theory. However, this complicates the subsequent evaluation to a considerable extent.
• e) The transmission times of a transmitter Ti must have a constant distance over all hops of a hopping scheme: t Ti n + 1 - t Ti n = t Ti n - t Ti n-1 ∀ i = 0, ... I - 1 ∧ n = 1, ... N - 2 This constant distance for a transmitter may vary from transmitter to transmitter. The transmission times do not have to meet any further requirements, that is not even after a synchronization between the stations.
• f) The relationship between the phase of the data stream and the phase of the carrier signal of each Ka nals (k _n ) must be constant for a transmitter Ti: φ Ti (k Ti n ) = φ Ti (k Ti m ) ∀ i = 0, ... I - 1 ∧ n = 0, ... N - 1 ∧ {m | c tj n = c tj n } This requirement can be met in the transmitters with suitable signal generation devices (eg integer PLL).

The Rules a), e) and f) are mandatory, rules b), c) and d) may be disregarded to be left.

It is conceivable, an emergent from the described education law Hopping scheme by adding additional channels to expand in the midst or after the hopping scheme, however not be used for the measurement. Such a hopping scheme is also to be added to the scope of the invention. In a preferred variant of the invention becomes a special Hopping scheme used, which defines further below and a simple estimate of the error between the averaged and the actual phase difference allows.

In a particularly preferred embodiment of the invention the position of the at least one transmitter is corrected from the Phase differences in the channels of the sequence by a Transformation into the time domain, in particular by a Inverse Fourier transform determined. This results from a Maximum in the time domain a runtime difference, from the the position of the at least one transmitter is determined.

In a variant of the invention, the error is estimated or determined for each channel c with the aid of the following error function err [c]: err [c] = - (φ * TDOA [c] - 2φ * TDOA [c - 1] + φ * TDOA [c - 2]) - err [c - 2] ∀ c = 2, ..., C - 1 where φ * / TDOA [c] is the average phase difference in channel c and C represents the total number of channels used according to the hopping scheme.

These Variant of the invention makes assumptions about the channel model and is suitable for use in a location where Only a few multipath paths through reflections occur, in particular when locating in open terrain outside of Buildings.

In a further preferred embodiment are for the above error function err [c] the values of err [0] and / or err [1] taking into account parameters regarding determines the arrangement of the radio subscriber, in particular of maximum and / or minimal possible intervals between the at least one transmitter and the other transmitter. In this way the uniqueness of the error function err [c] is ensured.

In a further variant of the method according to the invention, the error is estimated using the following function: E [c] = A (c) -B (c) -C (c) -D (c) in which
A (c) is the transmission time of a signal transmitted by the at least one transmitter in the first half of the sequence of the hopping scheme in channel c;
B (c) is the transmission time of the signal transmitted by the further transmitter in the first half of the sequence of the hopping scheme in the channel c;
C (c) is the transmission time of the signal transmitted by the at least one transmitter in the second half of the sequence of the hopping scheme in channel c;
D (c) is the transmission time of the signal transmitted by the further transmitter in the second half of the sequence of the hopping scheme in the channel c.

These Variant of the method is characterized by the fact that no assumptions about the channel model are taken and the method thus also in Measuring environments can be used with multipath. In the process a detailed error model of the measuring system is used, where realistic assumptions about the measuring system are taken become.

wobei i = 0, ..., C – 1 die Kanäle indiziert und C die Gesamtanzahl der Kanäle ist;
wobei

die gemessene Phase beim Empfänger Ry für ein vom Sender Tx im Kanal c gesendetes Signal im Intervall [0, ..., I / 2 – 1] der aufeinander folgenden Sendezeitpunkte der Sequenz des Hoppingschemas bezeichnet, wobei I der Gesamtanzahl an Sendezeitpunkten einer Sequenz ist; wobei

die gemessene Phase beim Empfänger Ry für ein vom Sender Tx im Kanal c gesendetes Signal im Intervall [ I / 2, ..., I – 1] der aufeinander folgenden Sendezeitpunkte der Sequenz des Hoppingschemas bezeichnet, wobei I der Gesamtanzahl an Sendezeitpunkten einer Sequenz ist.In a particularly preferred embodiment, the error is determined by means of an error function err [c] by the solution of the following equation: 1 2 (M φ, up [c] - M φ, down [c]) + err [c] = s · E [c] where s is a constant,
in which

where i = 0, ..., C-1 indicates the channels and C is the total number of channels;
in which

denotes the measured phase at the receiver Ry for a signal transmitted by the transmitter Tx in the channel c in the interval [0, ..., I / 2 - 1] of the successive transmission times of the sequence of the hopping scheme, where I is the total number of transmission times of a sequence ; in which

denotes the measured phase at the receiver Ry for a signal transmitted by the transmitter Tx in the channel c in the interval [I / 2, ..., I-1] of the successive transmission times of the sequence of the hopping scheme, where I is the total number of transmission times of a sequence ,

In a preferred variant, in turn, parameters of the arrangement of the radio subscribers are taken into account in order to unambiguously determine the error. With the help of the parameters a value for s is determined and based on that the error is determined with the help of the following error function err [c]: err [c] = s · E [c] - 1 2 (M φ, up [c] - M φ, down [C])

In a particularly preferred embodiment of the method according to the invention, a hopping scheme is used which is designed at least partially and preferably in the entire sequence in such a way that the value E [c] is constant. If such a hopping scheme is used, the error function err [c] can be easily determined for the part of the sequence of the hopping scheme with constant E [c] as follows: err [c] = err [c - 1] - 1 2 (M φ, up [c] - M φ, down [c - 1] - M φ, down [c] + M φ, down [c - 1]) ∀ c = 1, ..., C - 1

The Inventors were able to show that in a hopping scheme with constant E [c] the error is no longer of the above size s depends and therefore particularly simple only from appropriate measured phases of the considered and previous channel can be.

The inventive method can be used with any, wirelessly transmitted signals. In a preferred variant, however, signals according to the Standard IEEE 802.15.4 uses, for example, the standards Zig-Bee and WirelessHART is used as a PHY layer.

Next In the method described above, the invention further comprises System for locating wirelessly communicating radio subscribers, comprising at least one transmitter and another transmitter and at least two receivers, with the system in operation the position of the at least one transmitter with the help of the other Sender and the at least two receivers determined. The System is designed such that each variant of the above in accordance with the invention the system is feasible.

embodiments The invention will be described below with reference to the attached Figures detailed.

It demonstrate:

1 a schematic representation of an arrangement of several radio subscribers for locating one of the participants shown;

2 a tabular overview of examples of hopping schemes usable in the invention;

3 a representation of several diagrams to illustrate the errors contained in the averaged phase differences; and

4 and 5 Charts showing preferred embodiments of hopping schemes used in the invention.

1 shows a schematic representation of an embodiment of an arrangement of radio subscribers for carrying out the method according to the invention. The arrangement contains two transmitters T1 and T2, which emit radio signals in predetermined channels according to the standard IEEE 802.15.4 (ZigBee). These signals are received by the receivers R1 and R2. In this case, preferably 16 radio channels in the ISM band (ISM = Industrial Scientific Medical) are used around 2.45 GHz, wherein in the embodiment described here the channels are designated in ascending order with numbers 0 to 15 and the center frequency of adjacent channels differs by 5 MHz. In particular, channel 0 has a center frequency of 2405 MHz, channel 1 of 2410 MHz, etc. Thus, the channel with the highest channel number 15 has a center frequency of 2480 MHz. In the scenario of 1 the position of the transmitter T1 is located as distance d _{T1, T2} to the transmitter T2. The positions of the receivers R1 and R2 and of the transmitter T2 are known. For location, the transmitters T1 and T2 send unsynchronized signals according to a predetermined hopping scheme, and in the respective receiver Rj (j = 1, 2), for each channel c, an arithmetically averaged phase φ [Ti; Rj] / c of the Transmitter Ti (i = 1, 2) determines the incoming signal.

2 shows examples of possible usable hopping schemes for N transmission times, wherein the hopping schemes numbered 1 to 9 relate to an embodiment with two transmitters T1 and T2 and the hopping scheme number 10 represents an embodiment with 16 transmitters T1 to T16. In this case, c (Tx) denotes the channel in which a corresponding transmitter Tx at a transmission time n (n = 0, ..., 31). In the 2 reproduced hopping schemes correspond to those in the patent application DE 10 2007 043 649.3 used hopping schemes. Due to the characteristics of the hopping schemes, it is possible to perform a location of one of the participants for unsynchronized radio subscribers. According to the invention, the in 2 hopping schemes used are shown, but in a preferred variant, another hopping scheme is used with particular advantages, as will be described in detail below. Each of the hopping schemes used is characterized in that the sequence of the respective hopping scheme has a first and a second half which are symmetrical to one another, ie the channels used in the first half of the sequence at the respective transmission times are in reverse order in the second half the sequence used. The corresponding symmetry axes for each hopping scheme are in 2 indicated by dashed lines.

In analogy to the method of the patent application DE 10 2007 043 649.3 For example, in the embodiment of the invention described herein, the phase positions φ [Ti; Rj] / c are determined as an arithmetic mean of the phases of a channel measured twice in a sequence of the hopping scheme. This averaging is critical to the result and exploits the advantageous symmetry properties of the hopping scheme. To determine the transit time τ of a signal of the channel c between the transmitters T1 and T2, the following phase difference is determined: φ TDOA [c] = φ [T1, R1] c - φ [T1, R2] c - φ [T2, R1] c + φ [T2, R2] c

With the help of the relationship φ TDOA [c] = 2π · f c · Τ ∀ c ∈ C can be calculated by the transit time difference τ. Here, f _C corresponds to the center frequency of the corresponding channel c, where a total of C channels exist.

The Use of a symmetric hopping scheme and the arithmetic Averaging the signal phases are necessary to correct the errors by the lack of synchronization of the transmitter and receiver forcibly resulted in largely eliminating. It remains a small and unavoidable residual error in the difference estimation, which is of the order of the frequency errors the transmission crystals of the corresponding transmitter is and usually less than 100 ppm (= 1/10000).

The determination of the transit time difference τ with a symmetrical hopping scheme just described corresponds essentially to that in the patent application DE 10 2007 043 649.3 disclosed calculation. According to the invention, however, it has been recognized that an error can result from the arithmetic averaging of the phase positions. In the method according to the invention, this error is estimated and included in the determination of the transit time difference and the resulting position of the transmitter.

In general, the arithmetic averaging of two phases creates ambiguity. This ambiguity is again due to the ambiguity of the phase information, which can be represented as follows: φ * = φ + n · 2π ∀ n ∈ Z

If you average two phases φ * / A and φ * / B in the real plane, you get the following arithmetic mean: 1 2 (φ * A + φ * B ) = 1 2 [(Φ A + n A · 2π) + (φ B + n B · 2π)] ∀ n ∈ Z = 1 2 (φ A + φ B ) + (n A + n B ) · Π

In the above equation, φ * / A and φ * / B denote the measured phases, and φ _A and φ _B represent the actual phases. It can be seen from the above equation that to the expected arithmetic mean of the actual phases φ _A and φ _B integer multiple of π is added. As a result, each combination of two measured phase information has two arithmetic mean different from π.

This can also be seen in the complex representation plane in which the arithmetic mean is as follows:

Generally has the nth root of a complex number of exactly n solutions, evenly distributed on the unit circle are. The square root of a complex number thus has exactly two solutions whose phases differ by π.

In the location method according to the invention, two possible solutions for the arithmetic mean thus exist for each channel number c from the phase positions of the received signals. The corresponding phase slope curve, which represents the functional relationship between the channel numbers and the averaged phase differences φ * / TDOA [c], thus has an error function which has 2 ^c possible states when C is the number of channels used. In the following, this error is referred to as err [c].

In 3 the occurrence of this error is illustrated by the diagrams D1, D2 and D3. The diagram D1 shows the actual phase _{slope curve} , which shows the relationship between the channel c and the actual phase φ _TDOA [c]. As explained above, the averaged phase φ * / TDOA [c] represented in the diagram D3 has a corresponding error err [c] shown in the diagram D2. The error results from the multiple significance of the arithmetic averaging and assumes either the value 0 or the value π. One recognizes 3 in that the mean faulty phase slope curve according to diagram D3 differs significantly from the actual phase slope curve according to diagram D1.

In the embodiment of the invention described here, the transit time difference τ of signals between two transmitters is determined by means of an inverse, discrete Fourier transform IDFT as follows:

In the case of location in environments without multipath, ie without reflections of the transmitted signals to corresponding objects, the maximum of the magnitude spectrum is | H [k] | proportional to the sought transit time difference τ. Multipaths that are longer than the resolution of this transformation are represented as their own local maxima. Shorter multipaths merge with the global maximum and move it. Due to the finite resolving power, there is thus a certain resistance to multipath, which is proportional to the total used bandwidth of the measuring system. The effect of the error function err [c] on the spectrum H [k] is as follows: φ * TDOA [c] = φ TDOA [c] + err [c] ⇒ exp {jφ * TDOA [c]} = exp {jφ * TDOA [c]} · exp {j · err [c]} ⇒ H * [k] = H [k] · ERR [k]

The Spectrum H [k] is compared with the Fourier transformed ERR [k] of the error err [c] folded. The transformed ERR [k] of the binary Function err [c] results from a superposition of many Sinc functions, making the maximum information in H [k] irrevocable is falsified. The magnitude of the Error can correspond to the uniqueness range of the measuring system, making localization impossible. Since exp {j · err [c]} real and ERR [k] is thus symmetric, is also a lossless one Unfolding impossible.

In 3 are the effects of the error err [c] after performing the inverse Fourier transform IDFT illustrated by the diagrams D4, D5 and D6. Along the abscissa of these diagrams, the transit time difference τ in meters and along the ordinate the normalized amount B of the inverse Fourier transform of the corresponding overlying phase curve is reproduced. It can be seen from the diagram D4 that for the actual, non-faulty phase _{slope curve .PHI. TDOA} [c] an unambiguous transit time difference results from a maximum value, the maximum value in the example of _FIG 3 at about 5 m. Diagram D5 shows the Fourier transform ERR [k] of the error err [c]. This Fourier-transformed is folded with H [k], so that a spectrum H * [k] according to the diagram D6 results for the measured, error-prone phase slope curve φ * / TDOA [c]. It can be seen that not only a clear maximum is read from the spectrum, which corresponds to the transit time difference. Out 3 Thus, it becomes clear that an estimate of the corresponding error err [c] is required to determine the transit time difference. Hereinafter, embodiments will be described which suitably estimate the error err [c].

In the following two variants are described how the error function err [c] can be estimated. In the first variant, a favorable channel model is adopted and in the second variant is a exploited detailed error model of the measuring system. After estimating the error function err [c], it can be removed from the _errored phase _{slope curve} φ _TDOA [c] as follows: φ TDOA [c] = φ * TDOA [c] - err [c]

Due to the uniqueness of the phase information from 0 to 2π, the following also applies: φ TDOA [c] = φ * TDOA [c] + err [c]

In front the estimation of the error function has this equation c value-discrete unknowns from {0, π} in err [c], since the Error due to arithmetic averaging is either 0 or π.

In the first variant of the method according to the invention, it is assumed that the measurements for locating a radio subscriber are carried out in a reusable-poor environment. Based on this, appropriate assumptions can be made about the channel model and the problem of determining the error function can be simplified. This variant of the method is particularly suitable for locating in environments outside of buildings, such. B. on parking lots, green areas, parks and the like. Due to the assumption of a reusable-poor environment, it is assumed that the probability spectrum H [k] consists of only one peak at the unknown and searched position k ₀ of the radio subscriber to be located.

This assumption can be expressed mathematically as follows: H * [k] · ERR [k]! / = δ [k - k ₀ ] with the diracpulse δ [k] shifted by k ₀ .

Transformed in the time domain then the following relationship arises: exp {jφ * TDOA [c]} · exp {j · err [c]} = exp {j · k 0 · C} φ * TDOA [c] + err [c] = k 0 · c

It can be seen that for a single peak in the spectrum, the phase slope curve corrected by the error function err [c] increases linearly with the channel number. The slope is proportional to the sought, but unknown transit time difference. Two-fold derivation gives the following relationship:

2err [c - 1] = 0, since exp {j2π} = 0. This leads to the following error function: err [c] = - (φ * TDOA [c] - 2φ * TDOA [c - 1] + φ * TDOA [c - 2]) - err [c - 2] ∀ c = 2, ..., C - 1

There err [c] can take only the values 0 and π, the in value determined for the last equation for err [c] always rounded to a multiple of π and then by adding multiples of 2π to {0, π} be displayed in the correct phase. According to the just Thus, the error described err [c] in a channel for reusable environments based on those in the corresponding Channel and measured in the two previous channels Phase differences as well as the error in the previous channel be determined.

err [c] can thus be determined without knowing the actual position k ₀ by a simple sequence of additions and subtractions, where only meaningful assumptions have to be made for err [0] and err [1]. It can be assumed err [0] = 0, which does not distort the result, since a constant phase offset on the phase slope curve causes only one rotation of the complex IDFT spectrum, which remains without consequences in the magnitude spectrum. Such a simple assumption can not be made for err [1]. This is because a correction of the phase slope curve with the above error still contains a residual ambiguity. In particular, the smoothing of the faulty phase slope curve according to the above error function always leads to two identically good results, the phase slopes of which differ exactly by π. This leads to two equal term difference estimates, which differ exactly by half the uniqueness range of the measuring system. From the initial ambiguity of C variables has thus become an ambiguity of only one variable. To eliminate this ambiguity, suitable additional assumptions for the measuring system are considered in the variant of the invention described here, such. B. a maximum possible transit time difference, the accumulation of intersections in two-dimensional position determinations and the like. In particular, in a first step, err [1] = 0 can be assumed, and later this assumption can possibly be revised to err [1] = π, provided that a contradiction arises from the further assumptions, for example that a runtime difference results in the Fourier transformation which is greater than a maximum possible transit time difference.

The above variant for determining the error function has the Disadvantage of making assumptions about the channel model and based on these assumptions only for multipath-free measurement environments suitable is. In contrast to this, the following is described second variant of the invention can be used universally. At this second variant is a detailed error model of the measuring system exploited to thereby estimate the error as from the further explanations.

The Measuring system used according to the invention starts from unsynchronized transmitters and receivers whose frequency standards are flawed. In order nevertheless nevertheless a transmitter with unknown position To locate a synchronization of the receiver is mathematical produced by additionally the phase position of the signals a stationary and local transmitter is measured and linked to the phasing of the station to be located becomes. An error model of the measuring system can show that this procedure the errors resulting from the unsynchronized frequency normal eli miniert in the receivers. Based on this error model In addition, a method of avoidance can be found derive the ambiguity of the phase slope curve.

The reception phase of the ith signal of a given hopping scheme, which is transmitted by a transmitter T and received by a receiver R, can be written as follows:

τ^[T,R]:

Laufzeit des Signals von Sender T zu Empfänger R.

i:

Position in der Hoppingsequenz, i = 0, 1, ..., I – 1 mit der Länge der Hoppingsequenz I.

c [T] / i:

Kanalnummer 0, ..., C – 1 des Signals an Hoppingsequenzposition i im Sender T. Die Menge der c [T] / i über alle Sender wird als „Hoppingschema” bezeichnet.

ω_RI,c:

Ideale Kreisfrequenz des Hochfrequenz-Trägersignals in Kanal c. In der Regel gilt ω_RI,c = ω₀ + c·Δω mit der Trägerkreisfrequenz im ersten Kanal ω₀ und dem Kreisfrequenzschritt zwischen zwei Kanälen Δω.

ω_LI:

Ideale Kreisfrequenz des lokalen Oszillators (sog. LO-Frequenz) im Empfänger, der zum Heruntermischen genutzt wird.

ω_SI:

Ideale Abtastkreisfrequenz des Empfängers.

ω_CI:

Ideale Taktkreisfrequenz des Mikrocontrollers im Sender, der das Aussenden veranlasst.

φ_R0,c:

Phasendifferenz zwischen Taktkreisfrequenz des Mikrocontrollers und Phase des ausgesendeten Signals in Kanal c. Durch eine geeignete Vorrichtung zur Erzeugung der LO-Frequenz (z. B. Integer-PLL) und einer Ableitung der LO-Frequenz aus dem Mikrocontroller-Takt kann dieser Term vernachlässigt werden.

φ [R] / L0:

Phase des lokalen Oszillators im Empfänger R bei t = 0. Durch eine geeignete Vorrichtung zur Erzeugung der LO-Frequenz (z. B. Integer-PLL) kann dieser Term vernachlässigt werden.

φ [R] / S0:

Phasendifferenz zwischen lokalem Oszillator und Abtastvorgang im Empfänger R. In der Regel ist dieser Term durch eine Ableitung des Abtasttakts aus dem Mikrocontroller-Takt (oder umgekehrt) vernachlässigbar.

φ [T] / C0:

Anfangsphase der Taktkreisfrequenz des Mikrocontrollers im Sender T.

δω [T] / T:

Relativer Fehler der Sendefrequenz in Sender T (z. B. 100 ppm = 1/10000).

δω [R] / L:

Relativer Fehler der Frequenz des lokalen Oszillators in Empfänger R.

δω [R] / S:

Relativer Fehler der Abtastrate in Empfänger R.

N:

Ideale Anzahl von Abtastpunkten im Empfänger zwischen dem Aussenden zweier Signale im Sender.

k [T] / D0:

Anzahl der Taktzyklen im Sender von t = 0 bis zum Aussenden des ersten Signals i = 0.

Δk_R,c:

Anzahl der Taktzyklen im Sender, die den Phasenunterschied zwischen dem aufmodulierten Datenstrom und dem Trägersignal beschreiben.

The individual variables of the above equation are defined as follows:

τ ^{[T, R]} :

Duration of the signal from transmitter T to receiver R.

i:

Position in the hopping sequence, i = 0, 1,..., I-1 with the length of the hopping sequence I.

c [T] / i:

Channel number 0, ..., C-1 of the signal at hopping sequence position i in the transmitter T. The amount of c [T] / i across all transmitters is referred to as "hopping scheme".

ω _{RI, c} :

Ideal angular frequency of the high frequency carrier signal in channel c. In general, ω _{RI, c} = ω ₀ + c · Δω with the carrier circuit frequency in the first channel ω ₀ and the angular frequency step between two channels Δω.

ω _LI :

Ideal angular frequency of the local oscillator (so-called LO frequency) in the receiver, which is used for downmixing.

ω _SI :

Ideal sampling frequency of the receiver.

ω _CI :

Ideal clock frequency of the microcontroller in the transmitter, which causes the emission.

φ _{R0, c} :

Phase difference between clock frequency of the microcontroller and phase of the transmitted signal in channel c. By a suitable device for generating the LO frequency (eg integer PLL) and a derivation of the LO frequency from the microcontroller clock this term can be neglected.

φ [R] / L0:

Phase of the local oscillator in the receiver R at t = 0. By a suitable device for generating the LO frequency (eg integer PLL) this term can be neglected.

φ [R] / S0:

Phase difference between the local oscillator and the sampling process in the receiver R. As a rule, this term is negligible by a derivation of the sampling clock from the microcontroller clock (or vice versa).

φ [T] / C0:

Initial phase of the clock frequency of the microcontroller in the transmitter T.

δω [T] / T:

Relative error of the transmission frequency in transmitter T (eg 100 ppm = 1/10000).

δω [R] / L:

Relative error of the frequency of the local oscillator in receiver R.

δω [R] / S:

Relative error of the sampling rate in receiver R.

N:

Ideal number of sampling points in the receiver between the transmission of two signals in the transmitter.

k [T] / D0:

Number of clock cycles in the transmitter from t = 0 to the transmission of the first signal i = 0.

Δk _{R, c} :

Number of clock cycles in the transmitter that describe the phase difference between the modulated data stream and the carrier signal.

• Term (1): Mit Sendefehler behafteter Laufzeitterm. Dieser Term enthält als einziger die Laufzeitdifferenz zwischen einem Sender und einem Empfänger und bein haltet somit als einziger eine gesuchte Nutzinformation.
• Term (2): Differenzfehler zwischen den Fehlern der Sende- und Empfangsfrequenzen in den Hochfrequenzteilen der in den Sendern bzw. Empfängern verwendeten Schaltungen.
• Term (3): Anfangsfehler durch einen verzögerten Beginn der Sequenz des Hoppingschemas und Phasenfehler zwischen dem aufmodulierten Datenstrom und dem Trägersignal im Sender.
• Term (4): Aufintegrierter Differenzterm zwischen den Fehlern der Sende- und Empfangsfrequenzen in den Hochfrequenz-Teilen der in den Sendern bzw. Empfängern verwendeten Schaltungen, wobei der Differenzfehler durch die zeitliche Pause zwischen zwei benachbarten Positionen in der Hoppingsequenz entsteht.

The errors contained in each of the above terms (1) to (4) can be interpreted as follows:

• Term (1): Transit term with send error. This term is the only one containing the transit time difference between a sender and a receiver, and thus, as the only one, holds a wanted payload.
• Term (2): difference error between the errors of the transmission and reception frequencies in the high-frequency parts of the circuits used in the transmitters or receivers.
• Term (3): Initial error due to a delayed start of the sequence of the hopping scheme and phase errors between the modulated data stream and the carrier signal in the transmitter.
• Term (4): Integrated difference term between the errors of the transmission and reception frequencies in the high-frequency parts of the circuits used in the transmitters or receivers, the difference error arising from the time interval between two adjacent positions in the hopping sequence.

For the measuring system, it can be assumed that the initial phases of each receiver are linked together. This results in that the receiver phases can all be assumed to be 0. Furthermore, the frequencies of the local oscillator and the sampling process in the receiver are linked together and thus subject to the same error. Consequently, the following simplifications can be assumed: φ R0, c = 0 φ [R] L0 = 0 φ [R] S0 = 0 φ [R] L = δω [R] S

(x, y = 1, 2) wie folgt:

The error-prone phase slope curve results when using two receivers R1 and R2 and two transmitters T1 and T2 by arithmetic averaging of the respective reception phases

(x, y = 1, 2) as follows:

die gemessene Phase beim Empfänger Ry für ein vom Sender Tx im Kanal c ausgesendetes Signal im Intervall [0, ..., I – 1] der aufeinander folgenden Sendezeitpunkte der Sequenz des Hoppingschemas, wobei I wiederum die Gesamtanzahl an Sendezeitpunkten einer Sequenz ist.Here, C [Tx] / i denotes the channel used by the transmitter Tx at the time of transmission i, and c denotes the channel number of one of the possible channels between 0 and C-1

the measured phase at the receiver Ry for a signal transmitted by the transmitter Tx in the channel c in the interval [0, ..., I-1] of the successive transmission times of the sequence of the hopping scheme, where I is again the total number of transmission times of a sequence.

Of the Error term in the last line of the above equation has due the symmetry of the hopping scheme a very small slope and carries not significant for error consideration. He results from the Breaks between two transmission times and is realistic Systems negligible. Only with very long waiting times between two transmission times this error becomes dominant.

The Runtime terms according to the first line of the last one Equation are still with the relative errors of the respective transmission frequencies Afflict, which, however, only minimal errors on the order of magnitude cause the frequency error. Are the signals according to the Standard IEEE 802.15.4 sent out, is a relative error of Transmission frequencies that is less than 40 ppm, resulting in an error in the transit time difference estimate of up to 0.004 can. This residual error is unavoidable, but negligible small. Only the ambiguities through arithmetic averaging are still disturbing.

φ*TDOA [c] = 12 (Mφ,up[c] + Mφ,down[c]) If one divides the sequence of a hopping scheme into a front half (so-called "Up Ramp") and a rear half (so-called "Down Ramp") and one leads the arithmetic averaging not on channel level, but for corresponding phase differences M _{φ, up} [c ] and M _{φ, down} [c] of the Up Ramps and Down Ramps, you get the following result:

φ * TDOA [c] = 1 2 (M φ, up [c] + M φ, down [C])

die gemessene Phase beim Empfänger Ry für ein vom Sender Tx in Kanal c ausgesen detes Signal im Intervall [i ∈ 0, ..., I / 2 – 1] der aufeinander folgende Sendezeitpunkte der Sequenz des Hoppingschemas, wobei I die Gesamtanzahl an Sendezeitpunkten einer Sequenz ist.This designates

the measured phase at the receiver Ry for a signal emitted by the transmitter Tx in channel c in the interval [i ∈ 0, ..., I / 2 - 1] of the successive transmission times of the sequence of the hopping scheme, where I is the total number of transmission times of a hopping scheme Sequence is.

die gemessene Phase beim Empfänger Ry für ein vom Sender Tx im Kanal c ausgesendetes Signal im Intervall [ I / 2, ..., I – 1] der aufeinander folgenden Sendezeitpunkte der Sequenz des Hoppingschemas, wobei I wiederum die Gesamtanzahl an Sendezeitpunkten einer Sequenz ist.Analog called

the measured phase at the receiver Ry for a signal transmitted by the transmitter Tx in the channel c in the interval [I / 2, ..., I-1] of the successive transmission times of the sequence of the hopping scheme, where I is again the total number of transmission times of a sequence ,

The function φ * / TDOA [c] again contains the error function err [c]. However, considering now the error models separately for M _{φ, up} [c] and M _{φ, down} [c], one finds that both terms contain the same searched frequency ramp as φ * / TDOA [c], but also with a similar one Error term are afflicted, which now no longer grows linearly with a small slope, but is unsteady. In addition, the two terms can not contain an error function of the form err [c], since no averaging has taken place so far.

The terms M _{φ, up} [c] and M _{φ, down} [c] can be transformed as follows:

there are the functions A (c), B (c), C (c) and D (c) of the used Hopping sequence dependent. They describe in which transmission time the hopping sequence uses channel c. In particular, corresponds A (c) the relationship between the channel c and the transmission time for the transmitter T1 in the first half of the hopping sequence. B (c) corresponds to the relationship between the channel c and the transmission time for the transmitter T2 in the first half of the hopping sequence. C (c) corresponds to the relationship between the channel c and the transmission time for the transmitter T1 in the second half of the hopping sequence. D (c) represents the relationship between the channel c and the transmission time for the transmitter T2 in the second half the hopping sequence.

In the in 2 These hopping schemes are usually not linear in parameter c, but have one or more discontinuities. M _{φ, up} [c] and M _{φ, down} [c] can therefore not be used directly to estimate the transit time difference. The discontinuities in the error terms are eliminated by the subsequent averaging, but the error function err [c] remains. The aim of the variant of the method according to the invention described here is now, taking into account the special properties of the error terms in M _{φ, up} [c] and M _{φ, down} [c] the error function err [c] on φ * / TDOA [c] appreciate and correct.

Since the hopping sequences used according to the invention are symmetrical, the following relationship exists between the above functions A (c), B (c), C (c) and D (c): A (c) + C (c) = B (c) + D (c) = const.

Using the realistic assumption δω [x] / x * δω [y] / y << δω [z] / z, the error terms in M _{φ, up} [c] and M _{φ, down} [c] can each be summarized as follows :

sowie der für eine Hoppingsequenz charakteristischen Funktion E[c], welche wie folgt lautet: E[c] = A(c) – B(c) – C(c) + D(c) = 2[A(c) – B(c)] = 2[D(c) – C(c)] If one subtracts the above functions from one another and divides them by 2, the following relationship arises: 1 2 (M φ, up [c] - M φ, down [c]) = s [c] · E [c] - err [c] with an error err [c] and the slope function

and the characteristic E [c] characteristic of a hopping sequence, which reads as follows: E [c] = A (c) -B (c) -C (c) + D (c) = 2 [A (c) -B (c)] = 2 [D (c) -C (c)]

Under the realistic assumption that Δω << ω ₀ , s [c] simplifies to a constant function, which reads as follows:

The function 1/2 (M _{φ, up} [c] - M _{φ, down} [c]) is thus a version of the function E [c] scaled by the factor s. It is also subject to an error function err [c], which is unknown. Since E [c] is known from the hopping scheme, this error function can be determined very easily. An essential feature of the invention is that this error function is identical to the error function on φ * / TDOA [c] - 1/2 (M _{φ, up} [c] + M _{φ, down} [c]). It is true that:

Where n _{φ, up} [c] π denotes the phase shift between the measured phase difference and the actual phase difference for the first half of the hopping sequence and n _{φ, down} [c] π the phase shift between the measured phase difference and the actual phase difference for the second half of the hopping sequence. Were M φ, up [C] and M φ, down [C] determined from the actual and not from the measured reception phase.

Since n _{φ, down} [c] π is an integer, in complex notation exp {jn _{φ, down} [c] π} = exp {-jn _{φ, down} [c] π} = {0, -1}. Thus, adding the phase n _{φ, down} [c] π as well as subtracting the phase n _{φ, down} [c] π results in the same error function. The error function err [c] for φ * / TDOA [c] can thus be determined simply by determining the error lerfunktion on the halved subtraction 1/2 (M _{φ, up} [c] - M _{φ, down} [c]) take place.

Taking into account the error function err [c], the following relationship thus results: 1 2 (M φ, up [c] - M φ, down [c]) + err [c] = s · E [c] ⇒ err [c] = s · E [c] - 1 2 (M φ, up [c] - M φ, down [C])

There err [c] can take only the values 0 and π, the in value determined for the last equation for err [c] again always rounded to a multiple of π and then by adding multiples of 2π to {0, π} be displayed in the correct phase.

The only remaining unknown is the constant value of s, where this in turn z. B. by considering restrictions of the measuring system, such. B. a maximum possible distance between the transmitters or other parameters can be determined.

In a particularly preferred embodiment, however, it is also possible to dispense with the determination of s. This is ensured by the use of a special hopping scheme chosen such that E [c] is constant. For such a hopping scheme, the following condition results: E [c] = 2 [A (c) -B (c)] = 2 [D (c) -C (c)] ! = const. ⇒ A (c) - B (c) = D (c) - C (c) = const. = Δi

If we now derive the error function err [c] after the channel number c, the following relationship arises: 1 2 (M φ, up [c] - M φ, down [c]) + err [c] ! = s · E [c] d dc 1 2 (M φ, up [c] - M φ, down [c]) + d dc err [c] = s · d dc E [c] 1 2 (M φ, up [c] - M φ, up [c - 1] - M φ, down [c] + M φ, down [c - 1]) + err [c] - err [c - 1] = 0 ⇒ err [c] = err [c - 1] - 1 2 (M φ, up [c] - M φ, up [c - 1] - M φ, down [c] + M φ, down [c - 1]) ∀ c = 1, ..., C - 1

Also Here, err [c] must be rounded to a multiple of π and then by adding multiples of 2π {0, π} are displayed in the correct phase. According to the the last line of the equation can thus be the error function err [c] also based on the measured phases of the respective channel and of the previous channel and based on the error of the previous one Channels are determined. The assumption err [c] = 0 is allowed and does not curtail the uniqueness of the solution. you recognizes that this error function err [c] no longer depends on s, which is achieved by the term containing s through the first derivative is omitted, since E [c] is assumed to be constant becomes.

4 shows a diagram representing the sequence of a hopping scheme in which E [c] is constant. Along the abscissa of 4 is the hopping sequence position i, ie the corresponding i-th transmission time, reproduced and along the ordinate the channel c, in which is sent to the respective time i. The individual circles in the diagram correspond to the transmission of a signal at the corresponding transmission time with the corresponding channel number. The functional relationship based on the left upper straight line and the right upper straight line corresponds to the function A (c) or C (c) defined above. On these lines are thus transmission times for the transmitter T1. Analogously, the left lower straight line and the right lower straight line respectively correspond to the above function B (c) or D (c). The transmission times for the transmitter T2 thus lie on these straight lines. In the diagram of 4 Furthermore, the corresponding symmetry axis S of the hopping scheme is reproduced. It can be seen that in such a hopping scheme the above condition A (c) -B (c) = D (c) -C (c) = const. = Δi is satisfied. The hopping sequence length of such a hopping scheme is no longer I = 2C, but increases to I = 2 (C + Δi). In particular, in the hopping scheme of 4 n = 16 channels and i = 38 transmission times used and the constant channel spacing Δi is 3. The shared bandwidth remains maximum. However, there are times when only one of the transmitters T1 and T2 transmits. In the diagram of 4 these are the transmission times I = 0, 1, 2, 16, 17, 18, 19, 20, 21, 35, 36, 37. All hopping Schematics in which the differences between the straight lines A (c) and B (c) and the straight lines D (c) and C (c) are equal and constant, allow a simplified estimation of the error err [c], in which it is not necessary to determine the constant parameter s. Another example of a hopping scheme satisfying the above condition is schematized in FIG 5 reproduced, wherein in this figure, only the corresponding lines A (c), B (c), C (c) and D (c) are reproduced without specification of the individual transmission times.

As can be seen from the foregoing, can according to the invention by the use of a favorable Channel model or the exploitation of a detailed error model of the measuring system distinguished by the arithmetic mean of the phase differences resulting errors are estimated. This way you can a clearly corrected phase slope curve is determined out of a term difference and thereby the position of a to local transmitter can be determined more accurately.

QUOTES INCLUDE IN THE DESCRIPTION

This list The documents listed by the applicant have been automated generated and is solely for better information recorded by the reader. The list is not part of the German Patent or utility model application. The DPMA takes over no liability for any errors or omissions.

Cited patent literature

• - WO 2008/025713 A1 [0002]
• - DE 102007043649 [0003, 0004, 0007, 0011, 0034, 0035, 0038]

Cited non-patent literature

• - S. Schwarzer, M. Vossiek, M. Pichler and A. Stelzer, "Precise Distance Measurement with IEEE 802.15.4 (ZigBee) Devices", IEEE Radio and Wireless Symposium, Orlando, Florida, USA, January 2008, pages 779- 782 [0003]

Claims (14)

Method for locating wirelessly communicating radio subscribers, in which the position of at least one transmitter (T1) is determined with the aid of a further transmitter (T2) and at least two receivers (R1, R2), wherein: - the transmitters (T1, T2) each have one Sending a sequence of a plurality of signals on channels (c), the sequence being determined by a hopping scheme which defines for predetermined transmission times (i) the channel or channels (c) in which one or more of the transmitters (T1, T2) is a signal send; The signals from the receivers (R1, R2) are received and phases of the received signals are measured, wherein from the measured phases of a respective channel (c) an averaged phase difference (φ * / TDOA [c]) of the respective channel (c) it is determined which depends on the position of the at least one transmitter (T1) with respect to the further transmitter (T2); An error (err [c]) between the averaged phase difference (φ * / TDOA [c]) and the actual phase difference of the respective channel (c) by a combination of the measured phases and / or the averaged phase differences (φ * / TDOA) c]) of the respective channel (c) and / or further channels of the sequence is estimated; - the averaged phase difference (φ * / TDOA [c]) of each channel (c) of the sequence is corrected by the estimated error (err [c]); - From the corrected phase differences (φ _TDOA [c]) of the channels (c) of the sequence, the position of the at least one transmitter (T1) is determined. Method according to claim 1, characterized in that that for each individual transmitter (T1, T2) its own Hoppingsschema is provided, which comprises N entries, where - the Hopping schemes are symmetrical about their center; - the Send times (i) within a hopping scheme a constant temporally spaced from each other; and - the Signals from a carrier signal, whose frequency through the Channel (c) is given, and a data stream modulated thereon exist, for a transmitter (T1, T2) the difference between the phase of the data stream and the phase of the carrier signal of each channel (c) is constant. The method of claim 2, wherein never two or more transmitters (T1, T2) use the same channel (c) at the same time. Method according to claim 2 or 3, wherein the hopping schemes all transmitters (Ti) contain the same channels (c). Method according to one of the preceding claims, _wherein the position of the at least one transmitter (T1) from the corrected phase differences (φ _TDOA [c]) of the channels (c) of the sequence by a transformation into the time domain, in particular by an inverse Fourier transform , is determined. Method according to one of the preceding claims, in which the error for each channel c is determined by means of the following error function err [c]: err [c] - (φ * TDOA [c] - 2φ * TDOA [c - 1] + φ * TDOA [c - 2]) - err [c - 2] ∀ c = 2, ..., C - 1 where φ * / TDOA [c] is the average phase difference of the channel c and C represents the total number of channels used according to the hopping scheme. Method according to claim 6, wherein the values of err [0] and / or err [1] taking into account parameters with regard to the arrangement of the radio subscribers, in particular of maximum and / or minimum possible distances between at least one transmitter (T1) and the other transmitter (T2). Method according to one of the preceding claims, in which the error err [c] is estimated using the following function: E [c] = A (c) -B (c) -C (c) -D (c) wherein A (c) is the transmission time (i) of a signal transmitted by the at least one transmitter (T1) in the first half of the sequence of the hopping scheme in the channel c; B (c) is the transmission time (i) of a signal transmitted by the further transmitter (T2) in the first half of the sequence of the hopping scheme in channel c; C (c) is the transmission time (i) of a signal transmitted by the at least one transmitter (T1) in the second half of the sequence of the hopping scheme in the channel c; D (c) is the transmission time (i) of a signal transmitted by the further transmitter (T2) in the second half of the sequence of the hopping scheme in the channel c. Method according to Claim 8, in which the error is determined by means of an error function err [c] by the solution of the following equation: 1 2 (M φ, up [c] - M φ, down [c]) + err [c] = s · E [c] where s is a constant, where

where i = 0, ..., C-1 indicates the channels and C is the total number of channels; in which

the measured phase at the receiver Ry for a signal transmitted by the transmitter Tx in the channel c in the interval [0, ..., I / 2 - 1] of the successive transmission times (i) of the sequence of the hopping scheme, where I the total number of transmission times a sequence is; in which

denotes the measured phase at the receiver Ry for a signal transmitted by the transmitter Tx in the channel c in the interval [I / 2, ..., I-1] of the successive transmission times of the sequence of the hopping scheme, where I is the total number of transmission times of a sequence , Method according to claim 8 or 9, wherein, taking into account parameters of the arrangement of the radio subscribers, in particular of maximum and / or minimum possible distances between the at least one transmitter (T1) and the further transmitter (T2), a value for s is determined, and based on the error is determined using the following error function err [c]: err [c] = s · E [c] - 1 2 (M φ, up [c] - M φ, down [C]) Method according to one of claims 8 to 10, in which E [c] in at least part of the sequence of the hopping scheme, especially in the entire sequence, is constant. Method according to claim 11 in combination with claim 9, wherein for the at least part of the sequence of the hopping scheme with constant E [c] the error function err [c] is determined as follows: err [c] = err [c - I] - 1 2 (M φ, up [c] - M φ, up [c - 1] - M φ, down [c] + M φ, down [c - 1]) ∀ c = 1, ..., C - 1 Method according to one of the preceding claims, in the signals according to the standard IEEE 802.15.4 to be sent out. System for locating wirelessly communicating Radio subscribers, comprising at least one transmitter (T1) and one further transmitter (T2) and at least two receivers (R1, R2), wherein the system is in operation, the position of at least one Transmitter (T1) with the help of the other transmitter (T2) and the at least two receivers (R1, R2) determined, the system such is designed that a method according to one of the preceding Claims with the system is feasible.