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Using two GPS satellites to improve WiFi positioning accuracy in urban canyons Binghao Li, Yong Khing Tan, Andrew G. Dempster School of Surveying and Spatial Information Systems, University of New South Wales, Sydney, Australia
Abstract It is well known that a GPS receiver needs to “see” at least four satellites to provide a 3D fix solution. But in difficult environments such as an urban canyon, the number of “visible” satellites is often not enough. WiFi signals have been utilized for positioning mainly based on the fingerprinting technology. However, the accuracy of WiFi positioning outdoors is from several tens of meters to more than one hundred meters. This paper proposes a new methodology to integrate WiFi positioning technology and GPS to improve positioning accuracy in urban canyons. When only two GPS satellites are visible, the pseudorange observations can be used to generate a Time Difference of Arrival (TDOA) measurement. The TDOA generates a hyperboloid surface which can be intersected with the surface of the earth and shows the possible location of the user on that line of position. Integrating this method with the WiFi fingerprinting technology can increase the positioning performance significantly. The test results show that the positioning accuracy can be improved by more than 50% if the new method can be applied.
1. Introduction
GPS is widely used for positioning and navigation. It is well known that a receiver needs to “see” at least four GPS satellites to calculate the user’s 3D position. Furthermore, to obtain an accurate position, the geometric distribution of the “visible” satellites should be good – that is evenly spread in the sky. Dilution of precision (DOP) is used to indicate the impact of the geometric distribution of the satellites on positioning accuracy. Ideally, the more satellites that can be seen and the lower the DOP, the better the positioning result that can be achieved. Hence open sky is the best environment for GPS applications. However, in reality, users are often indoors or in urban canyons where GPS suffers from satellite signal blockage, signal attenuation and multipath. In difficult environments, GPS cannot continuously provide a reliable solution and other positioning technologies are required.
Many specific indoor positioning systems have been developed since the 1980s, such as active badge [1], Bat [2], Cricket [3], smart floor system [4] and Indoor Messaging System [5]. These technologies have found their applications. However, they cannot be deployed widely since specific infrastructure is needed. Utilizing current infrastructure for positioning purposes is more attractive as it is much cheaper and it can be deployed much more quickly. Mobile phone networks, Wireless Fidelity (WiFi), and TV systems, originally designed for other purposes have been used for positioning [6-8]. WiFi is a very attractive alternative positioning technology due to wide deployment of WiFi access points (AP) and the growing number of WiFi enabled mobile devices. Over the past five years, tens of millions of WiFi access points have been deployed by individuals, businesses, academic institutions etc. According to ABI Research (http://www.abiresearch.com), global WiFi AP shipments were over 40million in the first three quarters of 2009. It forecasts that 802.11n WiFi AP shipments alone into consumer markets are expected to reach 32.2 million in 2010. Shipments of WiFi-enabled mobile phones will double in volume by the end of 2010, compared to January 2008.
There are many companies which provide positioning systems or positioning services based on
WiFi
signals,
Ekahau
and
Skyhook
are
two
examples
(www.ekahua.com,
www.skyhookwireless.com). Obviously WiFi positioning systems can only be used where many WiFi access points have been deployed – such as indoors, university campuses and city centres. Indoors, as the satellite signals are very weak (less than -142 dBm) and most of signals received are affected by multipath, WiFi positioning is far more accurate than GPS. The accuracy is several meters using WiFi [9] compared to 60 meters or worse using Assisted-GPS (with a high sensitivity GPS receiver) [10]. Quite often GPS simply does not work or the time to first fix (TTFF) is extremely long (several minutes) indoors. Outdoors, the situation is slightly different. For example, the density of WiFi access points is not as high as indoors, and the obstacles to WiFi signals are larger and have more mobility (e.g. buses and cars). This makes WiFi positioning results much worse outdoors than for indoors. Tests using Ekahau and Skyhook show that the accuracy of WiFi positioning is tens of meters to a hundred meters [11]. Another difference between outdoors and indoors is that line of sight visibility of 2 or more GPS satellites is more likely. As we know, fewer than 3 satellites cannot generate a 2D position. So a new question arises: if only 2 GPS satellites are visible, can we utilise those satellites to improve WiFi positioning accuracy? This question will be discussed in the following sections. Firstly WiFi fingerprinting technology is introduced, and then the use of two GPS satellites for positioning is discussed. It is followed by the methodology for an experiment using two satellites and geographic information (map matching) to assist WiFi positioning. Finally, conclusions and future work are given.
2. WiFi Fingerprinting Positioning Using WiFi signals for positioning was first applied by Microsoft Research [7]. Since then, researchers have put much effort into this area and several algorithms have been proposed.
Basically, there are two approaches: trilateration and fingerprinting. The trilateration approach requires at least 3 base stations with known coordinates. If the distance r from the AP to a mobile user (MU) can be measured, a circle with radius r can be drawn. Circles centred on several APs intersect at one point which is the position of MU. The problem is the measurements obtained are based on signal strength (SS) rather than the distance. Hence, the SS should be converted to a distance first which is essential for the trilateration approach. Finding a good signal propagation model to convert SS to AP-MU distance is not an easy job since the environment varies significantly from place to place. Once the distances are obtained, least squares or other methods (such as the geometric method) can be used to compute the coordinates [7, 9, 12].
Since it is extremely difficult to build a sufficiently good general model of signal propagation that coincides with the real world, the fingerprinting approach is more attractive. The fingerprinting approach consists of two phases: ‘training’ and ‘positioning’ [9, 13]. The objective of the training phase is to build a fingerprint database. In order to generate the database, reference points (RP) must first be selected. In the positioning phase, the MU measures the received SS (RSS) at a place where it requires its position. An appropriate search/matching algorithm is used to compare the measurements with the data in the database. The MU’s location is estimated based on the similarity of the “fingerprint”.
The fingerprinting approach has been accepted as an effective method for WiFi positioning although it has its own problems. There are two categories of methods to estimate the unknown location: the deterministic method and the probabilistic method. The deterministic method [7] is relatively simple. In the training phase, the average RSS of each AP measured at each RP is used to create the fingerprint database. And in the positioning phase, the mean of the RSS measured at the location of interest is calculated. Then many algorithms can be used
to estimate the position of MU. However, no matter how complex the algorithms appear, they are derived from the same basic one - nearest neighbour (NN). The signal distance between the measured SS vector [s1 s2 … sn] and the SS vector in the database [S1 S2 … Sn] is computed. The definition of the distance (L) between two vectors is
1
⎛ n q ⎞q Lq = ⎜ ∑ s i − S i ⎟ ⎠ ⎝ i =1
(1)
Different q values indicate different distance measures. The two most common distance measures are Manhattan distance and Euclidean distance (L1 and L2 respectively). Li et al. [9] investigated the relationship between mean distance error and different signal distance, and showed that when q is close to 1 (Manhattan distance) the smallest distance error can be achieved (although the improvement is not significant). The nearest neighbour is the point with the shortest signal distance. Many other issues related to the deterministic method have been investigated such as the impact of the orientation [14, 15], and the relationship between signal distance and geometric distance [16, 17].
Since the variation of the SS measured at each point is large, simply averaging the RSS loses much useful information. In order to utilize this information and achieve more accurate results, the probabilistic method based on Bayes rule was developed [13, 18]. For positioning, Bayes rule can be written as:
P ( Lr | M ) =
P ( Lr ) P ( M | Lr ) P( M )
(2)
Where Lr denotes location and M denotes a measurement. P( Lr | M ) is a conditional probability representing the likelihood that the MU is at location Lr, given observation M. P ( M | Lr ) is the likelihood function: the probability of making observation M at location Lr.
P(Lr) is the prior probability of the MU being at location Lr when the measurements (of MU) are unknown. This can be determined from background information such as the user profiles. If this prior information cannot be obtained or to simplify the process, a uniform distribution can be assumed. The denominator P(M) does not depend on the location variable L, it is a constant and can be ignored since only the relative probabilities are required. The only unknown term is the likelihood function. To calculate it, the data collected during the training phase is needed. The distribution at location Lr for RSS from APs should be recorded rather than the average RSS in the deterministic method. Assuming the measurements from all APs at a fixed location are independent, the likelihood function is calculated by multiplying the probability of observing each reading in the measurement vector m={s1,…sn} n
P ( M | Lr ) = ∏ P( RSS APi = si )
(3)
i =1
P( RSS APi = si ) is the probability of receiving the signal from APi with the SS equal to si at location L. The maximum value of P ( M | Lr ) gives the likeliest position of the MU, similar to NN. There are two common ways to generate the empirical distribution at location Lr for SS from an AP: using either a histogram or a Normal distribution. The probabilistic method can provide a better solution [18]. However, it is more complex and increases the database size and the computational burden.
3. GPS Positioning Using Two Satellites In urban canyons, it is not unusual to see fewer than 4 GPS satellites. If there are 3 satellites available, and the altitude is known or can be estimated, a GPS receiver can still provide a useful position [19]. The accuracy of the altitude will greatly affect the accuracy of the 2D coordinate (1m error in altitude can introduce 1 to 2m error in latitude and longitude). Another
approach is providing a precise clock so a pseudorange measurement is no longer required to solve for the local clock offset [20]. This is only theoretically applicable as in most cases very accurate atomic clocks are too expensive and too large for the applications under consideration. If there is only one satellite available, it is not very useful for positioning. Mok and Lau [21] investigated using one satellite and some geometric information for vehicle location tracking in urban canyons when the clock error of the receiver can be modeled. In reality, the clock error of low-cost receivers is difficult to model, so the use of betweensatellite-differenced ranges to remove the receiver clock error is necessary. Under such conditions, at least two satellites are required. However, if two satellites can be tracked simultaneously for one epoch or several epochs, some useful information may be used for positioning.
Tan et al. [22] present a new method using the Time Difference of Arrival (TDOA) from two satellites which does not yield position directly. The basic idea is that the TDOA measurement removes the receiver clock error and generates a hyperboloid surface which can be intersected with the surface of the earth and shows the possible location of the user on that line of position (refer to Fig. 1).
The pseudorange data collected by a GPS receiver r from satellite s at epoch t can be expressed as Rrs (t ) = ρ rs (t ) + c(dt r (t ) − dt s (t )) + d rs ion (t ) + d rs trop (t ) + ε rs (t )
where
ρ rs (t ) is the geometric range (true range) from receiver to satellite at epoch t, c is the speed of light,
(4)
dt r (t ) is the receiver clock error,
dt s (t ) is the satellite clock error , d rs ion (t ) and d rs trop (t ) are ionospheric delay and tropospheric delay respectively,
ε rs (t ) is other errors. When the pseudoranges from two satellites can be obtained at the same epoch t, the TDOA measurement can be written as TDOA s1s2 (t ) = ρ rs1 (t ) − ρ rs2 (t )
= Rrs1 (t ) − Rrs2 (t ) + cdt s1 (t ) − cdt s2 (t ) − d rs1 ion (t ) + d rs2 ion (t ) − d rs1 trop (t ) + d rs2 trop (t ) − ε rs1 (t ) + ε rs2 (t )
(5)
The major error in the pseudorange, receiver clock error, has been eliminated. The differenced components of ionospheric and tropospheric delays may be reduced if the zenith angles to the two satellites are similar. Models if available can also be used to mitigate these errors. Also the satellite clock error can be minimized by applying the satellite clock correction in the ephemeris.
A 3D hyperboloid equation with two foci at (x1,0,0) and (-x1,0,0) can be represented as y2 + z2 4x 2 − =1 Δd 2 x12 − 0.25d 2
(6)
where d is the TDOA measurement. To generate the hyperboloid in space and find the intersection with the spheroid, or more precisely the ellipsoid modelling the earth, transformation and other manipulations are needed [22]. Once the intersection is created, and the area of interest is known (using other positioning technology), a further narrowing down
of the area by the intersection can be generated. Obviously, WiFi positioning in urban canyons can be considered to integrate with this TDOA result.
4. Using Two GPS Satellites to Assist WiFi Positioning The idea behind using a GPS TDOA measurement to improve WiFi positioning is straightforward. The WiFi result is not very accurate, but most of the time it can locate the user on the right street. The two satellite TDOA hyperbolic-spheroid intersection curve will usually cross the street at a useful (i.e. large) angle because the visible satellites are distributed along the gap above the street between high buildings. The intersection of this curve with the nominated street is the position estimate output by this technique. Hence this is a loosely coupled GPS/WiFi integration (Fig. 2 describes the principles of the integration). To integrate these two methods successfully, two things must first be established: i) how accurate are these two methods and ii) what can be used to indicate the accuracy of these two methods?
4.1. WiFi Positioning Accuracy
WiFi positioning in urban canyons is not very accurate. Two commercial systems, Ekahau and Skyhook have been tested in the Sydney Central Business District (CBD) using survey points with accuracy better than 1m, and errors were found to be from 10m to more than 100m [11]. These commercial systems basically use fingerprinting technology; however, the details of the systems are confidential. A WiFi fingerprinting positioning system developed by University of New South Wales was also tested. The test bed is shown in Fig. 3. The test area has dimensions of about 500m by 800m. Thousands of APs were detected including fixed infrastructure created by telecommunications companies for public usage, private APs for personal usage and those APs created by institutions or companies for their customers. At each RP, the number of detected APs varies over a range from 2 to 70. Only at least one AP is
required using fingerprinting technology, however, the more APs and the stronger the signal strength, the better accuracy can be achieved. All these APs were used for positioning. In this test, 172 RPs were used to create the fingerprint database and 26 test points were evenly distributed in the test area. The list of detected WiFi APs was logged by a PDA (personal digital assistant) for about 30 to 60 seconds at each RP or TP. When the WiFi SS was collected at the test points, the number of visible satellites was logged by a handheld GPS receiver (Garmin etrex). Fig. 4 shows that none of the test points could see more than 3 satellites during the experiment (the visibility of satellites varies with location and time). A directional database was created and a deterministic algorithm was used to estimate the test points’ position (for details refer to [15]). The coordinates obtained from Google Earth were collected as true values. Fig. 9 gives the WiFi positioning results (dotted circle line). The average error is about 25m. The results are quite good compared with that of the commercial systems, owing to the well surveyed test bed and the utilization of directional information.
4.2. GPS TDOA Measurement and Positioning Accuracy
Assuming the area of interest is flat – the height is constant, using two satellites can only generate a curve on the earth’s surface. It can be simplified by using a tangent line of the curve [22], but no specific point can be obtained. To investigate the potential positioning accuracy of this method, the positioning error was defined as the closest distance between the line and the receiver. Two tests were carried out. In the first test, a Leica MC500 connected to an antenna which was mounted on a roof of a multistory building was used to log the GPS pseudorange data for a period of 24 hours with sampling interval of 30s. In the second test, a NovAtel OEM4 was carried in a backpack to log the data in the Sydney CBD. The antenna was put in a hat worn by the researcher (see Fig. 5). In total, there are 10 test points. Data were logged by a laptop for about 1 minute at each test point with the sampling rate of 1 Hz to
get enough data for the experiment. In both tests, the true values of the test points are known – they are survey marks with accuracy better than 1m, often cm. The pseudorange is corrected by applying the satellite clock drifts, ionospheric and tropospheric delay and other errors such as relativity effects (refer to (5)). Fig. 6 shows the positioning error versus the angle between the two satellites used to create the hyperbolic-spheroid intersection curve of the first test. It is clear that the bigger the separation angle, the better result can be achieved, consistent with earlier results [22]. However, for the antenna on the roof, it has a clear view of the sky, and very little multipath. In other words, the first test was in an “ideal” environment. In reality, these near-optimum results can rarely be achieved. Hence, test two provides more relevant information. The NovAtel OEM4 can output pseudorange measurements and pseudorange measurement standard deviations. Although it is not clear how the standard deviation is calculated, it can show the quality of the pseudorange measurement. The smaller the standard deviation, the better the TDOA measurement that can be generated based on it. However, not many receivers can report the standard deviation of the pseudorange, but the carrier to noise density ratio (SNR) is often reported. Similar to the open sky test, the angle between the two satellites can be used as a DOP-like quality measure. Another parameter should be considered is the elevation angle of the satellite. Generally, a satellite with low elevation angle (say less than 10 degrees) is masked out in standard GPS positioning applications. In urban canyons, only satellites with relatively high elevation angle can be seen. The higher the elevation angle, the more likely the satellite is to have LOS. Fig. 7 depicts the relationship between the positioning error and the four parameters discussed previously based on the CBD test results. It shows clearly that a similar figure (to the open sky test) can be obtained when separation angle vs. error is plotted, but the error is much larger. In the cases of SNR and pseudorange standard deviation, if only good values are considered (for SNR >85, for standard deviation
