 Open Access
 Total Downloads : 66
 Authors : Wantong Chen
 Paper ID : IJERTV6IS120077
 Volume & Issue : Volume 06, Issue 12 (December 2017)
 Published (First Online): 18122017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
New Method for GPS Direct Position Estimation Based on Collective Detection Approach
Wantong Chen
Tianjin Key Lab for Advanced Signal Processing Civil Aviation University of China
Tianjin, China
Abstract Collective detection is a direct position estimation method, which is shown to perform effectively in weak signal navigation applications. Different from the traditional GPS signal individual acquisition and tracking, this technique combines the received power from all GPS satellites in view and directly leads to a position solution, thus resulting in a very high sensitivity. However, the huge computation and computational complexity may limit its practical application. We then present a new method for position estimation based on collective detection scheme. We take full account of the structure of the problem to make our algorithm efficient and easy to realize. Real data test results suggest that our algorithm is effective and also good in terms of accuracy.
Keywords GPS; collective detection; weak signal navigation; vectorbased tracking; acquisition

INTRODUCTION
In recent two decades, GPSbased position and location requirements have become more and more ubiquitous for many different vehicles in terrestrial, sea, air and space. However, growing interest in indoor positioning is motivating research on techniques for weak GPS signal acquisition and tracking. Also, poor signal reception in other than opensky environments is still a problem. Hence, a lot of effort is being directed to enhance signal sensitivity such as extending signal integration times [1] and using assisted GPS techniques [2]. For these traditional methods, the signal of each satellite is acquired and processed individually, thus neglecting the association of different satellite signals on the same location.
More recently, it has been proposed that combining information from multiple satellites is also a feasible solution, represented by the collective detection technique. By combining the received power from all GPS satellites in view and directly leads to a position solution, this technique is suitable for any application that requires a navigation solution in a signal environment that challenges traditional acquisition techniques [3]. In essence, it is a vectorbased acquisition approach. Even if all signals are too weak to be acquired and tracked by the traditional framework, a quick and coarse position solution can be directly estimated by combining the received signal power from each satellite. In addition, this approach could be used to aid deeplycoupled GPS/INS navigation and assist with terrain/featurelandmark recognition in an urban environment.
Although there is no required hardware change, it is shown that the computational complexity is huge for the
This project is supported by National Natural Science Foundation of China (Grant No. 61401468).
traditional collective detection. The present new method aims to reduce the complexity of the algorithm and attempts to mitigate the shortcomings in practical application. Different from the simulated results in current literature, the experiments with actual data have also been performed.
The rest of this contribution is organized as follows. Section II provides a brief review on the traditional approach to signal acquisition and tracking. Section III describes the collective detection algorithm and its assumptions. Section IV proposes a new method for GPS direct position estimation based on collective detection approach. Section V elaborates on the actual experiments based on GPS observations, which have been performed to verify the correctness of new method and the accuracy of coarse position solution. Section VI concludes the overall contributions of this work and possible improvements are also discussed.

THE TRADITIONAL ACQUISITION THEORY
A. Motivation and Principle
The purpose of acquisition is to determine visible satellites and coarse values of carrier frequency and code phase of the satellite signals. GPS satellites are differentiated by the different PRN sequences. Only when a local PRN code that is perfectly aligned with the incoming code, a high correlation peak occurs and then the incoming code can be removed from the signal. It is also important to know the received frequency of the signal to be able to generate a local carrier signal, which is used to remove the incoming carrier from the signal. Based on both motivations, the acquisition algorithm assesses the signals correlation power in discrete bins on a grid of code delay and Doppler frequency.
In detail, the correlation power calculations are based on multiplication of locally generated PRN code sequences and locally generated carrier signals with the sampled signal from the receivers RF front end. Multiplication with the locally generated carrier signal generates the inphase signal I, and multiplication with a 90 phaseshifted version of the locally generated carrier signal generates the quadrature signal Q. The correlation power is the sum of the I and Q components, I2 + Q2. By mixing the sampled signal with a family of receivergenerated replica signals that span the grid, we can plot the power as a function of code delay and frequency shift, thus producing a correlogram. If the highest correlation peak exceeds a predefined threshold, we assume that the frequency shit and code phase parameters are correct and both parameters can be passed on to the tracking algorithms, which produce more precise measurements of delay dubbed pseudoranges from which the receivers navigation solution is calculated.
B.Strong Signal Case
The acquisition algorithm expects that a distinct peak appears in the correlogram bin that corresponds to the true GPS signals code delay and Doppler frequency, as is shown in Figure 1. Normally, if a received signal is sufficiently powerful, a distinct peak appears in the correlogram bin.
Fig.1 The correlograms for a strong GPS signal acqusitiuon (IF Frequency:4.309MHz;Sampling Frequency:12MHz)
C.Weak Signal Case
However, based on the given integration times, the fact that peak power exceeds a predefined threshold is not a certain event. In particular, when the weak signal is present, the correlation peak cannot be distinguished, resulting in the failure of the conventional acquisition approach, see Figure
2. The typical weak signal environments like indoors, foliage, forest, tunnel and deep urban canyons. The signal strength in these scenarios is normally 1025 dB weaker than the lower bound of that in opensky conditions [4].The theoretical probability of detection for traditional acquisition algorithm is discussed in [5].
Fig.2 The correlograms for a weak GPS signal acqusitiuon (IF Frequency:4.309MHz;Sampling Frequency:12MHz)
D.Solution for Enhancing Signal Sensitivity
Increasing the coherent integration time is an effective solution for giving GPS some degree of capability to operate indoors and in other restricted environments [6]. It uses the fact that the zeromean Gaussian noise accumulates
slower than the signal of interest by a longer integrated period. However, the databit transitions in the signals navigation message should be carefully wipedoff [1]. Any other adverse factors such as receiver clock instability and dynamics should also be sufficiently considered.

COLLECTIVE DETECTION THEORY
In the traditional acquisition, the signals correlation power is evaluated in discrete bins on a grid of code delay and Doppler frequency. Different from that, in the collective detection algoritm, the combined correlation power is evaluated on the position and clock offset grid. Thus, it leads directly to the navigation solution. In other words, collective detection is a direct position estimation method. All the individual GPS signal correlations map into the navigation domain, in which the combined correlation power is evaluated. However, the mapping requires the receiver to have a priori knowledge.
A.Priori Informaiton
As a priori knowledge, the approximate position of the receiver, the GPS ephemerides and the current GPS time are often required for the collective detection technique. The approximate position can be provided by the extrapolation of the past positions or other positioning method like GSM and WiFi. The GPS ephemerides can be obtained from the Internet, the wireless communication or the previous satellite data. The current GPS time is an important assumption, which can be attained after the first successful estimation of navigation solution. Then, the receiver clock can be corrected to GPS time and the clockbias is assumed insignificant in a short period of time.
B.The Search Space
With the priori knowledge above, the collect detection algorithm defines the position and clock offset search grid centered on the assumed receiver state. The mapping then relates each one of the position and clock offset grid points to a specific code delay and Doppler frequency for each GPS satellite. Different from the grid of code delay and Doppler frequency which is used in traditional acquisition scheme, the search space of collective detection scheme is set up with all the possible position and clock bias of the receiver. In other words, the search space has four dimensions: three search dimensions for positions and a fourth dimension for the clockbias. Next, for each candidate NorthEastDownClock value in the search space, projections are performed from the codephase/Doppler domain to position/clockbias domain.
C.The Basic Principle
Collective detection is a direct position estimation method, which combines the received power from all GPS satellites in view and directly leads to a navigation solution. Based on the search space described above, the correlation power is summed over all the GPS satellites at each position
/clockoffset grid point to create a navigation domain correlogram. The grid point that has the highest combined correlation power denotes the optimal position and clock offset estimation. Since the correlogram is built based on the scheme of noncoherent combination of multiple satellites, the correlation power detection is assumed as collective. It
indicates that the signals which are too weak to be acquired and tracked can also be incorporated into the estimation of navigation solution.
D.The Computation Process
For each grid point of the search space, we should compute the correlation power for each satellite. The correlator values are taken as the multiplication of the sampled IF signal and the locally generated signal. We can use the computed pseudorange to compute the received codephase by the following equation:
Since the search space has four dimensions dubbed NorthEastDownClock, the number of points to be evaluated is huge and requires large computational time. The computational complexity can be reduced to a certain extent by decreasing the step size of the grid, but the accuracy of navigation solution will be reduced significantly. In fact, the largest step size is limited by the length of one ranging code. Hence, the existing collective detection scheme has limited practical applications.

NEW METHOD AND ITS IMPLEMENTATION
= mod c,Tc
(1)
This section presents a new method for position estimation based on collective detection scheme. The
c
where is the computed codephase and T is the period of the ranging code and is the computed pseudorange of
each point in the search grid. We can compute each satellites position using the ephemeris data and then compute the pseudorange with it. Assuming that is the
pseudorange at the center of the search space, is given by
=N cos cos E sin cos Dsin b (2)
where is the azimuth of the satellite and is the elevation of the satellite and N, E, D, b is the
difference between the candidate grid and the center grid. The details of the collective detection approach are presented in [7, 8]. Figure 3 demonstrates the basic principle and computation process of collective detection approach.
E.The Computational Complexity
Although the sensitivity can be improved significantly with collective detection, the main issue of the algorithm is the computational complexity.
proposed algorithm is efficient and easy to realize. Real data test is also performed to verify the correctness of the new method.
A.The Reduction of Search Space
In order to accelerate the traditional collective detection, a practical strategy is to cut down the dimension of the search space. Since the clockbias dimension is much larger than the other three dimensions, it is assumed to be the major factor that increases the complexity of the collective detection algorithm. Thus, a very finetime assistance will alleviate the computational load. More specifically, the reduction in clockbias search domain can be achieved in the following two scenarios.
The first scenario is that a successful positioning has been done. Then, the receiver clock can be corrected to GPS time and the clockbias is assumed insignificant in a short period of time. The second scenario is that the estimation of receiver clock bias is too coarse but as least one satellite is strong enough to be acquired individually by the acquisition block. In this case, the reference [9] proposed one method to estimate the clockbias. The basic principle is that the clock bias can be computed by the difference between the measured codephase and the geometric codephase. The former can be extracted by the strong satellites correlogram and the latter is calculated by the computed geometric range.
Navigation
Domain
Code Delay and Doppler Search Domain
Signal Power
SVN
Grid Point
Parameter Estimation of SV1
Noncoherent
SV2
Correlation Power of SV1
Com bined Correlation
Power
combination
SV2
on
North[m]
Priori Informait
SVN
Doppler
Doppler
Doppler
East[m]
Traversing all the grids
Code Delay
Code Delay
Code Delay
The Combined Correlation Power Over All the Grids
The Highest Combined Correlation Power
Fig.3 The basic principle and computation process of collective detection approach
B.The Calculation of Code Phase and Doppler
mt , nt , kt arg max E
We assume that the receiver clock is synchronous with GPS time and the tiny clockbias could be ignored. For each grid, the corresponding code phase and the Doppler
K i m,n,t i1
m, n, t
(8)
frequency of each satellite are thus calculated as follows. Here the position coordinate of the candidate grid is denoted as u , thus we have the following equation:
rx u
rx u u
u s i (tGPS i ) T i u I i u c i (3) where t GPS is the GPS time for the received signal; i is

he Fast Estimation of Signal Transmission Time
Note that there is no analytic solution for (3) due to its nonlinearity. However, the signal transmission time can be resolved by the dichotomy algorithm. The specific steps are as follows:

Supposing that the transmission time at epoch k for
satellite i is i and the maximum of fluctuation range of the
the signal transmission time from the satellite i to the
candidate grid u ; s i (tGPS i ) is the satellite position when
k
trnsmission time at the next epoch is , the interval of
rx u
the electric signal is sent from the satellite, which can be
i
k 1
can be given by
computed with the known GPS ephemerides;
I i u is
i
i , i ,if
fi tGPS 0
k 1 k k
k rx
(9)
k 1
k k
k
rx
ionosphere error and
T i u
is the troposphere error; c
i
i – , i ,if
fi tGPS 0
denotes the velocity of light.
Equation (3) can be solved by the dichotomy algorithm, which is described in the following section. Assuming that
the transmission delay i is resolved, the signal sending
where fi tGPS is the Doppler frequency of satellite i at epoch k.
k rx

Compute the middle time in the interval given by (a):
u
time of satellite clock is given by
m L H /2
(10)
tx rx u rx u
ti tGPS i dti (tGPS i )
i GPS i
(4)
where L is the lower boundary of the interval and H is the upper boundary of the interval.

Let i be , if we have
where dt (trx u ) is the satellite clock bias at the GPS
GPS i
k +1 m
u s i (tGPS i ) T i u I i u c i
(11)
time (trx u ) . Thus, the received codephase at GPS time
rx k 1
k 1
rx
rx k 1
k 1
t GPS can be computed by the following equation:
then the interval will be updated with L,m .Otherwise, if
Di
tGPS
= mod
u s i (tGPS i
) T i u I i u c i
(12)
where
D i tGPS
rx tx c
is the computed codephase and Tc
ti ,T (5)
is the
then the interval will be updated with m , H .

Repeat step (b) and step (c), until the following

rx
k 1
period of the ranging code (1ms for GPS L1 C/A). The condition is required:
rx k 1
k 1
Doppler frequency of satellite i is
u s i (tGPS i
) T i u I i u c i
104
(13)
rx
fi tGPS =
d u s i (tGPS i )
rx u
dt
(6)
Here i
can be treated as the solution of (3) at epoch k+1.
rx


RESULTS AND DISCUSSION
With the estimated codephase
D i tGPS
and the Doppler
In order to verify the correctness of proposed collective detection method, actual static pointing experiment has been
rx
frequency fi tGPS , a local signal is generated. Next, the
correlation power is calculated by the multiplication of the locally generated signal and the sampled signal from the receivers RF front end. By combining information from multiple satellites, the total correlation power is given by
K
carried out. The coordinates of the location of the data acquisition are (39.97995 Âº N,116.33410 Âº E,28.9m). For comparison purposes, a power divider is used to split the GPS signal from the antenna into two branches equally. For one branch, the GPS L1 data were logging by JAVAD Alpha2 receiver with advanced multipath reduction. This
E m, n, k Ei m, n, k
i1
(7)
branch is denotes as the normal branch. For the other branch, the GPS signal was first attenuated about 8dB by an
where K is the number of visible satellites and Ei m, n, k
is the correlation power corresponding to satellite i for the grid m, n, k . By traversing all grids, the grid point that has
the highest combined correlation power is assumed as the best position. Without loss of generality, we assume that a distinct peak appears in the correlogram bin mt , nt , kt ,
thus giving by
attenuator and then data were collected by a RF front end and processed by SoftwareDefined Receiver. The important parameters for the signal processing are

Sampling frequency: 12MHz

Intermediate frequency: 4.309 MHz, and

Onebit sample.
Figure 4 shows the constellation of GPS satellites, with seven satellites visible. The carriertonoise ratio of each satellite is given in Table 1 for both branches.
TABLE I. SIGNAL POWER FOR BOTH BRANCHES TABLE II. COMPUTING TIME FOR DIFFERENT STEP SIZE
GPS Satellites PRN
18
21
24
15
9
22
14
Normal Branch C/N0(dBHz)
49
46
46
43
42
41
40
Attenuated Branch C/N0(dBHz)
41
38
38
35
34
33
32
Step Size
Position Estimation
Averaging computing time(second)
Standard deviation(meter)
25m
2.668
12.3
50m
0.958
30.2
100m
0.389
59.8
200m
0.245
119.5
30
330
0
300
30
60
45 9
22
60
18 15
270
75
90
90
24
120
240
14 21
150
180
210
Fig.4 The constellation of GPS satellites
Note that the traditional positioning will not be achieved for the attenuated branch, because the satellites with strength 35 dBHz or lower are not acquired and are almost as noisy as the satellites not visible to the receiver. As is shown in Table 1, PRN 18, 21 and 24 have strong signals and they can be acquired using the standard method. However, the number of satellites with strong signal is less than four satellites, thus making the standard positioning impossible.
Different from the standard positioning method, the proposed collective detection approach combines the received power from all GPS satellites in view and directly leads to a position solution, as is shown in Figure 5. The priori knowledge about the approximate position of the receiver is provided by a cellphone tower, and the receiver clock bias is estimated using the averaging clockbias estimations across all strong satellites, based on the approach proposed in [9]. Both the position accuracy and computational load are determined by the step sizes or the density of grid partition.
Fig.5 Direct position estimation using the proposed collective detection approach (The step sizes of both the north component and east component are 50m, using the priori height)
The elapsed times for the proposed method are measured at every epoch using Visual Studio 2008 development platform at a PC with IntelÂ® Pentium(R) 4 CPU 2.40GHz and 2048MB RAM.
Since the accuracy of position decreases as the computing time decreases, a balance should be achieved for the step size between the computing time and accuracy.


CONCLUSIONS
This contribution provides a detailed implementation method of collective detection, and the example results from actual GPS signals show how the noncoherent combination of multiple satellite signals improves the GPS position error in cases where some of the signals are too weak to be acquired and tracked by traditional methods. This capability is particularly useful to a user who benefits from a rapid, but coarse, position solution in a weak signal environment such as indoors and urban Canyon. Although the accuracy of collective detection is in general lower than hat of the traditional GPS positioning algorithm, the proposed method has obvious advantage for the quick position solution under the weak signal scenario. Thus, this technique could provide a new way to aid deeplycoupled GPS/inertial navigation.
ACKNOWLEDGMENTS
This work is supported by the National Natural Science Foundation of China (Grant No. 61401468)
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