Real-time Cycle-slip Detection and Correction for Land Vehicle Navigation Using Inertial Aiding

M.O. Karaim, T.B. Karamat, A. Noureldin, M. Tamazin, M.M. Atia

Abstract: Carrier phase measurements are much more precise than pseudorange measurements but they are ambiguous by an integer number of cycles. When these ambiguities are resolved, a sub-centimetre level positioning can be achieved. However, in real time kinematic applications, the (Global Positioning System) GPS signal could temporarily be lost because of various disturbing factors such as trees, buildings, bridges and vehicle dynamics. This signal loss causes a discontinuity of an integer number of cycles in the measured carrier phase, known as cycle slip. Consequently, the integer counter is reinitialized, meaning that the integer ambiguities become unknown again. In this event, ambiguities need to be resolved once more to resume the precise positioning and navigation process. This is a computation-intensive and time-consuming task. Typically it takes few minutes before ambiguities are resolved. The ambiguity resolution is even more challenging in real time navigation due to the receiver dynamics and time sensitive nature of the application. Therefore, it would save effort and time if we could instead detect and estimate the size of these cycle slips and correct our measurements accordingly. Inertial Navigation Systems (INS) on the other hand, can provide a smoother and continuous navigation solution at a higher data rates since it is autonomous and immune to interferences which plague GPS positioning. However, INS errors grow with time due to inherent integration in the mechanization process. Thus, both GPS and INS systems exhibit mutually complementary characteristics, and their integration provides a more accurate and robust navigation solution than either stand-alone system. Lately, the Micro Electro Mechanical Systems (MEMS) grade inertial sensors are being used for low cost navigation applications. However, these inexpensive sensors have complex error characteristics which limit their use in navigation. One of the latest research trends is to use fewer MEMS sensors in partial IMU configuration to obtain the navigation solution. Advantage of this trend is twofold. The first is to obviate unnecessary inertial sensor errors and the second is to reduce the cost of the IMU in general. One such approach is known as the RISS (Reduced Inertial Sensor System). The RISS configuration uses one gyroscope, two accelerometers, and vehicle wheel rotation sensor. The gyroscope is used to observe the changes in vehicle’s orientation in horizontal plane. The two accelerometers are used to obtain the pitch and roll angles. The wheel rotation sensor readings provide the vehicle’s speed in the forward direction. A filtering technique is usually employed to perform the GPS/INS integration. Owing to its estimation optimality and recursive properties, Kalman filter (KF) has been a method of choice for most GPS/INS applications. Major approaches of integration are loosely coupled GPS/INS integration and tightly coupled GPS/INS integration. The former strategy is simpler and easier to implement since the inertial and GPS navigation solutions are generated independently before being weighted together in a central Kalman filter. There are two main drawbacks to this approach: 1) signals from at least four satellites are needed for navigation solution which cannot always be guaranteed and 2) the outputs of the GPS Kalman filter are time correlated which has a negative impact on system performance. The latter strategy performs the INS/GPS integration in a single Kalman filter. This architecture eliminates the problem of correlated measurements which arises due to cascaded Kalman filtering in the loosely coupled approach. Also, the major limitation of visibility of at least four satellites is removed. In this paper, a tightly coupled GPS/RISS integrated system is introduced for cycle slip detection and correction for land vehicle navigation using relative-positioning technique. The principle of the algorithm is to compare double differenced (DD) phase measurements with estimated measurements derived from the output of the GPS/RISS system against a threshold. In case of a cycle slip, the measurements are corrected with the calculated difference. The system filter has a total of eleven states which include three position and three velocity errors. The attitude state consists of the azimuth error only. The sensor errors include the errors associated with wheel sensor-driven acceleration, and the gyroscope error. The two states added for the GPS system are the clock bias of the GPS receiver and its drift. First, pitch and roll are derived from the accelerometers readings after removing the accelerations due to forward speed and normal transversal acceleration component respectively. The azimuth angle is obtained by, first removing the rotational components due to transport rate and Earth rotation rate and then integrating the gyroscope measurements. Knowing azimuth and pitch angles, vehicle forward speed can be projected into East, North, and Up velocities. The East and North velocities are transformed into geodetic coordinates and then integrated over the sample interval to obtain positions in latitude and longitude. The vertical component of velocity is integrated to obtain altitude. Subsequently, knowing the receiver position and the satellite ephemeris data, satellite-to-receiver ranges can easily be computed and subsequently converted to DD phases. Herein, cycle slip detection process is performed by checking computed DD phases against DD measured phases. Differences between estimated and measured phases are compared against a threshold. Violation of this threshold is an indication of a cycle slip in the DD phase measurements. In case of a cycle slip, the DD phase measurement is instantly corrected for that slip by adding the corresponding difference. The performance of proposed algorithm was examined on several real-life land vehicle trajectories which included various challenging driving scenarios including high and slow speeds, sudden accelerations and decelerations, sharp turns and steep slopes. Results demonstrate the effectiveness of the proposed algorithm in these severe conditions with intensive and variable-sized cycle slips. This research has a direct influence on navigation in challenging environments where frequent cycle slips occur and resolving integer ambiguities is not affordable because of time and computational reasons. An additional consequence of this research is significant reduction in the cost of an integrated system due to the use of fewer MEMS inertial sensors.
Published in: Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013)
September 16 - 20, 2013
Nashville Convention Center, Nashville, Tennessee
Nashville, TN
Pages: 1290 - 1298
Cite this article: Karaim, M.O., Karamat, T.B., Noureldin, A., Tamazin, M., Atia, M.M., "Real-time Cycle-slip Detection and Correction for Land Vehicle Navigation Using Inertial Aiding," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 1290-1298.
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