Method and apparatus for determining location using phase difference of arrival

Abstract

An ultra-wideband (“UWB”) communication system comprising a transmitter and a receiver having two antennas. An UWB signal transmitted by the transmitter is received at each of the antennas. By comparing the carrier phases of the received signals, the phase difference can be determined. From this phase difference and the known distance, d, between the antennas, the Cartesian (x,y) location of the transmitter relative to the receiver can be directly determined.

Claims

1. In an ultra-wideband (UW) system comprising a UWB transmitter adapted to transmit a first signal in a first channel and a second signal in a second channel different from the first channel, and a UWB receiver having first and second antennas separated by a first distance, d, a method comprising the steps of: 1.1 using the first antenna to receive the first transmitted signal; 1.2 using the second antenna to receive the first transmitted signal; 1.3 using the receiver to: 1.3.1 develop a first range, r.sub.1, between the transmitter and a selected one of the first and second antennas; 1.3.2 develop a first phase value as a function of a complex baseband impulse response of the first transmitted signal received by the first antenna; 1.3.3 develop a second phase value as a function of a complex baseband impulse response of the first transmitted signal received by the second antenna; 1.3.4 develop a first path difference value, p.sub.1, as a function of the first and second phase values; 1.4 using the first antenna to receive the second transmitted signal; 1.5 using the second antenna to receive the second transmitted signal; 1.6 using the receiver to: 1.6.1 develop a second range, r.sub.2, between the transmitter and a selected one the first and second antennas; 1.6.2 develop a third phase value as a function of a complex baseband impulse response of the second transmitted signal received by the first antenna; 1.6.3 develop a fourth phase value as a function of a complex baseband impulse response of the second transmitted signal received by the second antenna; 1.6.4 develop a second path difference value, p.sub.2, as a function of the third and fourth phase values; and 1.6.5 develop an (x,y) location of the transmitter relative to the receiver as a function of d, r.sub.1, p.sub.1, r.sub.2, and p.sub.2.

2. The method of claim 1, wherein d is greater than one half a wavelength, λ.sub.1, of the first signal, and greater than one half a wavelength, λ.sub.2, of the second signal.

3. The method of claim 1, wherein step 1.3.4 is further characterized as: 1.3.4 develop the first path difference value, P.sub.1, as a function of the first and second phase values and of a selected first calibration function; and wherein step 1.6.4 is further characterized as: 1.6.4 develop the second path difference value, p.sub.2, as a function of the third and fourth phase values and of a selected second calibration function.

4. A location determination circuit configured to perform the method of claim 1.

5. An RF receiver comprising the location determination circuit according to claim 4.

6. An RF transceiver comprising the wireless receiver according to claim 5.

7. An RF communication system comprising the wireless transceiver according to claim 6.

8. A non-transitory computer readable medium including executable instructions which, when executed in an RF system, causes the RF system to perform the steps of the method according to claim 1.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) Our invention may be more fully understood by a description of certain preferred embodiments in conjunction with the attached drawings in which:

(2) FIG. 1 illustrates, generally in topographic perspective, an RF communication system, and, in particular, illustrates the different angles of incidence of the transmitted RF signal on two antennas spaced apart by a distance d;

(3) FIG. 2 illustrates, in block diagram form, the antennas of FIG. 1, together with the respective RF receivers;

(4) FIG. 3 illustrates, in block diagram form, one application of our invention to determine the location of a transmitter relative to a multi-antenna receiver; and

(5) FIG. 4 illustrates, in chart form, the relationship between range and phase difference for an antenna separation of λ/2 using a single carrier;

(6) FIG. 5 illustrates, in flow diagram form, a phase difference embodiment of a method adapted for use in the embodiment set forth in FIG. 3;

(7) FIG. 6 illustrates, in flow diagram form, a time of arrival difference embodiment of a method adapted for use in the embodiment set forth in FIG. 3;

(8) FIG. 7 illustrates, in flow diagram form, time of flight difference embodiment of a method adapted for use in the embodiment set forth in FIG. 3;

(9) FIG. 8 illustrates, in chart form, the relationship between range and phase difference for an antenna separation greater than λ/2 using a single carrier;

(10) FIG. 9 illustrates, in chart form, the relationship between range and phase difference for the same antenna separation as in FIG. 8, i.e., greater than λ/2, but using a different carrier than in FIG. 8;

(11) FIG. 10 illustrates, in chart form, one example of a correction function for compensating for path distortion resulting from real world effects; and

(12) FIG. 11, comprising FIG. 11A and FIG. 11B, illustrates, in flow diagram form, a multi-carrier, multi-transmission embodiment of a method adapted for use in the embodiment set forth in FIG. 3.

(13) In the drawings, similar elements will be similarly numbered whenever possible. However, this practice is simply for convenience of reference and to avoid unnecessary proliferation of numbers, and is not intended to imply or suggest that our invention requires identity in either function or structure in the several embodiments.

DETAILED DESCRIPTION OF THE INVENTION

(14) We have discovered that it is possible to get the Cartesian (x,y) location of a transmitter relative to a multi-antenna receiver directly from the range and the path difference without going through an intermediary step of calculating an angle of arrival. In accordance with our invention, the path difference can be determined either by using: the difference in the phase of a received frame at two of the antennas; the difference in time of arrivals of a received frame at two of the antennas; or the difference in ranges measured to two of the antennas. Further, our method can be implemented in an RF system comprising: multiple receivers, each with a respective antenna; a single receiver having multiple antennas; or any combination thereof.

(15) In the example illustrated in FIG. 3, the geometric distance between antenna A and antenna B is known to be d; and the path difference between antenna A and antenna B is determined to be p. Using well known methods, we can determine the range, r, between antenna A and antenna C, e.g., by measuring the time of flight between A and C. Provided that d is less than or equal to one half the wavelength, λ, of the signal transmitted from antenna C, p will always be between −λ/2 and +λ/2. We can now determine the (x,y) location of the transmitter relative to the receiver as follows:

(16) using the cosine rule:
cos(A)=(b.sup.2+c.sup.2−a.sup.2)/2bc [Eq. 7]
cos(α)=(r.sup.2+d.sup.2−(r−p).sup.2)/2rd [Eq. 8]
x/r=(r.sup.2+d.sup.2−r.sup.2+2rp−p.sup.2)/2rd [Eq. 9]
x=(d.sup.2+2rp−p.sup.2)/2d [Eq. 10]
r.sup.2=x.sup.2+y.sup.2 [Eq. 11]
y=±√{square root over (r.sup.2−x.sup.2)} [Eq. 12]
or, alternatively:
(x.sup.2+y.sup.2)=((d.sup.2+2rp−p.sup.2)/2d).sup.2+y.sup.2=r.sup.2 [Eq. 13]
y.sup.2=r.sup.2((d.sup.2+2rp−p.sup.2)/2d).sup.2 [Eq. 14]
y=±(√{square root over ((d.sup.2−p.sup.2)((2r−p).sup.2−d.sup.2))}/2d) [Eq. 15]
y=±(√{square root over ((d.sup.2−p.sup.2)(4r.sup.2−4rp+p.sup.2−d.sup.2))}/2d) [Eq. 16]
y=±(√{square root over ((1−(p/d).sup.2)(4r.sup.2−4rp+p.sup.2−d.sup.2))}/2) [Eq. 17]

(17) Note that we cannot tell if the y coordinate is positive or negative, so there is a front/back ambiguity.

(18) We note that d is small compared to r so d.sup.2 is very small compared to r.sup.2 and can be neglected:
y≈±(√{square root over ((1−(p/d).sup.2)(4r.sup.2−4rp+p.sup.2))}/2) [Eq. 18]
y≈±(r−(p/2))√{square root over (1−(p/d).sup.2)} [Eq. 19]

(19) We have determined that the maximum error by using this approximation is 0.22 mm for a 6.5 GHz carrier and a receiver antenna separation of λ/2. So, using Eq. 10 and Eq. 12, or Eq. 10 and Eq. 19, we can calculate the (x,y) coordinates of the transmitter without calculating the angle of arrival. We just need to know: r—the range to one of the antennas; d—the distance between the two antennas; and p—the path difference for the signal arriving at the two antennas.

(20) One of the most accurate ways to get the path difference is to get the phase difference of arrival of the transmitted signal in fractions of a cycle, and then multiply by the wavelength. Another way is to get the time difference of arrival of the transmitted signal, and multiply by the speed of light. A third way is to get the difference in time of flight, and multiply by the speed of light.

(21) As can be seen in FIG. 4, however, that the location uncertainty at phase differences near +/−180° is quite large. Thus, a very small change in phase gives a large change in y position. We can see this sensitivity in Eq. 19, resulting from the (1−(p/d).sup.2) term under the radical. Accordingly, small errors due to noise at these larger phase differences are amplified compared to when the phase difference is in the +/−90° region. Also, extra care must be taken when calculating the square root in this region.

(22) Consider, for example, the Taylor series for √{square root over (1−x.sup.2)}:

(23) $\begin{matrix} 1 - \frac{x^{2}}{2} - \frac{x^{4}}{8} - \frac{x^{6}}{16} - \frac{5 x^{8}}{128} - \frac{7 x^{10}}{256} - \frac{21 x^{12}}{1024} - \frac{33 x^{14}}{2048} - \frac{429 x^{16}}{32768} + O (x^{18}) & (Taylor series) \end{matrix}$
Using 6 terms in this Taylor expansion, the calculation is accurate to 2 cm up to a phase difference of 140° and to 5 cm up to 150°. Above 150°, however, the error increases rapidly. So, we will use a two-polynomial piece-wise approximation for the square root function:

(24) TABLE-US-00001 function y=polysqrt(x); p1=[107.81 −33.530 4.91940 0.05019]; % polynomial 1 coefficients p2=[0.3557 −0.9585 1.40389 0.20150]; % polynomial 2 coefficients y1=sum(p1.*x.{circumflex over ( )}[3 2 1 0]); % evaluate y1 for small x y=sum(p2.*x.{circumflex over ( )}[3 2 1 0]); % evaluate y for larger x y(x<0.144)=y1(x<0.144); % use y1 fox x<0.144 y(x<.002)=0; % set very small values to zero end
Using this approximation gives a worst case error in position of 2.5 cm within a 10 m radius, and an RMS error of 0.77 cm.

(25) By way of example, in FIG. 5, we have illustrated a phase difference embodiment of our method adapted for use in the embodiment illustrated in FIG. 3. Further, also by way of example, we have illustrated in FIG. 6 a time of arrival difference embodiment of our method adapted for use in the embodiment illustrated in FIG. 3. In FIG. 7, we have illustrated one example of a time of flight difference embodiment of our method adapted for use in the embodiment illustrated in FIG. 3.

(26) When the distance between the antennas is greater than half the wavelength of the center frequency, a particular phase difference can give more than one valid solution, because adding 360° will give the same phase difference. For instance, if the center frequency is 8 GHz and the distance between the antennas is 1 wavelength of a 6.5 GHz carrier, we would have the situation shown in FIG. 8. As we can see, for many values of phase difference, there are three possible solutions. But switching to a channel with a 6.5 GHz carrier would give the situation shown in FIG. 9. In this case, apart from the 0° case, there are always two possible solutions for each phase difference. Fortunately, we can use this fact to our advantage. If the distance between the antennas is greater than one half wavelength, we can set the carrier frequency to one channel, and then measure the range and phase difference as before. This will give us more than one (x,y) coordinate—let us call this set of possible solutions Set 1. We then switch the carrier frequency to a different channel, and repeat the measurement on the new channel. This will also give us multiple solutions—let us call this set of possible solutions Set 2. We can then discard all solutions which don't appear in both Set 1 and Set 2. This will generally leave only one (,y) coordinate. By way of example, in FIG. 11, we have illustrated one example of a multi-carrier, multi-transmission embodiment of our method adapted for use in the embodiment illustrated in FIG. 3.

(27) In practice, noise perturbations in the phase measurement will almost always ensure that the corresponding solutions will not be exactly the same, so we must pick pairs of solutions, one from each set, which are closest to each other in the Euclidean sense. A well known way to do this is to pick the (x.sub.i,y.sub.i) from Set 1 and the (x.sub.j,x.sub.j) from Set 2 that minimizes:
√{square root over ((x.sub.i+x.sub.j).sup.2+(y.sub.i−y.sub.j).sup.2)} [Eq. 20]

(28) To get even better results, we can repeat this on a third (or even fourth or fifth) channel. For a third channel, we could pick the (x.sub.i,y.sub.i) from Set 1, (x.sub.j,y.sub.j) from Set 2 and the (x.sub.k,y.sub.k) from a Set 3 that minimizes:

(29) $\begin{matrix} \sqrt{\begin{matrix} {(x_{i} - x_{j})}^{2} + {(x_{i} - x_{k})}^{2} + {(x_{j} - x_{k})}^{2} + \\ {(y_{i} - y_{j})}^{2} + {(y_{i} - y_{k})}^{2} + {(y_{j} - y_{k})}^{2} \end{matrix}} & [Eq . 21] \end{matrix}$

(30) Up to this point, we have assumed that the effective, i.e., measured, path difference is precisely equal to the Cartesian path difference. However, in a real system, the effective path difference and the Cartesian path difference will not be precisely equal. For example, when our two antennas are closer than a few wavelengths, the antennas interact through an effect known as mutual coupling; this causes the electromagnetic waves to behave differently than would be the case in free space resulting in different effective and Cartesian path differences as a function of the path difference. Another effect seen in the real world is that the feed wires to the antennas can have slightly difference lengths, or the paths from the down-mixer generator to the two separate down-mixers can have slightly different lengths. These two effects, and others, add a calculatable offset to the path difference.

(31) We propose to compensate for these cumulative effects by developing a Calibration Function between the effective and Cartesian path differences. In accordance with this embodiment, we first perform a system calibration process wherein a number of calibration measurements are taken, each from a different known (x,y) coordinate but, collectively, having a wide range of actual path differences. Since we know all of the (x,y) coordinates, we can calculate the respective expected path differences. By measuring the respective phase differences, we can also calculate the respective effective path differences. In this way we can develop a suitable Calibration Function, e.g., in the form of a look-up table or as apiece-wise linear generator function or by using a polynomial fitting function. Then we can use this Calibration Function to correct the effective path difference, p, before applying the formulas to calculate the (x,y) coordinates. By way of example, in FIG. 10, we have illustrated one possible Calibration Function.

(32) Although we have described our invention in the context of particular embodiments, one of ordinary skill in this art will readily realize that many modifications may be made in such embodiments to adapt either to specific implementations. For example, rather than calculating the path difference, p, one might directly determine the range, r.sub.2, between the second antenna and the receiver using the same method used to determine the range, r.sub.1, between the first antenna and the receiver. Further, the several elements described above may be adapted so as to be operable under either hardware or software control or some combination thereof, as is known in this art. Alternatively, the several methods of our invention as disclosed herein in the context of special purpose receiver apparatus may be embodied in computer readable code on a suitable non-transitory computer readable medium such that when a general or special purpose computer processor executes the computer readable code, the processor executes the respective method.

(33) Thus it is apparent that we have provided a method and apparatus for determining the location of a wireless transmission relative to a multi-antenna receiver. Although we have so far disclosed our invention only in the context of a packet-based UWB communication system, we appreciate that our invention is broadly applicable to other types of wireless communication systems, whether packed-based or otherwise, that perform channel sounding. Further, we submit that our invention provides performance generally comparable to the best prior art techniques but more efficiently than known implementations of such prior art techniques.

Method and apparatus for determining location using phase difference of arrival

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Abstract

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Description