Basic Theory of Positioning for Autonomous Driving

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Experienced drivers who drive frequently may have encountered this situation: when the vehicle passes through a road section with tall buildings or a tunnel, our navigation will show a "satellite loss condition" where the GPS signal is weak or even interrupted. This problem is also a key concern in the engineering practice of autonomous driving technology. In order to allow the vehicle to continue to navigate, how should the fusion algorithm handle this situation?


The answer is dead reckoning (DR) or inertial positioning (INS/IMU). The difference between the two is that the dead reckoning algorithm is an open-loop positioning algorithm, which mainly uses wheel pulses, steering wheel angles, combined with vehicle angular velocity and speed to deduce the position and attitude of the vehicle at each moment; it is a dependency of path planning and path tracking. The inertial positioning system is a navigation system that uses inertial sensors such as accelerometers and gyroscopes to measure the acceleration and rotation rate of an object, and calculates the position, velocity and attitude of the object through these data. IMU converts acceleration and angular velocity into velocity and position through integral operations, thereby achieving navigation and positioning. DR is more suitable for low-cost and simple navigation needs, while INS is suitable for scenarios with high precision and high reliability requirements. IMU is currently used more in autonomous driving vehicles.


At present, high-precision positioning technology can be roughly divided into: satellite navigation, inertial navigation, and environmental characteristic matching positioning. I believe everyone knows the principle of satellite signal positioning, while environmental characteristic matching positioning uses sensors such as on-board cameras and lidar to perceive the surrounding environment, and use the observed features and data to match the high-precision map to obtain the vehicle's position and posture. This article will then talk about the principle of positioning technology fusion, mainly focusing on the current hot spot in the industry: the combination of satellite navigation and inertial navigation.


1. First, let’s talk about the advantages and limitations of satellite positioning and dead reckoning:


Advantages and limitations of GNSS: In fact, in order to improve positioning accuracy, some auxiliary means of ground-based positioning are usually introduced, that is, real-time dynamic differential technology. GNSS can provide accurate position information worldwide. Although the accuracy has been improved, it is the backbone of global positioning and performs well in open areas and unobstructed sight. However, in environments such as confined spaces, high-density urban buildings and tunnels, GNSS signals may still be blocked, resulting in performance degradation or even disconnection.


Advantages and limitations of IMU: IMU consists of gyroscopes and accelerometers, which can provide relative motion information such as acceleration and rotation changes. Unlike GNSS, IMU is not affected by external signals, so it is very useful in GNSS-restricted environments. However, IMU is prone to drift due to error accumulation, resulting in inaccurate position and velocity estimates. Because the solution module has integral calculations, there is a cumulative error, which will increase over time.


In summary, we combine the two together, and the information complements each other. To describe it in a common saying, "a man and a woman work together, and the work is not tiring." It is expected to become the main positioning technology solution.


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2: What is the working principle of inertial navigation?


The working principle of inertial navigation positioning is based on the well-known Newton's second law: F=ma.


The inertial navigation system uses the previous position of the carrier, the acceleration and angular velocity measured by the inertial measurement unit to determine its current position. Among them, the velocity v and the offset s can be obtained by integrating the acceleration a. As shown in the following formula, the acceleration a is integrated to obtain the velocity v, and the offset s is obtained by double integration. Conversely, the velocity and acceleration can also be estimated by differentiating the displacement.

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Similarly, the pitch, yaw, roll and other attitude information of the car can be obtained by integrating the angular acceleration. The attitude information can be used to transform the navigation parameters from the inertial coordinate system to the navigation coordinate system. In summary, the inertial navigation system can be said to be an integration system composed of an inertial measurement unit and an integrator. The system measures the rotation information of the carrier through the gyroscope to obtain the attitude information of the carrier, and then converts the carrier specific force information measured by the accelerometer to the navigation coordinate system for integration of the acceleration information, so that the position and attitude information of the car can be calculated.

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Inertial navigation positioning is based on a simple principle, that is, the difference in position can be obtained by a double integration of acceleration, which can be described as a time-dependent function in a stable coordinate system and is well defined, which can be expressed as:

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Where s0 is the initial position, and at is the acceleration along the direction of motion measured by the inertial measurement unit in the coordinate system specified by st.


Inertial navigation is divided into one-dimensional inertial, two-dimensional inertial and three-dimensional inertial. The popular explanation is to put the vehicle into a coordinate system. One-dimensional only considers the acceleration of the X-axis (direction of movement), which is relatively simple. Two-dimensional needs to consider the position changes of acceleration and heading angle in the X-axis (consistent with the vehicle's heading) and Y-axis directions.


The figure below is a schematic diagram of the strapdown inertial navigation two-dimensional track recursion that approximates curved motion to linear motion. The black dot represents the position of the car, θ represents the angle between the car and the north direction, and the cylinder represents the accelerometer and gyroscope. The sensitive axis of the gyroscope is perpendicular to the paper and outward. Before performing an integral operation similar to the one-dimensional track recursion, the output of the inertial measurement unit needs to be converted to the navigation coordinate system. When the car turns, the gyroscope will generate an angular velocity ω relative to the direction angle change of the navigation coordinate system. Combined with the initial heading angle A0, the angular velocity measured by the gyroscope can be integrated to obtain the heading angle At.

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Three-dimensional means considering the acceleration and attitude in the three directions of X, Y, and Z. And three-dimensional recursion also needs to consider the gravity factor. A three-dimensional rotation matrix is ​​formed, and the three angles correspond to the three attitude angles of roll angle, pitch angle, and heading angle.

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3: What are the coupling methods of the satellite-inertial combination?


There are three coupling modes for satellite-inertial combination: loose coupling, tight coupling and deep coupling. From the naming method, there is a common misunderstanding among the public that the degree of coupling of these three modes ranges from low to high, and the positioning accuracy also ranges from low to high, but this is not the case.


Loose coupling: also known as the standard coupling model, is the basis and premise of tight/deep coupling technology. GNSS/RTK positioning results and IMU raw data are integrated, and the satellite-inertial system calculates the carrier's orientation and motion information (satellite output position and speed, inertial output position, speed and attitude, etc.), and the results are imported into the filter for further settlement to estimate the INS error.


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Tight coupling: Unlike the standard coupled (SFM) navigation system, the GNSS receiver outputs raw sampled data such as pseudorange and Doppler shift. Subtracting the pseudorange and Doppler shift obtained by the GNSS reception sampling from the predicted values ​​of the pseudorange and Doppler shift obtained by the INS system can obtain the measurement residual of the pseudorange and Doppler shift as the observation of the data fusion filter. After the observation is input into the data fusion filter, the INS calculation error and sensor bias can be obtained to complete the alignment of the INS system and obtain the optimal estimate of position and velocity, just like the standard coupled (SFM) system. The advantage over loose coupling is that tight coupling can better maintain satellite lock when working in an interference environment, but this advantage is difficult to quantify except for the interference-to-signal ratio.


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Deep coupling: Deep coupling is applied in high dynamic and RF interference environment, and there is no differential correction (no RTK). At this time, neither the GNSS/INS standard coupling (SFM) system nor the GNSS/INS tight coupling system can work properly, such as: artillery shells, missiles, rockets and other non-manned equipment. Compared with the tight coupling navigation system, the deep coupling navigation system adds the assistance of the INS unit to the GNSS receiver. The advantage of the deep coupling model is that it can improve the stability of the tracking loop under high dynamic conditions, improve the dynamics of the receiver, and thus improve the sensitivity of the receiver tracking loop, even in a strong RF interference environment. The disadvantage is that due to the deep coupling between the two, when the two systems are disconnected, the GNSS receiver not only cannot complete the positioning and speed control work, but also cannot continue to track the satellite signal. At this time, if there is no corresponding switching method to control, it will cause the satellite signal to lose lock.

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Reference address:Basic Theory of Positioning for Autonomous Driving

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