Satellite-Based Localization

Due to the universal availability of satellites and large penetration into the mass market, Global Navigation Satellite Systems (GNSSs) have become a de facto standard solution for outdoor positioning, especially for vehicle navigation. A GNSS refers to a constella-tion of multiple artificial satellites transmitting signals from space encoding navigaconstella-tion messages to enable the GNSS receivers to determine locations. Currently, the American NAVSTAR Global Positioning System (GPS) and the Russian Globalnaya Navigatsion-naya Sputnikovaya Sistema (GLONASS) are the only available GNSSs⁴. The European Galileo is in the process of launching and is expected to be fully operational by 2020. The three systems will be compatible with each other allowing GNSS receivers to work with Galileo, GPS and GLONASS simultaneously. In this section, we briefly present the most popular GPS system. Other GNSS systems are conceptually similar to the GPS but have several differences. More details about these systems can be found in many textbooks.

The GPS system consists of three major segments [4, 26–28]:

• The space segment consists of a constellation of 24 satellites orbiting at an altitude of about 20200 km and transmitting radio signals to users on shared L1 (1575.42 MHz), L2 (1227.60 MHz), and L5 (1176.45 MHz) frequencies for different applications based on code division multiple access (CDMA). Each satellite transmits different codes such as coarse acquisition (C/A) codes for public use and encrypted precision (P) codes or P(Y) codes for military uses.

4The Chinese BeiDou, the Indian IRNSS, and the Japanese QZSS are still regional services at the time this thesis is being written.

• The control segment consists of ground-based networked facilities of monitor stations, master control stations, and ground antennas for monitoring the satellites’ signals and status, performing analyses, and transmitting orbit and time corrections to the space segment, respectively.

• The user segment consists of a GPS receiver equipment capable of receiving the signals from the GPS satellites and processing the encapsulated information to de-termine its 3-D position and time information.

GNSS positioning relies on the principle of trilateration, which is a technique of deter-mining the position of a target by measuring its distances from known position marks (i.e., known position satellites herein). The GNSS receiver measures at least four ranges to four satellites, three for calculating the 3-D position and the fourth for correcting receiver clock error. The latter time synchronization is indispensable as the GNSS receiver determines the propagation time by correlating the satellite-generated ranging code with the receiver-generated replica code. This propagation time is transformed into a “pseudorange” after being simply multiplied by the speed of light. Yet the pseudorange does not match the geometric range due to several error sources as follows [26]:

ρⁱ_u =Rⁱ_u+cδ_u+cδⁱ+εⁱ+ζ_uⁱ, (2.1)

where ρⁱ_u is the pseudorange between receiver u and satellite i, Rⁱ_u the geometric dis-tance between them, c the speed of light, δ_u the clock error of receiver u, δⁱ the clock error of satellite i, εⁱ the error due to ionosphere, troposphere, and orbit of satellite i, and ζ_uⁱ the effect of thermal noise in receiver u and multipath error of satellite i. And Rⁱ_u =p

(x_i−x_u)²+ (y_i−y_u)²+ (z_i−z_u)², where (x_u, y_u, z_u) is the position of receiveru and (xi, yi, zi) is the position of satellite i using the ephemeris data encapsulated in the navigation messages. The position of the receiver can be estimated by iterative LS or EKF and is given in an Earth-centered Earth-fixed (ECEF) system, which can be trans-formed to World Geodetic System 1984 (WGS 84) in the form of latitude, longitude, and height [26].

Generally, the accuracy of the position estimation depends on both the pseudorange error (aka user equivalent range error (UERE)) and the user/satellite geometry (aka dilu-tion of precision (DOP)) [4, 26–28]. On the one hand, the UERE comprises common and

Table 2.2: Standard deviations of range measurement errors in a single-frequency GPS receiver [4].

Contributing source Standard deviation [m]

Common error

Satellite clock error 2

Ephemeris error 2.5

Ionospheric delay 5

Tropospheric delay 0.5

Noncommon error

Receiver noise 0.3

Multipath 1

Total (root sum squares) 6

noncommon errors. Common mode errors are highly correlated among receivers separated by baselines up to 200 km and are caused by satellite clock error, ephemeris error, and atmospheric effects (i.e., ionosphere and troposphere delays). Noncommon errors depend on environment and receiver hardware/software and are caused by multipath and receiver noise, respectively. The typical standard deviation of these errors for a single-frequency GPS receiver in Standard Precision Service (SPS) is given in Table 2.2. From the table, ionosphere error is dominant for single-frequency receivers. Dual-frequency equipment in Precise Positioning Service (PPS) can nearly completely remove this atmospheric error leading to a smaller pseudorange error budget of about 1.5 m [26].

On the other hand, when the satellites are clustered in a smaller region, the area of overlap of the signals (i.e., the area of uncertainty) is larger as illustrated in Figure 2.5.

For this reason, error propagation from pseudorange estimates to position estimates is as follows

cov(bxu) =Dσ²_UERE, (2.2)

where cov(xb_u) is the covariance of estimated state vector bx_u = [xb_u,yb_u,bz_u,bδ_u]^† whose the first three components are the estimated 3-D position and the last is the estimated clock error, σ_UERE² the standard deviation of the UERE (e.g., in Table 2.2), andDa 4×4 sym-metric matrix translating UERE to each component of cov(xbu). From this formula, differ-ent DOP variants are defined including Geometry DOP (GDOP), Position DOP (PDOP), Horizontal DOP (HDOP), Vertical DOP (VDOP), and Time DOP (TDOP) [4,26–28]. By using multiple constellations, the DOP can be improved resulting in better positioning and timing accuracies. It is worth noting that this principle will be reused in Section 3.5 for the selection of vehicular links.

range error from satellite 1

range error from satellite 2 satellite 1 satellite 2

(a) (b)

Figure 2.5: Effect of DOP in satellite-based positioning systems.

GNSS Augmentations

GNSS augmentations are techniques that enhance accuracy, robustness, and reliability by integrating external information in the position estimation. A number of techniques are briefly reviewed below.

Differential GNSS Differential GNSS (DGNSS) uses a network of ground-based refer-ence stations to broadcast the differential corrections to the common pseudorange errors such as ionosphere and troposphere errors to the users (rovers) in local region. DGNSS accuracy decreases as the distance from the reference station increases. An accuracy of about 1 m can be achieved for users in the range of few tens of kilometers from the refer-ence station [4]. However, this accuracy is only possible within much shorter baselines in dense multipath environments such as urban areas because multipath error decorrelates very quickly.

Real-time kinematic Real-time kinematic (RTK) in principle is a carrier-phase DGNSS.

The carrier-phase of GPS signal is modeled as

ϕⁱ_u = 1

λRⁱ_u+ c λδ_u+ c

λδⁱ+ 1

λεⁱ+N_uⁱ +ς_uⁱ, (2.3) where ϕⁱ_u is the carrier phase of the signal received from satellite i by receiver u, λ the wavelength of the GPS signal, ς_uⁱ the carrier phase observation noise, N_uⁱ the integer ambiguity, which corresponds to the number of cycles between the receiver and satellite when phase tracking starts. The carrier wave for the GPS signal is about 19 cm (for L1) enabling centimeter-level ranging accuracy [4]. The configurations of DGNSS and RTK

in terms of deployment and architecture are similar as both systems require a reference station (base) to broadcast differential corrections to a user (rover) through communication links. The difference is that the noise of carrier-based ranging is much smaller than that of the code-based one in the DGNSS. Yet, integer ambiguity resolution in (2.3) has to be fixed and this processing can take time from seconds to minutes. The RTK can be used for baselines of up to 50 km, yielding positioning errors inferior to 10 cm [4]. In case of frequent GNSS signal blockage, RTK is not appropriate because the rover has to track the GNSS signals continuously to avoid reinitialization.

Precise point positioning Precise point positioning (PPP) requires a network of ref-erence stations located worldwide to generate the satellites clock and orbit corrections to users via satellites. Together with a dual-frequency GNSS receiver (to remove the first order effect of the ionosphere), PPP provides positioning accuracy of a decimeter or even better [4]. When compared to the RTK, the PPP does not depend on a base station, thus provides full accuracy given satellites availability (i.e., a global positioning approach) at the price of very long and uncontrolled convergence time up to 30 minutes in case of cold start from scratch. Both RTK and PPP use carrier-based techniques.

Satellite-based augmentation systems The satellite-based augmentation system (SBAS) uses geostationary (GEO) satellites to broadcast corrections to users in wide areas, even at continental scale. The system includes several reference stations that monitor and col-lect data from GNSS satellites, before relaying to its master stations to compute integrity and differential corrections. This information is then uplinked to the GEO satellites then relayed to the SBAS users. Thus, the SBAS improves the integrity by detecting erroneous measurements very quickly, as well as accuracy and availability by providing the differen-tial corrections and extra GEO range measurements [4, 26]. When compared to DGNSS, the SBAS yields similar accuracy but better integrity. Besides, the SBAS does not need any base stations. When compared to PPP, both receive corrections from satellites. Yet, the PPP is more accurate than the SBAS, because the PPP is a carrier-based method whereas the SBAS system is a code-based one.

Assisted GNSS Assisted GNSS (AGNSS) uses a cellular network to reduce the time-to-first-fix (TTFF) which is the actual time required by a GNSS receiver to achieve a position

estimation and thus improve the startup performance i.e., saving at least 30 seconds [29].

Nowadays AGNSS is extensively used in GNSS-capable cellular phones. There are two types of AGNSS [29, 30]:

• Mobile station (MS)-based: Assistance information (almanac and ephemeris) is sent to the handset to acquire satellites more quickly.

• MS-assisted: Assistance information (timestamped pseudoranges) is sent to the net-work server to calculate the position.