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AI-IMU Dead-Reckoning

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AI-IMU Dead-Reckoning 1 AI-IMU Dead-Reckoning ∗ y ∗ Martin BROSSARD , Axel BARRAU and Silvere` BONNABEL ∗MINES ParisTech, PSL Research University, Centre for Robotics, 60 Bd Saint-Michel, 75006 Paris, France ySafran Tech, Groupe Safran, Rue des Jeunes Bois-Chateaufort,ˆ 78772, Magny Les Hameaux Cedex, France Abstract—In this paper we propose a novel accurate method for dead-reckoning of wheeled vehicles based only on an Inertial 400 benchmark IMU proposed Measurement Unit (IMU). In the context of intelligent vehicles, robust and accurate dead-reckoning based on the IMU may prove useful to correlate feeds from imaging sensors, to safely navigate through obstructions, or for safe emergency stops in the extreme case of exteroceptive sensors failure. The key components of 200 the method are the Kalman filter and the use of deep neural GPS outage networks to dynamically adapt the noise parameters of the filter. The method is tested on the KITTI odometry dataset, and our end only dead-reckoning inertial method based on the IMU accurately ) 0 estimates 3D position, velocity, orientation of the vehicle and m self-calibrates the IMU biases. We achieve on average a 1.10% ( y start translational error and the algorithm competes with top-ranked methods which, by contrast, use LiDAR or stereo vision. We make our implementation open-source at: 200 − https://github.com/mbrossar/ai-imu-dr Index Terms—localization, deep learning, invariant extended Kalman filter, KITTI dataset, inertial navigation, inertial mea- 400 surement unit − I. INTRODUCTION 0 200 400 600 800 NTELLIGENT vehicles need to know where they are x (m) located in the environment, and how they are moving throughI it. An accurate estimate of vehicle dynamics allows validating information from imaging sensors such as lasers, ul- Fig. 1. Trajectory results on seq. 08 (drive #28, 2011/09/30) [3] of the KITTI trasonic systems, and video cameras, correlating the feeds, and dataset. The proposed method (green) accurately follows the benchmark also ensuring safe motion throughout whatever may be seen trajectory for the entire sequence (4:2 km, 9 min), whereas the pure IMU integration (cyan) quickly diverges. Both methods use only IMU signals and along the road [1]. Moreover, in the extreme case where an are initialized with the benchmark pose and velocity. We see during the GPS emergency stop must be performed owing to severe occlusions, outage that occurs in this sequence, our solution keeps estimating accurately lack of texture, or more generally imaging system failure, the the trajectory. vehicle must be able to assess accurately its dynamical motion. For all those reasons, the Inertial Measurement Unit (IMU) arXiv:1904.06064v1 [cs.RO] 12 Apr 2019 appears as a key component of intelligent vehicles [2]. Note adapt to the motion, e.g., lateral slip is larger in bends than that Global Navigation Satellite System (GNSS) allows for in straight lines. Using the recent tools from the field of global position estimation but it suffers from phase tracking Artificial Intelligence (AI), namely deep neural networks, we loss in densely built-up areas or through tunnels, is sensitive to propose a method to automatically learn those parameters and jamming, and may not be used to provide continuous accurate their dynamic adaptation for IMU only dead-reckoning. Our and robust localization information, as exemplified by a GPS contributions, and the paper’s organization, are as follows: outage in the well known KITTI dataset [3], see Figure 1. • we introduce a state-space model for wheeled vehicles as Kalman filters are routinely used to integrate the outputs well as simple assumptions about the motion of the car of IMUs. When the IMU is mounted on a car, it is common in Section II; practice to make the Kalman filter incorporate side information • we implement a state-of-the-art Kalman filter [4,5] that about the specificity of wheeled vehicle dynamics, such as exploits the kinematic assumptions and combines them approximately null lateral and upward velocity assumption in with the IMU outputs in a statistical way in Section III-C. the form of pseudo-measurements. However, the degree of It yields accurate estimates of position, orientation and confidence the filter should have in this side information is velocity of the car, as well as IMU biases, along with encoded in a covariance noise parameter which is difficult associated uncertainty (covariance); to set manually, and moreover which should dynamically • we exploit deep learning for dynamic adaptation of co- 2 variance noise parameters of the Kalman filter in Section stereo odometry experiment. Finally, [25] uses deep learning IV-A. This module greatly improves filter’s robustness for estimating covariance of a local odometry algorithm that and accuracy, see Section V-D; is fed into a global optimization procedure, and in [26] we • we demonstrate the performances of the approach on the used Gaussian processes to learn a wheel encoders error. Our KITTI dataset [3] in Section V. Our approach solely conference paper [20] contains preliminary ideas, albeit not based on the IMU produces accurate estimates and com- concerned at all with covariance adaptation: a neural network petes with top-ranked LiDAR and stereo camera methods essentially tries to detect when to perform ZUPT. [6,7]; and we do not know of IMU based dead-reckoning Dynamic adaptation of noise parameters in the Kalman filter methods capable to compete with such results; is standard in the tracking literature [27], however adaptation • the approach is not restricted to inertial only dead- rules are application dependent and are generally the result reckoning of wheeled vehicles. Thanks to the versatility of manual “tweaking” by engineers. Finally, in [28] the of the Kalman filter, it can easily be applied for railway authors propose to use classical machine learning techniques vehicles [8], coupled with GNSS, the backbone for IMU to to learn static noise parameters (without adaptation) of the self-calibration, or for using IMU as a speedometer in Kalman filter, and apply it to the problem of IMU-GNSS path-reconstruction and map-matching methods [9]–[12]. fusion. II. IMU AND PROBLEM MODELLING A. Relation to Previous Literature An inertial navigation system uses accelerometers and gyros Autonomous vehicle must robustly self-localize with their provided by the IMU to track the orientation Rn, velocity embarked sensor suite which generally consists of odometers, 3 3 vn R and position pn R of a moving platform relative IMUs, radars or LiDARs, and cameras [1,2,12]. Simultaneous 2 2 to a starting configuration (R0; v0; p0). The orientation is Localization And Mapping based on inertial sensors, cameras, encoded in a rotation matrix R SO(3) whose columns n 2 and/or LiDARs have enabled robust real-time localization sys- are the axes of a frame attached to the vehicle. tems, see e.g., [6,7]. Although these highly accurate solutions based on those sensors have recently emerged, they may drift A. IMU Modelling when the imaging system encounters troubles. As concerns wheeled vehicles, taking into account vehicle The IMU provides noisy and biased measurements of the constraints and odometer measurements are known to increase instantaneous angular velocity vector !n and specific acceler- the robustness of localization systems [13]–[16]. Although ation an as follows [17] quite successful, such systems continuously process a large IMU ! ! !n = !n + bn + wn ; (1) amount of data which is computationally demanding and a a aIMU = a + b + w ; (2) energy consuming. Moreover, an autonomous vehicle should n n n n ! a ! a run in parallel its own robust IMU-based localization algorithm where bn , bn are quasi-constant biases and wn , wn are zero- to perform maneuvers such as emergency stops in case of other mean Gaussian noises. The biases follow a random walk sensors failures, or as an aid for correlation and interpretation b! = b! + wb! ; of image feeds [2]. n+1 n n (3) a a ba High precision aerial or military inertial navigation systems bn+1 = bn + wn ; (4) achieve very small localization errors but are too costly for b! ba where wn , wn are zero-mean Gaussian noises. consumer vehicles. By contrast, low and medium-cost IMUs The kinematic model is governed by the following equations suffer from errors such as scale factor, axis misalignment and IMU IMU random walk noise, resulting in rapid localization drift [17]. Rn+1 = Rn exp ((!ndt)×) ; (5) This makes the IMU-based positioning unsuitable, even during IMU IMU IMU vn+1 = vn + (Rn an + g) dt; (6) short periods. pIMU = pIMU + vIMUdt; (7) Inertial navigation systems have long leveraged virtual and n+1 n n pseudo-measurements from IMU signals, e.g. the widespread between two discrete time instants sampling at dt, where we Zero velocity UPdaTe (ZUPT) [18]–[20], as covariance adap- let the IMU velocity be vIMU R3 and its position pIMU R3 n 2 n 2 tation [21]. In parallel, deep learning and more generally ma- in the world frame. RIMU SO(3) is the 3 3 rotation matrix n 2 × chine learning are gaining much interest for inertial navigation that represents the IMU orientation, i.e. that maps the IMU [22,23]. In [22] velocity is estimated using support vector frame to the world frame, see Figure 2. Finally (y)× denotes regression whereas [23] use recurrent neural networks for end- the skew symmetric matrix associated with cross product with 3 3 to-end inertial navigation. Those methods are promising but y R . The true angular velocity !n R and the true 2 3 2 restricted to pedestrian dead-reckoning since they generally specific acceleration an R are the inputs of the system (5)- 2 consider slow horizontal planar motion, and must infer ve- (7).
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