U.S. patent application number 16/232783 was filed with the patent office on 2020-07-02 for super resolution radio frequency location determination.
The applicant listed for this patent is TEXAS INSTRUMENTS INCORPORATED. Invention is credited to Anand DABAK, Marius MOE, Charles SESTOK.
Application Number | 20200209337 16/232783 |
Document ID | / |
Family ID | 71121713 |
Filed Date | 2020-07-02 |
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United States Patent
Application |
20200209337 |
Kind Code |
A1 |
DABAK; Anand ; et
al. |
July 2, 2020 |
SUPER RESOLUTION RADIO FREQUENCY LOCATION DETERMINATION
Abstract
Using a phase interferometry method which utilizes both
amplitude and phase allows the determination and estimation of
multipath signals. To determine the location of an object, a signal
that contains sufficient information to allow determination of both
amplitude and phase, like a packet that includes a sinewave
portion, is provided from a master device. A slave device measures
the phase and amplitude of the received packet and returns this
information to the master device. The slave device returns a packet
to the master that contains a similar sinewave portion to allow the
master device to determine the phase and amplitude of the received
signals. Based on the two sets of amplitude and phase of the RF
signals, the master device utilizes a fast Fourier transform or
techniques like multiple signal classification to determine the
indicated distance for each path and thus more accurately
determines a location of the slave device.
Inventors: |
DABAK; Anand; (Plano,
TX) ; MOE; Marius; (Fetsund, NO) ; SESTOK;
Charles; (Dallas, TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
TEXAS INSTRUMENTS INCORPORATED |
Dallas |
TX |
US |
|
|
Family ID: |
71121713 |
Appl. No.: |
16/232783 |
Filed: |
December 26, 2018 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04L 27/2634 20130101;
G01S 3/48 20130101; H04W 64/003 20130101; G01S 3/16 20130101; G01S
3/58 20130101 |
International
Class: |
G01S 3/16 20060101
G01S003/16; G01S 3/48 20060101 G01S003/48; G01S 3/58 20060101
G01S003/58; H04L 27/26 20060101 H04L027/26; H04W 64/00 20060101
H04W064/00 |
Claims
1. A method of determining object distance using radio frequency
signals, the method comprising: using a first oscillator,
transmitting a first measurement packet at a first frequency from a
master device to a slave device whose distance is to be measured;
using a second oscillator, receiving the first measurement packet
at the slave device; determining, by the slave device, phase and
amplitude of the first measurement packet; using the second
oscillator, transmitting from the slave device to the master device
the determined phase and amplitude of the received first
measurement packet; using the first oscillator, receiving the
determined phase and amplitude of the first measurement packet at
the master device; using the second oscillator, transmitting a
second measurement packet at a second frequency different from the
first frequency from the slave device to the master device; using
the first oscillator, receiving the second measurement packet at
the master device; determining, by the master device, the phase and
amplitude of the received second measurement packet; determining,
by the master device, multipath signals using the phases and
amplitudes of the first and second measurement packets; determining
the distance from the master device to the slave device, by the
master device, using the determined multipath signal; and
maintaining respective phases of the first and second
oscillators.
2. The method of claim 1, wherein determining the multipath signals
includes: performing a net channel estimate to determine the master
to slave channel response across frequency; and performing a fast
Fourier transform (FFT) on the net channel estimate; and wherein
determining the distance includes: performing an inverse fast
Fourier transform (IFFT) on the principal multi-path component of
the FFT result.
3. The method of claim 2, wherein the FFT is performed directly on
the net channel estimate when the phases of the measured
frequencies are coherent.
4. The method of claim 2, wherein determining the multipath signals
further includes performing phase change correction of the
determined phases of the first and second measurement packets prior
to performing the FFT when the phases of the measured frequencies
are incoherent.
5. The method of claim 2, wherein determining the multipath signals
includes determining the minimum phase roots of the determined
phases of the first and second measurement packets prior to
performing the FFT when the phases of the measured frequencies are
incoherent.
6. The method of claim 2, wherein determining the distance
includes: utilizing a super resolution algorithm on the IFFT
result.
7. The method of claim i, wherein the first and second measurement
packets each contain a sine wave portion for determining the phase
and the amplitude of the first and second measurement packets.
8. The method of claim 1, wherein the determined phase and
amplitude of the first measurement packet is provided in the second
measurement packet.
9. A master device for determining object distance using radio
frequency signals, the device comprising: a processor; a radio
frequency interface coupled to the processor and including an
oscillator used for transmitting and receiving packets; program
storage coupled to the processor and containing programs to cause
the processor to: using the oscillator, transmit a first
measurement packet at a first frequency to a slave device whose
distance is to be measured, the slave device including a slave
device processor and a slave device radio frequency interface
coupled to the processor and including a slave device oscillator
used for transmitting and receiving packets; using the oscillator,
receive a determined phase and amplitude of the first measurement
packet as received at the slave device; using the oscillator,
receive a second measurement packet at a second frequency different
from the first frequency from the slave device; determine the phase
and amplitude of the received second measurement packet; determine
multipath signals using the phases and amplitudes of the first and
second measurement packets; and determine the distance from the
master device to the slave device using the determined multipath
signal, wherein both the master device and the slave device
maintain the phase of their oscillators used to transmit and
receive the measurement packets over transmitting and receiving
steps.
10. The master device of claim 9, wherein determining the multipath
signals includes: performing a net channel estimate to determine
the master to slave channel response across frequency; and
performing a fast Fourier transform on the net channel estimate;
and wherein determining the distance includes: performing an
inverse fast Fourier transform (IFFT) on the principal multi-path
component of the FFT result.
11. The master device of claim 10, wherein the FFT is performed
directly on the net channel estimate when the phases of the
measured frequencies are coherent.
12. The master device of claim 10, wherein determining the
multipath signals further includes performing phase change
correction of the determined phases of the first and second
measurement packets prior to performing the FFT when the phases of
the measured frequencies are incoherent.
13. The master device of claim 10, wherein determining the
multipath signals includes determining the minimum phase roots of
the determined phases of the first and second measurement packets
prior to performing the FFT when the phases of the measured
frequencies are incoherent.
14. The master device of claim 10, wherein determining the distance
includes: utilizing a super resolution algorithm on the IFFT
result.
15. The master device of claim 9, wherein the first and second
measurement packets each contain a sine wave portion for
determining the phase and the amplitude of the first and second
measurement packets.
16. The master device of claim 9, wherein the determined phase and
amplitude of the first measurement packet is provided in the second
measurement packet.
17. A slave device for determining object distance using radio
frequency signals, the slave device comprising: a processor; a
radio frequency interface coupled to the processor and including an
oscillator used for transmitting and receiving packets; program
storage coupled to the processor and containing programs to cause
the processor to: using the oscillator, receive a first measurement
packet at a first frequency from a master device, the master device
including a master processor and a master radio frequency interface
coupled to the processor and including a master oscillator used for
transmitting and receiving packets; determine phase and amplitude
of the first measurement packet; using the oscillator, transmit to
the master device the determined phase and amplitude of the
received first measurement packet; and using the oscillator,
transmit a second measurement packet at a second frequency
different from the first frequency from the slave device to the
master device, wherein both the master device and the slave device
maintain the phase of their oscillators used to transmit and
receive the measurement packets over transmitting and receiving
steps.
18. The slave device of claim 17, wherein the first and second
measurement packets each contain a sine wave portion for
determining the phase and the amplitude of the first and second
measurement packets.
19. The slave device of claim 17, wherein the programs further
cause the processor to: enter receiving mode upon receiving an
indication that the distance measurement is starting.
20. The slave device of claim 17, wherein the radio frequency
signals are Bluetooth.RTM. signals.
Description
BACKGROUND
1. Field
[0001] The field relates to location determination using radio
frequency signals.
2. Description of the Related Art
[0002] It is often useful to use radiofrequency (RF) signals to
determine the location of items. The RF signals of most interest
are Bluetooth Low Energy (BLE), Wi-Fi.RTM. (especially with a
bandwidth of 80 MHz) and sub-GHz signals (especially with a
bandwidth of 20 MHz). One problem with the use of the RF signals is
the accuracy that can be developed. For example, simply using
time-of-flight of the RF signal can yield an accuracy of
approximately 3-5 m, which is insufficient in many cases.
[0003] For the above mentioned RF signals there are several
different methods of determining location from RF signals. A first
is radio signal strength indication (RSSI). RSSI is highly
susceptible to multipath issues so that it has an error of +/-10
dB. The second method is the previously mentioned time-of-flight
approach. In this time-of-flight approach the clock frequency
utilized to perform the measurements is critical. If a typical 40
MHz clock is utilized, the resolution that can be obtained by
time-of-flight is only approximately 15 m. Further, time-of-flight
is also susceptible to multipath problems. A third method is the
angle of arrival (AoA). In angle of arrival, a series of antennas
are utilized in various locations and then the location of the
object can be obtained based on the received angle at each of the
antenna groups. A typical accuracy is 5.degree. but again,
multipath is a problem. A fourth method that has been utilized is
phase interferometry, where the phase at two frequencies or two
locations is estimated and from that the distance can be
determined. Yet again, multipath is a problem in utilizing phase
interferometry.
[0004] If the desired location accuracy is small, such as 10 to 15
cm, the conventional approaches for BLE, WiFi, and sub-GHz systems
are not directly usable, and multipath issues further render them
problematic.
SUMMARY
[0005] Using a phase interferometry method which utilizes both
amplitude and phase, instead of just phase, provides additional
information that allows the determination and estimation of
multipath signals. To determine the location of an object, a signal
that contains sufficient information to allow determination of both
amplitude and phase, such as a packet that includes a sinewave
portion, is provided from a master device to a slave device. The
slave device measures the phase and amplitude of the received
packet and returns this information to the master device. The slave
device also returns a packet to the master that contains a similar
sinewave portion to allow the master device to determine the phase
and amplitude of the received signals. Based on the two sets of
amplitude and phase of the RF signals, the master device utilizes a
fast Fourier transform (FFT) or other techniques like multiple
signal classification (MUSIC) to determine the indicated distance
for each path and thus more accurately determines a location of the
slave device in relation to the master device.
BRIEF DESCRIPTION OF THE FIGURES
[0006] For a detailed description of various examples, reference
will now be made to the accompanying drawings in which:
[0007] FIG. 1 is a block diagram illustrating multipath.
[0008] FIG. 2 is a block diagram of a Bluetooth device.
[0009] FIG. 3 is a block diagram illustrating the control modules
in an automobile.
[0010] FIG. 4 is a block diagram of the Bluetooth control module of
FIG. 3.
[0011] FIG. 5 is a block diagram of a Bluetooth
microcontroller.
[0012] FIG. 5A is a block diagram of the RF section of the
microcontroller of FIG. 5.
[0013] FIG. 6 is a diagram illustrating the communications and
example packets exchanged in determining location.
[0014] FIG. 7 is a diagram illustrating the timing of the signals
and measurements and calculations performed.
[0015] FIGS. 7A-7D are graphs illustrating calculated
multipath.
[0016] FIG. 8 is a flowchart of operations to determine
location.
DETAILED DESCRIPTION
[0017] Referring now to FIG. 1, a phone 100 is trying to determine
the location of a first object 102 (which can be a BLE access
point) and a second object 104 (which can be another BLE access
point). In this example, and the examples described in this
description, Bluetooth.RTM. is used as the exemplary RF signal,
though it is understood that other protocols and signals could be
utilized. The phone 100 is transmitting a Bluetooth signal. With
regard to the first object 102, the target Bluetooth device, the
Bluetooth signal takes a direct signal path 106 and a reflected
signal path 108. The reflected signal path 108 proceeds from the
phone 100 to a reflector no and then to the first object 102.
Similarly, with regard to the second object 104, another target
Bluetooth device, the Bluetooth signal has a direct path 112 and a
reflected path 114, which is reflected from a reflector 116. The
presence of the reflectors no and 116 results in the first object
102 and second object 104 receiving the transmitted Bluetooth
signal at two different times and with two different amplitudes.
The reflected signals thus create interference to the direct
signals and hinder the development of accurate location values
because of the induced interference to the direct signals.
[0018] FIG. 2 is a block diagram of a simple Bluetooth device, in
the illustrated case a Bluetooth key fob 200. A Bluetooth
microcontroller 202, such as a Texas Instruments.RTM. CC2640
SimpleLink.TM. Bluetooth wireless MCU (microcontroller), is the
primary component in the key fob 200. An antenna 204 is connected
through an inductor 206 to the Bluetooth MCU 202 to allow
transmission and reception of the Bluetooth signals. First and
second buttons 208 and 210 provide user input, such as lock and
unlock. First and second light emitting diodes (LEDs) 212 and 214
provide visual feedback to the user of operations of the key fob
200. A speaker 216 is connected to the Bluetooth MCU 202 to provide
audible feedback to the user. A battery 218 provides power to the
key fob 200, particularly the Bluetooth MCU 202. This is a very
simple block diagram for purposes of this explanation and actual
units would use more and different components and be more
elaborate.
[0019] Referring now to FIG. 3, a block diagram of the control
system 300 of an automobile is illustrated. A CAN bus 302 in mode C
has connected to it an engine control module 304, an antilock
braking system module 306, a power steering control module 308, a
headlamps control module 310, an OBD-II port 312 and a body
computer module 314. A CAN bus 316 in mode B is connected to the
OBD-II port 312 and the body computer module 314 and has connected
to it a parking sensors module 318, an airbag control module 320,
an instrument contact panel cluster module 322, an audio control
module 324, a convergence module 326, an HVAC module 328 and a
Bluetooth module 330. These are just exemplary modules and
additional modules or fewer modules could be present in a
particular car, as could more or less CAN buses or alternative or
additional buses.
[0020] FIG. 4 is a simplified block diagram of the Bluetooth module
330 of FIG. 3. A Bluetooth MCU 402, such as the CC2640 described
above, forms the primary component of the Bluetooth module 330. An
antenna 404 is connected through an inductor 406 to the Bluetooth
MCU 402. A CAN bus interface 408 is connected to the CAN bus 316
and to the Bluetooth MCU 402 to allow the Bluetooth module 330 to
communicate with the remainder of the automobile. Again, this is a
simplified block diagram for the purpose of this explanation and
actual modules would include more and different components and be
more elaborate.
[0021] FIG. 5 is a block diagram of a Bluetooth MCU 500, such as
the Bluetooth MCU 402 or the Bluetooth MCU 202. The primary
components of a Bluetooth MCU 500, such as the CC2640
SimpleLink.TM. Bluetooth wireless MCU, include a main processor 502
to perform the primary processing and control functions of the
Bluetooth MCU 500. RAM 504 is coupled to the main processor 502 to
provide operating memory, while flash memory and/or a read-only
memory (ROM) 506 (flash memories and ROMs both being non-transitory
computer readable storage media encoded with computer-executable
instructions) are connected to the main processor 502 to store the
programs used and executed by the main processor 502 to perform the
functions of the key fob 200 or the Bluetooth module 330. An RF
section 508, which is preferably programmable for multiple
frequencies and protocols, is connected to the inductor 406 and the
antenna 404 in the illustrated example. As shown in more detail in
FIG. 5A, the RF section 508 is a programmable radio system and has
sufficient capabilities to allow the main processor 502 to set the
desired frequencies and to indicate the desired protocol, such as
Bluetooth, Wi-Fi.RTM. or the like. The RF section 508 contains a
processor 550 for interfacing with the main processor 502 and
controlling the RF section 508. SRAM 552 and ROM 554 are connected
to the processor 550 to provide the working memory and store the
programs. A digital signal processor (DSP) modem 556 is connected
to the processor 550, SRAM 552 and ROM 544 and handles the task of
converting the digital packets into signals to be transmitted in
analog form and converting the received analog signals into digital
packets. A digital phase locked loop (PLL) 558 is connected to the
DSP modem 556 to generate the frequencies needed for the RF signals
being used. An output buffer 560 is connected to the inductor 406
to provide the analog RF output signal. An input buffer 562 is also
connected to the inductor 406 to receive the incoming RF signals
and provide them to a mixer 564, which mixes the received RF
signals with digital PLL 558 outputs. The mixer 564 provides
outputs to analog to digital converters (ADC) 566 and 568, whose
outputs are provided to the DSP modem 556 for the receive decoding.
The DSP modem 556 determines the phase and amplitude of the
received Bluetooth signals as discussed below. Programs for the
processor 550 and DSP modem 556 are also stored in the flash memory
and/or ROM 506 if necessary.
[0022] A sensor section 510 is included in the Bluetooth MCU 500 to
allow the Bluetooth MCU 500 to perform functions beyond just the
Bluetooth communications. A general-purpose I/O section 512 is
provided, such as to drive a speaker or LEDs or receive button
inputs. A serial I/O section 514 is provided to allow communication
with a controlling processor, such as through the CAN bus interface
408.
[0023] Referring now to FIGS. 6, 7, 7A-7D and 8, operation of a
first example is provided. In this first example, a master 600 is
determining the location of a slave 602 with respect to the master
600. Referencing the automobile example, the master 600 can be the
Bluetooth module 330 and the slave 602 is the Bluetooth key fob
200. The determination of master 600 and slave 602 is performed in
a first step Boo as is conventional in Bluetooth operations. The
master 600 in step 802 provides a signal to the slave 602 that
indicates that distance measurement is commencing. The slave 602 in
step 804 enters a receive mode. In step 806 the master 600 sends a
measurement packet to the slave 602. Exemplary measurement packet
formats are illustrated in FIG. 6. A conventional Bluetooth data
packet is modified to include an extension portion 614 to allow a
pure sine wave to be transmitted. The first example packet 604 has
a preamble 606, followed by an access address 608, a data PDU 610
and a CRC 612 as in conventional Bluetooth. An extension or tone
portion 614 is provided after the CRC portion 612 and is an all
zero or all one transmission, which thus produces a pure sine wave
on the actual RF transmitter. A second example measurement packet
616 includes the preamble 606, access address 608, and data PDU
610, which is followed by the extension portion 614 and concludes
with the CRC portion 612. As the master 600 has indicated that
distance measurement is occurring, the slave 602 is prepared to
receive the packet 604 or 616 and determine the phase and amplitude
of the received signals by analyzing the extension portion 614.
[0024] In step 810, the slave 602 determines the phase and
amplitude of the sine wave portion and provides the phase and
amplitude information to the master 600. In step 812, the slave 602
sends a similar measurement packet 604 or 616 to the master 600. In
some examples, steps 810 and 812 are merged so that the packet
providing the determined phase and amplitude is also the slave to
master measurement packet. This measurement packet 604 or 616 from
the slave 602 to the master 600 is provided at a different
frequency than the measurement packet 604 or 616 provided from the
master 600 to the slave 602. This change in frequency occurs
naturally in Bluetooth due to the frequency hopping characteristics
of Bluetooth but must be performed differently in other protocols.
In step 814, the master determines the phase and amplitude of the
sine wave portion of the received packet 604 or 616. While this
explanation has used only a single measurement transmission from
the master 600 to the slave 602 and a single measurement
transmission from the slave 602 to the master 600, in other
examples this pair of measurement transmissions is performed many
times, such as 20 to 40 times, to obtain measurements at more than
just the two different frequencies. These multiple measurements
allow improved results by averaging results and thus reducing the
effects of aberrant measurements. By having the phase and amplitude
of both signals, in step 816, the master 600 calculates the
distance of the slave 602.
[0025] FIG. 7 illustrates the timing of these events and particular
parameters which are measured. At time t=0, the master, referred to
as A in FIG. 7, transmits a measurement packet to the slave,
referred to as B in FIG. 7. The phase of the transmitted signal at
A for the frequency f at t=0 is .PHI..sub.A(f) and that of B at the
same time is .PHI..sub.B(f). The transmitted signal reaches B at
time t.sub.d. The slave B processes the received signal, which
takes a processing time t.sub.proc. At the slave B the measured
phase of the signal assuming a single path channel is
.PHI..sub.A(f.sub.1)-.PHI..sub.B (f.sub.1)-2*.pi.*f.sub.1*t.sub.d.
The slave B then transmits a measurement packet to the master A.
Note that it is important that both the master A and slave B each
maintain their respective phase in their respective phase locked
loops for that particular frequency f.sub.1 while the measurements
are taking place. This way the initial phase .PHI..sub.A(f.sub.1)
and .PHI..sub.B (f.sub.1) is maintained while receiving and
transmitting the packets at both the Master A and the Slave B. The
phase of the transmitted signal at B during transmission now is
.PHI..sub.B(f.sub.1)+2*.pi.*f.sub.1*(t.sub.d+t.sub.proc). Note the
.PHI..sub.B (f.sub.1) in this term because of the phase maintenance
of the PLL at slave B. The transmitted signal reaches A at time
2t.sub.d+t.sub.proc. The master A processes the received signal,
which takes a processing time t.sub.proc. At the master A the
measured phase of the signal assuming a single path channel is
.PHI..sub.B(f.sub.1)+2*.pi.*f.sub.1*(t.sub.d+t.sub.proc)-.PHI..sub.A(f.su-
b.1)-2*.pi.*f.sub.1*(2*t.sub.d+t.sub.proc)=.PHI..sub.B(f.sub.1)-.PHI..sub.-
A(f.sub.1)-2*.pi.*f.sub.1*(t.sub.d). Again notice the phase the
.PHI..sub.A(f.sub.1) in the above term because of the phase
maintenance of the PLL at the master A.
[0026] For a multi-path channel the signal measured at the slave B
for frequency f is:
s B ( f l ) = p = 1 p = P a p exp ( j * ( .phi. A ( f l ) - .phi. B
( f l ) - 2 .pi. f l ( d p c ) ) ) ##EQU00001##
[0027] The signal measured at the master A is:
s A ( f l ) = p = 1 p = P a p exp ( j * ( .phi. B ( f l ) - .phi. A
( f l ) - 2 .pi. f l ( d p c ) ) ) ##EQU00002##
[0028] Where a.sub.p are the attenuation coefficients for the
different multi-path reflections with the total number of
multi-paths given by P. Since the channel between the master A and
the slave B is reciprocal, these attenuation coefficients and the
total number of multi-paths are the same in the two directions. The
distance d.sub.p is the distance traveled by the multi-path p
between the Slave and Master and vice versa. Just as the above
equations are for frequency similar equations can be written for
other Bluetooth frequencies. Note that Bluetooth uses a 1 MHz
bandwidth per channel from the 2400-2480 MHz band, implying there
can be up to 80 such measurements for Bluetooth.
[0029] Each of these measurements includes both the phase and the
amplitude of the received signal. After the master completes its
measurement of the signal, the master then computes the multipath
content as given below. There are two alternatives, depending on
whether the signals are phase coherent at the measured
frequencies.
[0030] If coherent, the master then performs a Fast Fourier
Transform (FFT) on the measured signals to get the channel impulse
response in time domain. This result is then used to estimate the
distance from the transmitter, the master, by using the occurrence
of the first multipath in the FFT with the assumption that the
first multi-path is the shortest distance between the master and
the slave. FIG. 7A is a graph showing the detected multipath when
the reflectors, a target or slave and a reflector to cause
multipath, are 20 m and 25 m away from the master. Two distinct
peaks are visible, one for each path. FIG. 7B is for a case where
the reflectors are 22.5 m and 25 m from the transmitter. In this
case there is only a single apparent peak as the reflectors are too
close in relation to the bandwidth of Bluetooth, which 80 MHz.
Since the bandwidth of the signal is 80 MHz, implying a wavelength
of about 3.75 meters, it implies that the accuracy of the FFT would
be limited to within this range. Hence the two paths at 22.5 m and
25 m do not give distinct peaks for the FFT algorithm.
[0031] For a system employing bandwidth B Hz and with signal to
noise ratio (SNR) snr the limits of how accurately time of flight
can be determined is given by the Cramer Rao and the Barankin
bounds as given in equation 7 in A. Zeira, P. M. Schultheiss,
"Realizable Lower Bounds for Time Delay Estimation: Part
2-Threshold Phenomena," IEEE Transactions on Signal Processing,
Volume: 42, Issue: 5, May 1994, pp 1001-1007, which is hereby
incorporated by reference [Zeira-paper], provided here.
BB ( .tau. ^ ) .apprxeq. .delta. 2 exp { SNR .beta. 2 .delta. 2 } -
1 + 2 exp { SNR .omega. o 2 2 } - 1 ##EQU00003##
[0032] Where .beta.=2*.pi.*BW .delta.=2.pi./.omega..sub.0 and
<< .beta. .omega. 0 . ##EQU00004##
For Bluetooth case, BW is about 80 MHz and the center frequency
.omega..sub.0=2440 MHz. For high SNR conditions, the first term
tends to zero since the bandwidth is much smaller than the center
frequency and the bound converges to
BB ( .tau. 2 ) .apprxeq. 1 .omega. o 2 SNR ##EQU00005##
which we call as the carrier frequency limited accuracy. On the
other hand for small SNR's the first term dominates the bound
by
BB ( .tau. 2 ) .apprxeq. 1 SNR ( 1 .beta. 2 + 1 .omega. o 2 )
.apprxeq. 1 .beta. 2 SNR ##EQU00006##
which we call the limit of the inverse of the bandwidth of the
signal.
[0033] What the above bounds say is that with high enough SNR
conditions the performance of locationing algorithm is limited by
the inverse of carrier frequency, which in case of Bluetooth would
be about 12.5 cm. Thus, with high enough SNR it is possible to beat
the apparent limit of FFT (which is the inverse of the bandwidth of
the signal--in case of Bluetooth about 3.75 m) to get to the
carrier wavelength which 12.5 cm. Super-resolution algorithms try
to achieve this carrier frequency limited higher accuracy to
resolve the multi-path as compared to the bandwidth limited
accuracy.
[0034] An example super resolution algorithm is MUSIC (MUltiple
SIgnal Classification). By knowing the multipath, applying the
MUSIC algorithm allows a resolution of 10 to 20 cm to be obtained.
Super resolution algorithms work on the net channel estimate
between the Master and Slave across different frequencies. Before
we describe this algorithm, we explain how the channel estimate is
obtained.
[0035] Further processing is needed before the FFT and subsequent
super resolution algorithm can be applied to obtain the master to
slave channel response across frequency. As a first step,
s.sub.A(f.sub.1) and s.sub.B(f.sub.1) are multiplied. This produces
the net channel estimate equation:
s B ( f l ) * s A ( f l ) = ( p = 1 p = P a p exp ( j * ( - 2 .pi.
f l ( d p c ) ) ) ) 2 ##EQU00007##
[0036] This is an equation in the form (H(w)).sup.2, which is
h(t)*h(t), and then h(t) needs to be found. A direct square root
cannot be taken because of the possibility of a phase ambiguity of
+/-pi across the frequency range.
[0037] In a first option, the phase change across consecutive
frequencies is checked to determine if the phase change is less
than a certain threshold, such as pi/2. If the phase change is
greater than the threshold, an additional pi phase is added or
subtracted. When this has been completed for all frequencies being
analyzed, then the FFT is applied and results as shown above for
the coherent instance are produced.
[0038] In a second option, it is noted that
|(H(w)).sup.2|=|H(w)|.sup.2. Solving for the minimum phase roots of
|H(w)|.sup.2 is equivalent to determining h(t)*h(-t). This is
because for minimum phase systems the frequency response can be
uniquely recovered from the magnitude alone as discussed in
"Discrete-Time Signal Processing, OpenCourseWare 2006, Lecture 3,
Minimum-Phase and All-Pass Systems," Massachusetts Institute of
Technology Department of Electrical Engineering and Computer
Science,
ocw.mitedu/courses/electrical-engineering-and-computer-science/6-341-disc-
rete-time-signal-processing-fall-2005/lecture-notes/leco3.pdf,
especially p. 2 on spectral factorization, which is hereby
incorporated by reference. The resulting h(t) is the solution and
the FFT is performed on the phase corrected net channel estimate as
given in the above equation. The root determination is illustrated
in FIG. 7C for a case having two reflectors, one at 7 m and one at
9 m, with the actual object or target being at 3 m. The result of
the FFT on the 7 m case is shown in FIG. 7D, with peaks at 2.8 m
and 7.4 m representing the target object and the reflector. The
error of 20 cm for the object is within the desired accuracy.
[0039] Following the FFT, the principal multi-path components (the
first 1-2 multi-path components) can be sorted while the rest of
the FFT in time domain can be set to zero. An inverse FFT (IFFT)
can now be performed to go back to frequency domain. This time the
channel is windowed in the time domain to keep the principal
multi-path components. A super resolution algorithm can now be
applied on this frequency domain channel (or the super resolution
algorithm can also be applied on the whole channel as given in the
channel estimate equation above). The basic MUSIC algorithm that
can be used for super-resolution is given in GIRD Systems, Inc.,
"An Introduction to MUSIC and ESPRIT,"
www.girdsystems.com/pdf/GIRD_Systems_Intro_to_MUSIC_ESPRIT.pdf,
esp. slides 9-12, which is hereby incorporated by reference. MUSIC
algorithms are typically applied for multiple antenna systems to
resolve multiple targets impinging on the array manifold. However
in the problem at hand, we can treat the different frequency
measurements in Bluetooth like a multiple antenna system. One of
the problems in the application of the MUSIC algorithm as given in
"An Introduction to MUSIC and ESPRIT" is the correlation between
the sources which will occur in the case of a multi-path channel
(since the source is the same for the different multi-paths). To
solve this problem of correlated sources a modification to the
basic MUSIC algorithm is proposed as given in Chongying Qi,
Yongliang Wang, Yongshun Zhang, and Ying Han, "Spatial Difference
Smoothing for DOA Estimation of Coherent Signals," IEEE Signal
Processing Letters, Volume: 12, Issue: 11, Nov. 2005, pp. 800-802,
which is hereby incorporated by reference. Again, the received
signal X(t) in "Spatial Difference Smoothing for DOA Estimation of
Coherent Signals" is equivalent to the net channel estimate
equation given above.
[0040] A series of experiments were conducted using the above
approaches for varying reflector distances. In the experiments, the
main path or target was at 0.5 m and the reflector location was
varied from 1 m to 4.5 m in 0.5 m steps. Table i presents the
estimates and errors for phase interferometry only, the addition of
amplitude measurements and FFT processing, and for the final MUSIC
processing.
TABLE-US-00001 TABLE 1 Signal paths (m) [0.5, 1] [0.5, 1.5] [0.5,
2] [0.5, 2.5] [0.5, 3] [0.5, 3.5] [0.5, 4.0] [0.5, 4.5] Estimate
(m) 0.64 1.1 1.2 1.4 1.2 1.1 1.6 1.2 phase interferometry Error (m)
0.14 0.6 0.7 0.9 0.7 0.6 1.1 0.7 Phase only Estimate (m) 0.7 1.0
1.1 1.3 [1.1] [-0.2, 4.4] [0.22, 4.4] [0.1, 5.1] (FFT) Error (m)
(FFT) 0.2 0.5 0.6 0.8 0.6 -0.7 -0.28 -0.4 Estimate (m) 0.69 0.9
[0.74, 1.9] [0.65, 2.2] [0.65, 3] [0.49, 3.51] [0.49, 3.98] [0.43,
4.7] (MUSIC) Error (m) 0.19 0.4 0.24 0.15 0.15 -0.01 -0.01 -0.07
(MUSIC)
[0041] As can be seen, after MUSIC processing, the error is
generally in the range of 10 cm-20 cm. This allows much more
accurate determination of the object as compared to other
techniques. In the automobile example, this allows a determination
of when the key fob is inside the automobile, as needed for not
locking and for starting, or outside of the automobile, as needed
for locking and unlocking.
[0042] While the above description has used Bluetooth as the
exemplary RF protocol, other protocols can be used as well, such as
Wi-Fi. Further, frequencies other than the 2.4 GHz of Bluetooth can
be used, such as the 900 MHz spectrum.
[0043] While an automobile and a key fob were used as the example
need for precise distance measurements, many other environments are
appropriate. For example, in a warehouse, the target objects are
the boxes and packages. In a construction environment, the power
tools are the target objects. In a retail environment, the various
items are the target objects. In a farm environment, the livestock
are the target objects. The particular protocol used depends on the
desired distance, but in all instances the protocols allow the
transfer of specific information about the object to aid in
identifying the object. In the automobile example, the security
code of the key fob is exchanged with the automobile to identify
the key fob association with the specific automobile.
[0044] The above-described examples may be used in combination with
each other. Modifications are possible in the described
embodiments, and other embodiments are possible, within the scope
of the claims.
* * * * *
References