Abstract—When the reception of GPS signals becomes
unreliable, an alternative is to explore signals of opportunity (SOOP) for positioning. Broadcast digital radio transmissions (e.g., digital TV signals) contain field and segment sync codes, which can be used for ranging even though it was not originally designed for so. Another example is the wireless local area network (WLAN) signals. However, there are two major difficulties. Although the location of SOOP sources is known, the number of independent SOOP sources and their geometric distribution may not be favorable for precise positioning. Besides, the clocks of SOOP transmitters are not synchronized, each subject to a different bias and drift. To respond to the 2009 NAECON Grand Challenge, we set forth a cooperative position location approach. The proposed concept makes use of differential ranges between cooperative devices to a common SOOP source, the relative ranges between the cooperative devices, and displacement measurements by the cooperative devices. The cooperation among networked location devices not only allows them to choose the most appropriate positioning mechanism but also provides them with additional measurements to reduce the number of SOOP otherwise required. In addition to data exchange, the radio link between two cooperative devices also allows for estimation of their clock offset. This leads to a joint position location solution via fixed-point smoothing. In this paper, we present the proposed system concept, its subsystems, and their operations and also analyze preliminary simulation results.
I. INTRODUCTION The Global Positioning System (GPS) has become a more
and more popular positioning device for military and civilian users alike [1, 2, 3, 4]. However, there are a number of situations where GPS may not be available or reliable. GPS satellites may stop functioning due to failure or destruction. GPS signals may be turned off purposely. GPS signals may be subject to jamming and/or unintentional interference. Blockage due to buildings and vegetation can severely attenuate the received signal strength, leading to poor accuracy and even loss of signals. In these cases, there is no GPS solution.
On the other hand, there are real-life needs for locating a team of cooperative users for military operations, fire fighting,
emergency response, search and rescue among others. In such GPS-denied environments, signals of opportunity (SOOP) may be explored for positioning to supplement or replace GPS [5, 6].
By signals of opportunity, we mean those signals that are not originally intended (designed) for positioning but they are freely available all the time and everywhere (within a certain range, of course). To be useful, the location of the transmitter of a SOOP needs to be known and so are some recognizable characteristics of the signal. However, there are some serious issues in positioning with SOOP. Due to limited terrestrial transmitter height, the solution is most likely two-dimensional (2D) rather than three-dimensional (3D). Compensation for slant ranges is required if the height difference is significant. More importantly, there may not be enough “independent” SOOP. Several antennas may be on the same transmission tower. This tends to produce a rather poor geometric dilution of precision (GDOP).
In addition, the SOOP are most likely not synchronized, each subject to a different bias and drift. There is no explicit timing information coded on the signal. Another issue of importance is integrity because they are of opportunity and signal authentication is needed. At reception, severe multipath is of concern, particularly in an urban environment.
Examples of SOOP include broadcast analog and digital signals such as AM/FM radio and analog/digital TV (transmission towers), wireless local area network (WLAN) signals such as WiFi and WiMax (access points), cellular and mobile phone network base stations, radar sites, RFID tags, RF beacons/transponders, eLoran, partially available GPS, tactical communication signals, communications satellite signals, and even celestial and other nature signals. This paper will focus on digital TV (DTV) and WiFi signals [7, 8].
To respond to the 2009 NAECON Grand Challenge: Signals of Opportunity (http://www.naecon.org/), we set forth a cooperative position location approach. The proposed concept makes use of differential ranges between cooperative devices to a common SOOP source, the relative ranges between the cooperative devices, and displacement measurements by one or more of the cooperative devices. The
Research supported in part under FA8650-09-M-1582, which is gratefully acknowledged.
cooperation among networked location devices not only allows them to choose the most appropriate positioning mechanism but also provides them with additional measurements to reduce the number of SOOP otherwise required. In addition to data exchange, the radio link between two cooperative devices also allows for estimation of their clock offset and relative range. Indeed, with displacements by one or more cooperative devices measured, the dependence on the number of independent SOOP sources and their geometry is alleviated. This leads to a joint position location solution via fixed-point smoothing.
The rest of the paper is organized as follows. Section II presents the proposed cooperative position location mechanism and methods of ranging with radio signals. Section III describes three enabling techniques in detail. Preliminary simulation results are presented in Section IV together with analysis. Section V concludes the paper with an outline of future work.
II. COOPERATIVE POSITIONING MECHANISM
A. System Concept Figure 1 is the block diagram illustrating the proposed
cooperative position location system concept where the SOOP can originate from surface, airborne, and/or space transmitters so long as their locations at the time of signal transmission are known [9].
Fig. 1 System Block Diagram
Two cooperative position location systems i and j are shown in the figure, each having a data link transceiver to communicate to each other. A broadcast digital transmission (BDT) receiver is used by each system to capture features of SOOP in common. Each has a displacement sensor to measure respective movements individually or in coordination.
Auxiliary sensors include a barometer for differential height. Other system components include a digital database (e.g., a list of SOOP and their characteristics and a local digital map), a user interface, a local clock (an oscillator) that drives all sensors and electronics of the system coherently and a cooperative position location processor for managing the system operations and delivering the final solution.
B. Positioning Mechanism For simplicity, consider a 2D scenario as shown in Figure
2. There are one SOOP transmitter k located at (ξ, η), which is
known, and two cooperative receivers i and j, located at (xi(t1), yi(t1)) and (xj(t1), yj(t1)) at an initial time t1, which are unknown and to be estimated.
With respect to the global coordinate system ξ-η, we are to estimate the unknown receiver locations. Assume that receiver i carries a local coordinate system of its own x-y, which is oriented with respect to the global coordinate system ξ-η by an unknown azimuth angle θ0. As a result, at t1, we have five unknowns, namely, xi(t1), yi(t1), xj(t1), yj(t1), and θ0.
At this point of time, two measurements can be made. One is the relative range between the two receivers rij(t1):
ijjijiij nyyxxr +−+−= 22 )()( (1)
where nij is the measurement noise of zero-mean white Gaussian with variance 2
rrσ . The clock offset between the two receivers is removed by calibration (see (13b) in III.B).
The other is the differential range from the two receivers to the common SOOP rk
ij(t1):
=−= kj
ki
kij rrr 22 )()( i
ki
k yx −+− ηξ
kijj
kj
k nyx +−+−− 22 )()( ηξ (2)
where kir and k
jr are the ranges to the SOOP from receivers i and j, respectively, and k
ijn is the differential measurement noise of zero-mean white Gaussian with variance 2
drσ . Again, the clock offset between the two receivers is assumed to be removed and any residual errors are grouped into the noise term. However, these two measurements are not enough to solve for the five unknowns.
Fig. 2 Cooperative Positioning Mechanism
Now assume that receiver i makes a displacement (r1, θ1) relative to its own coordinate system while receiver j remains stationary as shown in Figure 2. At t2, two more measurements are made. One is the relative range between the two receivers rij(t2) and the other is the differential range from the two
Transmitter k at (ξk, ηk)
ξ
η
Receiver i at t1xi(t1), yi(t1)
rij(t1)
θ0
θ0
rki(t1)
rkj(t1)
Receiver j at t1xj(t1), yj(t1)
Receiver i at t2xi(t2), yi(t2)
θ1
θ2
r1
rki(t2)
rij(t2)r2
x
y
ξ
η ξ
η
Receiver i at t3xi(t3), yi(t3)
Displacement by (r1, θ1)
Displacement by (r2, θ2)
rkj(t2)
SatelliteTransmitters
AirborneTransmitters
SurfaceTransmitters
DigitalDatabaseDigital
Database
DisplacementSensor
DisplacementSensor
Broadcast DigitalTransmission
(BDT) Receiver
Broadcast DigitalTransmission
(BDT) Receiver
Cooperative Position Location System i
Data LinkTransceiverData Link
Transceiver
Local Clock(Oscillator)Local Clock(Oscillator)
CooperativePositionLocationProcessor
CooperativePositionLocationProcessor
AuxiliarySensors
AuxiliarySensors
DigitalDatabaseDigital
Database
DisplacementSensor
DisplacementSensor
Broadcast DigitalTransmission
(BDT) Receiver
Broadcast DigitalTransmission
(BDT) Receiver
Cooperative Position Location System j
Data LinkTransceiverData Link
Transceiver
CooperativePositionLocationProcessor
CooperativePositionLocationProcessor
Local Clock(Oscillator)Local Clock(Oscillator)
AuxiliarySensors
AuxiliarySensors
UserInterface
UserInterface
UserInterface
UserInterface
19
receivers to the same SOOP rkij(t2). Up to t2, there are four
measurements but they are still not enough to solve for the five unknowns. The reason there are still five unknowns is because the unknown location of receiver i at t2 can be related to the unknown location at t1 (a fixed-point smoothing) by:
⎥⎦
⎤⎢⎣
⎡∆∆
+⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡
1
1
1
1
2
2
)()(
)()(
yx
tytx
tytx
i
i
i
i (3)
where the displacement vector is given by:
101
011
1
1
00
00
1
1
)sin()cos(
sincos
cossinsincos
rryx
⎥⎦
⎤⎢⎣
⎡−−
=⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡−
=⎥⎦
⎤⎢⎣
⎡∆∆
θθθθ
θθ
θθθθ (4)
Then receiver i makes another displacement (r2, θ2) relative to its own coordinate system again while receiver j remains stationary as shown in Figure 2. At t3, two more measurements are made, namely, rij(t3) and rk
ij(t3). The unknown location of receiver i at t3 can be related to the unknown location at t1 by equations similar to (3) and (4). Up to t3, there are six measurements, which are now enough to solve for the five unknowns.
Given a sufficient number of measurement equations (1) and (2), the unknowns can be found by, say, using a direct search method such as the Nelder-Mead simplex method [10]. For a function of n variables, the Nelder-Mead method starts with (n+1) points that form a simplex containing the desired solution. It attempts to minimize the scalar-valued nonlinear function using only function values, without any derivative information (explicit or implicit). The optimization problem can be written as:
)ˆ,ˆ,ˆ,ˆ,ˆ( 0θjjii yxyx
∑ ∑= =
−− −+−=N
t
M
k
kij
kijdrijijrryxyx
trtrtrtrjjii 1 1
2222
,))()(())()((minarg
0
σσθ
(5)
where M is the number of SOOP, N is the number of displaced sampling points, and k
ijr and ijr are the predicted differential
and relative ranges, respectively.
From an initial estimate )( jjii y, x, y, x=x (drop θ0 off for simplicity), the least squares method can be used. The measurement equations can be put into a vector-matrix format:
xHz ∆= (6a)
where
[ ]Tjjii yxyx ∆∆∆∆=∆x (6b)
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
−
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
=
Mij
ij
ij
Mij
ij
ij
r
rr
r
rr
11
z (6c)
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
−
−−
=
Mj
Mi
ji
ijij
ee
eeee
H11 (6d)
where ije is the line of sight (LOS) vector from receiver j to
receiver i kie is the LOS vector from receiver i to SOOP k.
The initial estimate is improved by:
xxx ˆˆ ∆+= (7a)
where the estimation error is obtained by:
zRHHRHx 111 )(ˆ −−−=∆ TT (7b)
where R is the measurement error covariance matrix.
The estimation error covariance is given by: 11 )(}{ −−=∆∆= HRHxxP TTE (8)
A scalar quantity that is frequently used to characterize the problem geometry is the GDOP defined as:
111 )()( −−− == HHHRH TT tracetraceGDOP , R = I (9)
The second equality of (9) is obtained by assuming R = I. That is, all measurements are of the same quality and the remaining quantity depends purely on the LOS vectors contained in the geometry matrix H (6d).
The positioning accuracy is determined by ranging errors on the one hand and by GDOP on the other hand. For the 2D case, the circular probably error (CEP) is given by [11]:
GDOPCEP 75.0 σ≈ (10)
where σ is the ranging error determined by the signal to noise ratio (SNR), signal bandwidth, code structure, and multipath among others. This ranging error σ can be reduced by good antenna and RF front-end designs with low noise figure (NF) and advanced baseband signal processing algorithms [12].
The GDOP is determined by the number of independent SOOP and their geometric distribution, the separation between cooperative users, and their displacements. Although the users have no control of SOOP, they can take a proactive approach to coordinating their movement (separation and displacement) so as to obtain a joint position solution, which is otherwise unavailable to them. In addition, advanced data processing algorithms can be used for data fusion with other sensors and digital databases for better results.
In summary, the proposed cooperative position location mechanism ties the relative positioning via displacement (dead-reckoning) to the global coordinate system with radio ranging (multilateration) by a fixed-point smoothing process.
C. Ranging by Radio Signals Radio ranging is based on time of flight, which is the
difference between the arrival time and the transmit time of a radio signal event. For one-way ranging at the receiver end, the arrival time can be tagged with the receiver clock. How to determine the transmit time therefore holds the key. For round-trip ranging, both the transmit time and arrival time can be tagged with the transceiver clock but the turn-around time at the far end is unknown and needs to be determined.
In one-way ranging, the transmission can take place within pre-defined, known, timeslots as in a synchronous time-
20
division multiple access (TDMA) network, which is adopted by the Joint Tactical Information Distribution System (JTIDS) and enhanced Position Location Reporting System (ePLRS) [13]. The transmission time can also be embedded into the signal itself as in GPS. Another method is to have a third party using a monitor station to estimate the transmit time as done by Rosum [7]. The transmit time of a common source can also be eliminated by the differentiation between two receivers. Finally, two one-way messages can be exchanged between two receivers to estimate their relative range.
In round-trip ranging, the turn-around time at the far end can be zero (i.e., instantaneous) as in radar or a fixed amount as in a RF transponder (JTIDS uses a fixed turn-around time to synchronize the network using for the Round-Trip Timing or RTT messages) [13]. The actual turn-around time can also be sent by a cooperative user in a separate message [14].
In our proposed positioning mechanism, three methods, namely, time difference of arrival (TDOA), two one-way messages, and separate messages, are used for timing and ranging, which are detailed below.
III. THREE ENABLING TECHNIQUES Three enabling techniques necessary to implement the
proposed cooperative position location mechanism as described in Section II are detailed below.
A. Differential Ranging to a SOOP Figure 3 shows three time bases, one for transmitter k,
which is unknown, and two for cooperative receivers i and j, which are offset by a clock bias εij to be calibrated. A common feature is transmitted at tk (time of transmit) and arrives at the two receivers at ti
k and tjk (times of arrival), respectively.
The differential range between the two receivers to the common source rij
k (2) is related to the time difference of arrival (TDOA) ∆tij
k, which eliminates the common time of transmit tk from the equation but introduces the clock bias εij.
Fig. 3 Time Bases for Differential Ranging to a SOOP
A particular SOOP of interest in this study is the Advanced Television System Committee (ATSC) 8-nary vestigial sideband signals (8-VSB), adopted in the Unites States [15]. The 8VSB ATSC DTV is made of frames, each frame has 2 fields, each field has 313 segments, and each segment has 832 symbols, as illustrated in Figure 4.
Some known characteristics of DTV signals that can be used for estimating TOA include (1) segment sync codes (4 symbols per segment), (2) field sync segments (728 known
Fig. 4 8VSB ATSC DTV as SOOP
symbols), and (3) RF watermarking codes. The symbol rate is 10.76 mega symbols per sec, which is slightly higher than GPS P(Y)-code chipping rate of 10.23 mega chips per sec. The DTV signal bandwidth of 5.38 MHz is narrower than that of P(Y)-code of 10.23 MHz but the signal is much stronger. Assume a timing accuracy of 10% of a chip/symbol duration (i.e., code phase). The expected ranging accuracy is about 3 m. Figure 5 shows the block diagram of a DTV tuner and a software-implemented baseband signal processor for timing.
Fig. 5 Block Diagram of a DTV Software Baseband Signal Processor
B. Relative Ranging & Clock Calibration The second enabling technique is the data link between
cooperative receivers. It is used to exchange data between the receivers for differential ranging and to coordinate their actions. More importantly, by doing so (i.e., exchanging data), the cooperative receivers also perform relative ranging and calibrating of their clock offset.
Figure 6 shows the two time bases of cooperative receivers i and j, which are offset by a clock bias εij. Two one-way messages can be exchanged between them for relative ranging and clock calibration. As shown, receiver i sends out a ranging request message with the transmit time t1 (request send) embedded. Receiver j time-tags the arrival time τ1 (request receive). The apparent time of flight ∆t1 is given by:
1111 nttt ij ++∆=−=∆ ετ (11)
where ∆t is the true time of flight and n1 is the measurement noise.
Receiver j Time Base
Receiver i Time Base
Transmitter k Time Base
TimeOffset εij
tk
Common Feature/EventBroadcast from Transmitter k
Common Feature/EventCaptured by Receiver i
Common Feature/EventCaptured by Receiver j
Time of Flight (TOF) (Range )kit∆ k
ir
Time of Flight (TOF) (Range )kjt∆ k
jr
Time Difference of Arrival (TDOA) (Differential Range )
kijt∆
kijr
Time Difference of Arrival (TDOA) (Differential Range )
kijt∆
kijr
kit
kjt
Time of Arrival (TOA)
Time of Transmit (TOT)
TOA
7531
-1-3-5-7
1-1-11
Randomized Data (Data + FEC)= 828 Symbols
Data Segment
Segment Sync Code= 4 Symbols
PAM in aSuppressed
CarrierVestigialSideband
832 Symbols per SegmentSymbol = 8 Levels, Raised-Cosine,
92.9 ns, 10.76 Mega Symbols/s(Derived from a 27 MHz Clock)
Field # 1, 313 Segments, 24.2 ms, 41.32 Fields/s Field # 2, 313 Segments
Segment = 832 Symbols,77.3 µs, 12.94 k Segments/s
Field Sync SegmentData Segment # 1
260,416 Symbols
Data Segment # 312• • •
LNA/BPFLNA/BPF
RF to IFConverterRF to IF
Converter
FrequencySynthesizerFrequencySynthesizer
Analog toDigital
Converter
Analog toDigital
Converter
RF Front-End
Software Running on DSP/µPor Hardwired on FPGA/ASIC
AntennaAntenna
Baseband Signal Processor
▪ Signal Detection▪ Acquisition/Tracking▪ Feature/Event Extraction▪ Time-Tagging
AMP/BPFAMP/BPF
ChannelsSelectorChannelsSelector
To CooperativePosition LocationProcessor
To Data LinkTransceiver
From CooperativePosition LocationProcessor
From Oscillator(Local Clock)
BDT Receiver Data Processor
TOA (ti)
Channel #
21
After a certain turn-around time, receiver j sends out a ranging reply message in return, which contains the transmit time τ2 (reply send), the request receive τ1, and other data. Upon tagging the reply message with t2 (reply receive) and demodulating the embedded time tags from the message, the apparent time of flight ∆t2 can be obtained as:
2222 nttt ij +−∆=−=∆ ετ (12)
where n2 is the measurement noise.
The relative range and clock offset can be calculated as:
ntnntttt +∆=+
+∆=∆+∆
=∆22
ˆ 2121 (13a)
nnnttijijij
~22
ˆ 2121 +=−
+=∆−∆
= εεε (13b)
where n is the averaged noise sum and n~ is the averaged noise difference. The measurement noise can be significantly reduced by repeating the process several times assuming that ∆t remains constant.
Fig. 6 Time Bases for Relative Ranging and Clock Calibration
The process described above is the ranging protocol with embedded time tags, which was employed in the ePLRS between remote stations (RS) [13]. There are other protocols such as the ranging protocol with separate message used in IR-UWB (IEEE 802.15.4a) [14]. Other examples include two-way time of arrival based ranging, differential two-way ranging, and symmetric double-sided ranging among others.
It was reported in [16] that four ways averaged WLAN ranging accuracy is about 4 m in an indoor environment. For IR-UWB, the pulse width is about 8 ns (or 3 m) and the resulting ranging accuracy is about 0.03 m to 0.3 m.
Figure 7 shows the block diagram of a typical data link transceiver, which contains a data receive channel and a data transmit channel with their respective receive signal processor and transmit signal processor. In addition to WiFi and UWB, conventional full duplex data links in the S, C, and UHF-band may be used to serve this purpose.
C. Displacement Sensing Displacement sensing is the third enabling technique used
to implement our cooperative position location approach. An animal such as a honey bee does this effortlessly. A foraging bee travels 2.5 to 10 km around its hive. It measures displacement in terms of direction and distance. It is believed that a honey bee determines its azimuth relative to the Sun and knows how to compensate for temporal variation in elevation (the Sun compass) [17]. In a clouded day, the polarized UV light is used for direction-finding. Sometimes, the magnetic
Fig. 7 Block Diagram of a Data Link Transceiver
field is used. With a low-resolution vision due to compound eyes, landmarks are less used for long-distance azimuth reference. A honey bee may determine the distance it has traveled by the amount of efforts it expended in flight. Experiments show a visual odometer is used by the bee based on optical flow measurements for long-distance traveling [18].
A rudimentary displacement sensor that can be operated manually is shown in Figure 8. A magnetic compass is used to find the magnetic north, with respect to which the direction of a displacement can be measured. A tape measure can be used to determine the distance travelled. If walking steady, a person can even estimate the distance from the number of strides.
Fig. 8 Rudimentary Displacement Sensor However, such a manual measurement of displacements is
slow in operation and has some practical constraints. It is also subject to many source errors such as magnetic anomaly and deflection. Nevertheless, the measurement process can be automated with such precise instruments as a digital magnetic compass and a laser range finder.
As a standard feature, today’s automobiles are configured with an anti-lock break system (ABS). The wheel speeds are measured and are readily to be picked up from the CAN bus. As a result, the displacement vector of the center gravity (CG) can be estimated, in terms of the longitudinal and lateral speeds, by [19]:
⎥⎦⎤
⎢⎣⎡ +
= rbvv lrrrCG
2v (14)
where vrr is the speed of the right rear wheel, vlr is the speed of the left rear wheel, b is the distance from the rear axial to the CG, and r is the yaw rate given by:
Cooperative positionlocation receiver iLocal time base t
Cooperative positionlocation receiver jLocal time base τ
t1
τ1 = t1 + ∆t + εij
∆t ∆t
τ2 = t2 – ∆t + εij
t2
Random turn-around time
Ranging request message
Ranging reply message
Requestsend
Requestreceive
Replysend
Replyreceive
Time offset ε21Cooperativetransceivers
t1 (t1)τ1
τ1τ2
(t1, t2, τ1, τ2)(t1)
LNA/BPFLNA/BPF
RF to IFConverterRF to IF
Converter
FrequencySynthesizerFrequencySynthesizer
Analog toDigital
Converter
Analog toDigital
Converter
Data Receive Channel
AntennaAntenna
Receive Signal Processor
▪ Signal Detection▪ Acquisition/Tracking▪ Receive Time-Tagging▪ Data Demodulation
Receive Signal Processor
▪ Signal Detection▪ Acquisition/Tracking▪ Receive Time-Tagging▪ Data Demodulation
AMP/BPFAMP/BPF
To CooperativePosition LocationProcessor
PowerAmp
PowerAmp
IF to RFConverterIF to RF
ConverterData
Modulator
Data Transmit Channel
AntennaAntenna AMP/BPFAMP/BPF
Transmit Signal Processor
▪ Request/Reply Messaging▪ Data Formatting▪ Receive Time-Tagging▪ Other messages
where vrf is the speed of the right front wheel, vlf is the speed of the left front wheel, wr is the width between the two rear wheels, wf is the width between the two front wheels, and δ is the steering angle of the front wheel with respect to the longitudinal axis. Tire pressure, wheel diameter, and wheel slip affect measurement accuracy and thus need calibration.
Figure 9 is the block diagram of a vehicle displacement sensor. It also shows the use of level/title/compass sensors for attitude determination as well as digital map matching for position location.
Fig. 9 Block Diagram for a Vehicle Displacement Sensor
Another category of displacement sensors is based on inertial sensors (tri-axis accelerometers and gyroscopes). The availability of low-cost, small-size, and light-weight MEMS inertial sensors makes this implementation attractive [21]. The use of fixed-point smoothing actually offers an alternative way to integrate inertial sensors with other navigational aids [9].
IV. PRELIMINARY SIMULATION RESULTS & ANALYSIS In this section, the simulation results of joint positioning of
two cooperative receivers are presented for two scenarios. In the first scenario, there are enough SOOP and the solution is obvious and easy. In the second scenario, there are no enough SOOP. Conventional approaches provide no solution whereas our proposed method creates the conditions to generate a solution, thus being proactive. Additional results for such scenarios where one receiver is at a known location can be found in [9]. The known location can be obtained from a nearby landmark, be an intersection of known streets, or can be determined via the self-calibrating method [20].
A. Joint Positioning with Enough SOOP Figure 10 shows the first simulation where two devices are
separated by 200 m. In this 2D scenario, there are four SOOP marked with blue circles (o), named SOOP1 at (0 m, 5000 m), SOOP2 at (5000 m, 0 m), SOOP3 at (5000 m, 5000 m), and SOOP4 at (3000 m, 1000 m), respectively. At each sampling time, the two cooperative devices generate a relative range between them and four differential range measurements to the four SOOP. As a result, the 5 measurement equations are enough to solve for the 4 unknowns, namely, the respective x and y coordinates of device 1 and device 2.
The true locations of device 1 and device 2 are marked in Figure 10 with red and blue stars (*). The initial guesses are marked with red and blue triangles (∆). The estimates for
device 1 and device 2 using the direct search method are marked with red and blue squares ( ). The estimates for device 1 and device 2 using the least squares method are marked with red and blue crosses (×). The two solutions are comparable in accuracy. In the simulation, the standard deviations for the relative and differential ranges are set as σrr = 7 m and σdr = 5 m, respectively.
Fig. 10 Cooperative Positioning with Enough SOOP (d = 200 m)
In the second simulation, the four SOOP remain the same but the two devices are separated by 1000 m, as shown in Figure 11. The same standard deviations σrr = 7 m and σdr = 5 m are used. The same colors and marks are used to present the estimation results.
Fig. 11 Cooperative Positioning with Enough SOOP (d = 1000 m)
Figure 12 shows the GDOP of the joint positioning solution as a function of the separation between the two devices, normalized to the size of the SOOP network, which is 5000 m in the simulated cases.
As shown in Figure 12, when the separation is increased, the GDOP is reduced. For given ranging errors, the reduced GDOP leads to improved position accuracy as given by (10). This is understandable because when the devices are widely separated, their LOS vectors to the same SOOP significantly differs, thus providing a better geometry for solving the multilateration problem. This offers a practical guideline when
coordinating cooperative devices for their separation, which of course should be within the operating range of their data link
Fig. 12 GDOP of Joint Solution with Enough SOOP
B. Joint Positioning without Enough SOOP In the second simulation, there is only one SOOP at (0 m,
5000 m) as shown in Figure 13 (the blue circle o).
There are still four unknowns but at each time, there are only two measurements, not enough to solve the problem by any conventional methods.
However, after one displacement of 1000 m with θ = 25 degrees relative to the x-axis, two additional measurements are available. This allows for a full solution.
The two devices are separated by 1500 m now. The true locations of device 1 and device 2 are marked with red and blue stars (*) in Figure 13. The initial guesses are marked with red and blue triangles (∆). The estimates for device 1 and device 2 using the direct search method are marked with red and blue squares ( ). The estimates for device 1 and device 2 using the least squares method are marked with red and blue crosses (×). Again, both the estimation methods produced comparable results.
Fig. 13 Cooperative Positioning with 1 SOOP
Figure 14 shows the GDOP as a function of the separation between the two devices for different displacements (for the case with θ = 25 degrees). The GDOP decreases when either the separation or the displacement increases. Again, this is because when the devices are widely separated either initially or by displacement, their LOS vectors to the same SOOP differs significantly, thus creating a geometry better for positioning. An analogy to this situation is GPS surveying wherein GPS receivers collect data over several hours waiting GPS satellites to move across the sky so as to provide a favorable geometry.
Fig. 14 GDOP of Joint Solution with 1 SOOP
In the second simulation, there are two SOOP, named SOOP1 located at (0 m, 5000 m) and SOOP2 at (5000 m, 0 m), respectively. Both devices make displacement as shown in Figure 15. Device 1 makes 4 displacements, each with the same step size of 800 m but at a different angle (θ = 25, 35, 45, and 55 degrees). At the same time, device 2 also makes 4 displacements, each with the same step size of 200 m and at a different angle (θ = 125, 135, 145, and 155 degrees).
Fig. 15 Cooperative Positioning with 2 SOOP
Figure 16 shows the GDOP as a function of the separation between the two devices for different displacements. It indicates that by properly placing cooperative devices
(separation), a desired GDOP can be achieved when one or both devices make a suitable number of displacements (step size and direction). More results and discussions can be found in [9].
Fig. 16 GDOP of Joint Solution with 2 SOOP
V. CONCLUSIONS In this paper we investigated the use of broadcast digital
transmission and asynchronous wireless network as signals of opportunity (SOOP) for position location. Critical issues for positioning with SOOP were analyzed, which include the lack of independent SOOP, SOOP clock errors, and solution in 2D vs. 3D solution among others. Our proposed cooperative position location mechanism was described. More specifically, it uses differential ranging to eliminate the SOOP clock errors and relative ranging to calibrate cooperative clocks. Displacement by at least one receiver creates fictitious SOOP so as to improve GDOP. The relative positioning via displacements (akin to dead-reckoning) is then tied to a global coordinate system with radio ranging (akin to multilateration) using the fixed-point smoothing formulation. Both a direct search method and the least squares solution were simulated, which produced similar results for the scenarios considered.
The positioning mechanism study presented in this paper showed promising preliminary results. Our ongoing effort is focused on computer simulation of advanced signal processing algorithms. A logic step forward is to prototype the hardware and software systems for demo and to develop a practical operation procedure for performance evaluation in the field.
ACKNOWLEDGMENTS Thanks go to Dr. Di Qiu of Stanford University and Dave
Muskat, Camarillo, CA, for their helpful discussions. Self-Calibrating Position Location Using Periodic Codes in Broadcast Digital Transmissions, US Pat. 7,388,541, June
2008. Cooperative Position Location via Wireless Data Link Using Broadcast Digital Transmissions, US Pat. Pending (12/436,868), Sept. 2008.
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Theory and Applications, AIAA, 1996. [2] J.B.Y. Tsui, Fundamentals of Global Positioning System Receivers - A
Software Approach, John Wiley & Sons, Inc., 2000. [3] P. Misra and P. Enge, Global Positioning System, Signals,
Measurements, and Performance, Ganga-Jamuna Press, 2001. [4] E.D. Kaplan and C. Hegarty (eds.), Understanding GPS: Principles and
Applications (2nd ed.), Artech House Publishers, Norwood, MA, 2005. [5] G. Duckworth, Geolocation and Navigation via Signals of Opportunity,
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