Journal of Sensors

Volume 2017, Article ID 5965716, 11 pages

https://doi.org/10.1155/2017/5965716

## A Tightly Coupled Positioning Solution for Land Vehicles in Urban Canyons

^{1}School of Instrument Science and Engineering, Southeast University, Nanjing, China^{2}Key Laboratory of Technology on Intelligent Transportation Systems, Ministry of Transport, Research Institute of Highway Ministry of Transport, Beijing 100088, China

Correspondence should be addressed to Xu Li; moc.361@liam.uxil

Received 14 November 2016; Revised 11 January 2017; Accepted 6 February 2017; Published 5 March 2017

Academic Editor: Pietro Siciliano

Copyright © 2017 Xu Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The integration between Global Navigation Satellite System (GNSS) and on-board sensors is widely used for vehicle positioning. However, as the main information source in the integration, the positioning performance of single- or multiconstellation GNSSs is severely degraded in urban canyons due to the effects of Non-Line-Of-Sight (NLOS) and multipath propagations. How to mitigate such effects is vital to achieve accurate positioning performance in urban canyons. This paper proposes a tightly coupled positioning solution for land vehicles, fusing dual-constellation GNSSs with other low-cost complementary sensors. First, the nonlinear filter model is established based on a cost-effective reduced inertial sensor system with 3D navigation solution. Then, an adaptive fuzzy unscented Kalman filter (AF-UKF) algorithm is developed to achieve the global fusion. In the implementation of AF-UKF, the fuzzy calibration logic (FCL) is designed and introduced to adaptively adjust the dependence on each received satellite measurement to effectively mitigate the NLOS and multipath interferences in urban areas. Finally, the proposed solution is evaluated through experiments. The results validate the feasibility and effectiveness of the proposed solution.

#### 1. Introduction

The importance of accuracy and integrity in a positioning system has increasingly been emphasized in many intelligent transportation system or intelligent vehicle applications such as advanced driver assistance systems, intersection collision warnings, and traffic control [1–3]. During the past years, the satellite-based positioning system like the Global Positioning System (GPS) has become the primary solution for vehicle navigation. However, in critical environments such as urban canyons, the satellite signal is often blocked and/or reflected by surrounding objects causing multipath and Non-Line-Of-Sight (NLOS) signal interferences [4, 5]. The multipath means that the direct path and reflected path are received together. In contrast, the NLOS signal is only received via reflection, that is, no direct Light of Sight (LOS) path exists. In such environments, the standalone GPS cannot guarantee an accurate and continuous positioning.

To solve the issues mentioned above, there have been a number of techniques presented in the literature. Among them, the fusion of GPS with inertial navigation system (INS) and/or odometer and so forth has been a common one due to their complementary natures [6–8]. To fuse the information from multiple sensors, the Kalman filter and extended Kalman filter (EKF) are widely utilized [9–11]. Although the EKF-based methods can provide an efficient performance in many practical applications, its linearization process may suffer from divergence due to approximations during the linearization process and system mismodelling. Besides, note that nowadays, only the low-cost INS based on microelectromechanical systems (MEMS) is affordable for land vehicle applications [12, 13]. However, such low-cost INS and odometer errors diverge rapidly over time, and thus the fusion above still cannot provide acceptable navigation performance for long GPS signal outages or in the event of considerable NLOS delays.

With the rapid development of other Global Navigation Satellite Systems (GNSS) such as GLONASS and BeiDou, a possible way to fill this gap is to adopt the multiconstellation approach [14–16]. Just like GPS, GLONASS has also been fully operational. BeiDou attained initial regional operational status at the end of December 2011. It can now provide positioning, navigation, and timing services in the whole Asia-Pacific region and is expected to be fully operational in 2020. The combination of GPS, BeiDou, and other satellite constellations will provide far superior satellite geometry and signal availability compared to GPS alone. However, due to the serious impact of NLOS and multipath on the positioning accuracy in urban areas, such improvements in the availability of satellite signals do not necessarily facilitate high-precision positioning at the same time.

A series of technologies has been developed to mitigate the multipath and NLOS effects. For the multipath, they are mainly cataloged into three: antenna-based, receiver-based, and navigation-processor-based techniques [17–20]. Generally speaking, the multipath can be effectively mitigated via such techniques (the error is less than few meters). In contrast, the NLOS signals have more severe impact (can cause the positioning error as large as a few hundred meters) and are difficult to be discriminated in urban canons. In recent years, various 3D maps have been proposed and constructed to detect, exclude, or compensate NLOS delays [4, 21–24]. Though viable and useful, it is prerequisite to measure and map the building height information of the driving environments beforehand. Moreover, it may lead to huge errors if the constructed 3D map has not enough accuracy. Generally, how to mitigate the NLOS effect to improve the positioning result is still an open research topic.

In this paper, we propose a tightly coupled positioning solution for land vehicles in urban environments, which fuses low-cost complementary sensors including dual-constellation GNSSs, in-vehicle sensors, and electronic compass. The nonlinear filter model is firstly established based on a cost-effective reduced inertial sensor system with 3D navigation solution. Further, the adaptive fuzzy unscented Kalman filter (AF-UKF) algorithm is developed to execute the global fusion. Specifically, a fuzzy calibration logic (FCL) is designed and introduced, which can determine the dependable degree of each received satellite measurement according to its features including current geometrical distribution and carrier-to-noise ratio. Through such mechanism, the NLOS and multipath interferences can be effectively mitigated, and accurate positioning in urban canyons can be achieved. The main novel aspect of the proposed solution is that it does not need the prior information about the driving environment and has better adaptability and accuracy.

The remainder of this paper is organized as follows. In Section 2, the filter model used for multisensor fusion is presented in detail. Then, the fusion algorithm for implementing multisensor integrated positioning is proposed in Section 3. Experimental results are provided in Section 4. Section 5 is devoted to the conclusion.

#### 2. Nonlinear Filter Model

##### 2.1. System Model

A nonlinear motion model involving the position, velocity, and attitude states based on a reduced inertial sensor system (RISS) is adopted in this paper to cut the cost. Specifically, the RISS integrates the measurements from the vertically aligned gyroscope and two horizontal accelerometers with speed readings provided by wheel speed sensors. Though reduced, it can still provide an effective 3D navigation solution for land vehicles via 3D RISS calculation mechanization [25].

###### 2.1.1. Position and Velocity Calculation

Before describing the system equations for position and velocity, the relation between the vehicle velocity in the body frame and in the local-level frame is given bywhere , , and denote the velocity components along east, north, and up directions, respectively. , and are the azimuth, pitch, and roll angles of vehicle, respectively. is the vehicle speed derived from the vehicle’s wheel speed. is represented as

In (1), the velocity in the body frame is assumed to consist only of the forward longitudinal speed of the vehicle, while the transversal and vertical components are assumed to be zeros. Such constraints are very effective to improve the state estimates along the lateral and vertical directions.

Further, the latitude can be expressed as

Similarly, the longitude is

The altitude iswhere , , and denote the latitude, longitude, and altitude of vehicle, respectively. is the meridian radius of curvature of the Earth. is the normal radius of curvature of the Earth. is the sampling time.

###### 2.1.2. Pitch, Roll, and Azimuth Calculation

When the vehicle is moving, the forward accelerometer measures the forward vehicle acceleration as well as the component due to gravity. To calculate the pitch angle, the vehicle acceleration derived from the odometer measurements is removed from the forward accelerometer measurements:

Similarly the transversal accelerometer measures the normal component of the vehicle acceleration as well as the component due to gravity, and to calculate the roll angle, the transversal accelerometer measurement must be compensated for the normal component of acceleration:

Besides, the azimuth angle directly in local-level frame can be written aswhere is the vehicle acceleration derived from the vehicle’s wheel speed. and devote the transversal accelerometer measurement and forward accelerometer measurement, respectively. is the angular rate obtained from the vertically aligned gyroscope. is the Earth’s rotation rate. is the acceleration of gravity.

###### 2.1.3. Stochastic Errors

In order to compensate for the stochastic errors associated with the gyroscope and the vehicle’s wheel speed and enhance the estimation accuracy of the filter, these stochastic errors are also included as states, which are modeled by a Gauss-Markov model:where is the scale factor error of the wheel speed. is the stochastic gyroscope drift. is the reciprocal of the autocorrelation time for the scale factor of the wheel speed. is the reciprocal of the autocorrelation time for the gyroscope’s stochastic drift. is the variance of the noise associated with the wheel speed. is the variance of the noise associated with the gyroscope’s stochastic drift.

Based on 3D RISS as described by (1)–(9), the nonlinear system transition model about vehicle states is given by

Moreover, the receiver’s clock bias and drift errors of GPS and BeiDou can be modeled aswhere and are GPS receiver’s clock offset and drift error, respectively. and are BeiDou receiver’s clock offset and drift error, respectively.

Combining (10) and (11), we can obtain the full system state transition model for the overall tightly coupled integration aswhere and represent the state and input vectors of the system, respectively, and and are the corresponding system and input noise vectors, respectively. is the nonlinear system function where the function components can be determined based on (10) and (11). and can be represented by

##### 2.2. Measurement Model

In the tightly coupled integration, the pseudorange measurements of dual-constellation GNSSs act as the observation vector. Therefore, the measurement model can be given aswhere is the measurement vector, is the process function of the measurement model, and is the measurement Gaussian noise vector. can be depicted aswhere and are the corrected GPS and BeiDou pseudorange measurements, respectively. and are the numbers of received GPS and BeiDou satellites whose elevation angle and carrier-to-noise ratio are both more than certain thresholds (e.g., 35° and 30 db-Hz, resp., in this paper), respectively. In urban areas, through such threshold processing, that is, abandoning the measurements of the satellites with low elevation angle and low carrier-to-noise ratio, the impact of NLOS and multipath can be preliminarily alleviated to some degree.

Note that in common INS/GNSS tightly coupled integration, each of received satellite measurements is generally regarded as Gaussian noise with the same noise covariance . That is, is usually assumed to have the noise covariance matrix** R, **which has equal diagonal elements; that is,where has dimension.

Satellite clock bias and ionospheric errors can be calculated from the satellite’s navigation message, and tropospheric error can also be estimated using an appropriate model [25]. Hence, after correcting all the errors except receiver clock errors, the corrected pseudoranges and can be described aswhere is the receiver’s rectangular coordinates in e-frame. and are satellites’ rectangular coordinates in e-frame. and are the GPS and BeiDou receiver’s clock biases, respectively. and are the total effect of residual errors.

The coordinate transformation between geodetic e-frame and rectangular e-frame is where is the eccentricity of ellipsoid. Utilizing this transformation, the measurement equation can be obtained as

#### 3. Fusion Positioning Algorithm

##### 3.1. EKF Algorithm

The extended Kalman filter (EKF) has been widely used for INS/GNSS integration. For system state model (12) and measurement model (19), the system, input, and measurement noises are assumed to be Gaussian with zero mean and their covariance matrices , , and , respectively. Further, the corresponding EKF process can be divided into the following two phases:

*Prediction*

*Update*where is an identity matrix, and are the Jacobian matrices of the system function with respect to and , and is the Jacobian matrix of the measurement function with respect to ; that is,

##### 3.2. UKF Algorithm

As shown in (12) and (19), both system and measurement models are nonlinear. Although the EKF can deal with such fusion through linearization, it will inevitably cause the approximation error. To enhance the integration performance, nonlinear estimation techniques that do not require linearized dynamic models should be considered to be used. The unscented Kalman filter (UKF) is one of the effective nonlinear Bayes filters which can directly use nonlinear system and measurement models without any linearization [26, 27]. Generally, it can achieve a good balance between computational complexity and accuracy [28]. In contrast to the EKF, the UKF does not need to compute the Jacobian matrix and can predict the means and covariance correctly up to the fourth order.

For (12) and (19), we can execute the recursive procedure of UKF according to the following steps [26, 27]:

*Step 1. *Calculate weights coefficient and sigma points:where is a scaling parameter. The constant determines the spread of the sigma points around a mean of state and is usually set to a small positive value. The constant is usually set to 0. is used to incorporate prior knowledge of the distribution of and is optimally set to 2 for Gaussian distributions; is the dimension of state vector.

*Step 2. *Estimate a priori state and a priori error covariance and then obtain the predicted observation by the unscented transform of which inputs are the sigma points and the weights:

*Step 3. *Calculate the UKF gain:

*Step 4. *Update the system state and error covariance:

##### 3.3. AF-UKF Algorithm

For the UKF above, the noise covariance matrix in (25) is usually set to be a constant diagonal one. This setting is generally appropriate in the open-sky situations but is not suitable for urban canyons. As mentioned earlier, the satellite signals in urban areas are often blocked and/or reflected by surrounding objects causing NLOS and multipath interferences. For the received LOS satellites, their measurement accuracy is superior. However, if one received satellite signal belongs to multipath and NLOS, its measurement accuracy is poor. Through simple threshold processing mentioned above, only partly obvious NLOS and multipath interferences can be alleviated. That is, such alleviation is very limited and rough. For the remaining satellite signals, it is still necessary to adaptively adjust the dependence on each satellite measurement whether from BeiDou or from GPS according to its specific conditions rather than utilize it invariably.

Generally, in unban canyon scenarios, the LOS satellite signals may be different from the satellite signals affected by the NLOS and multipath interferences in several aspects. First, the satellite signals along the vehicle’s longitudinal direction (i.e., along the street) are not obstructed by buildings and trees, while the signals going along the vehicle’s lateral direction (i.e., across the street) are prone to be blocked or reflected, as illustrated in Figure 1. Besides, the satellite signals with low elevation angles are more likely to be influenced than those with high elevation angles in urban canyons. Moreover, the LOS signals often have higher carrier-to-noise ratio (i.e.,* C/*) than the NLOS and multipath signals [29].