To enhance localization accuracy in urban environments, an innovative LiDAR-Visual-Inertial odometry, named HDA-LVIO, is proposed by employing hybrid data association. The proposed HDA_LVIO system can be divided into two subsystems: the LiDAR-Inertial subsystem (LIS) and the Visual-Inertial subsystem (VIS). In the LIS, the LiDAR pointcloud is utilized to calculate the Iterative Closest Point (ICP) error, serving as the measurement value of Error State Iterated Kalman Filter (ESIKF) to construct the global map. In the VIS, an incremental method is firstly employed to adaptively extract planes from the global map. And the centroids of these planes are projected onto the image to obtain projection points. Then, feature points are extracted from the image and tracked along with projection points using Lucas-Kanade (LK) optical flow. Next, leveraging the vehicle states from previous intervals, sliding window optimization is performed to estimate the depth of feature points. Concurrently, a method based on epipolar geometric constraints is proposed to address tracking failures for feature points, which can improve the accuracy of depth estimation for feature points by ensuring sufficient parallax within the sliding window. Subsequently, the feature points and projection points are hybridly associated to construct reprojection error, serving as the measurement value of ESIKF to estimate vehicle states. Finally, the localization accuracy of the proposed HDA-LVIO is validated using public datasets and data from our equipment. The results demonstrate that the proposed algorithm achieves obviously improvement in localization accuracy compared to various existing algorithms.

Trajectory planning is a fundamental task on various autonomous driving platforms, such as social robotics and self-driving cars. Many trajectory planning algorithms use a reference curve based Frenet frame with time to reduce the planning dimension. However, there is a common implicit assumption in classic trajectory planning approaches, which is that the generated trajectory should follow the reference curve continuously. This assumption is not always true in real applications and it might cause some undesired issues in planning. One issue is that the projection of the planned trajectory onto the reference curve maybe discontinuous. Then, some segments on the reference curve are not the image of any part of the planned path. Another issue is that the planned path might self-intersect when following a simple reference curve continuously. The generated trajectories are unnatural and suboptimal ones when these issues happen. In this paper, we firstly demonstrate these issues and then introduce an efficient trajectory generation method which uses a new transformation from the Cartesian frame to Frenet frames. Experimental results on a simulated street scenario demonstrated the effectiveness of the proposed method.

Learning rates in stochastic neural network training are currently determined a priori to training, using expensive manual or automated iterative tuning. This study proposes gradient-only line searches to resolve the learning rate for neural network training algorithms. Stochastic sub-sampling during training decreases computational cost and allows the optimization algorithms to progress over local minima. However, it also results in discontinuous cost functions. Minimization line searches are not effective in this context, as they use a vanishing derivative (first order optimality condition), which often do not exist in a discontinuous cost function and therefore converge to discontinuities as opposed to minima from the data trends. Instead, we base candidate solutions along a search direction purely on gradient information, in particular by a directional derivative sign change from negative to positive (a Non-negative Associative Gradient Projection Point (NN- GPP)). Only considering a sign change from negative to positive always indicates a minimum, thus NN-GPPs contain second order information. Conversely, a vanishing gradient is purely a first order condition, which may indicate a minimum, maximum or saddle point. This insight allows the learning rate of an algorithm to be reliably resolved as the step size along a search direction, increasing convergence performance and eliminating an otherwise expensive hyperparameter.

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to early formulations of the problem - with an object to be classified described as a vector in a relatively low-dimensional Euclidean space. Statistical shape data have two main properties that suggest a need for a novel approach: (i) shapes are inherently infinite dimensional with strong dependence among the positions of nearby points, and (ii) shape space is not Euclidean, but is fundamentally curved. To accommodate these features of the data, we work with the square-root velocity function of the curves to provide a useful formal description of the shape, pass to tangent spaces of the manifold of shapes at different projection points which effectively separate shapes for pairwise classification in the training data, and use principal components within these tangent spaces to reduce dimensionality. We illustrate the impact of the projection point and choice of subspace on the misclassification rate with a novel method of combining pairwise classifiers.

Representation-based classification methods such as sparse representation-based classification (SRC) and linear regression classification (LRC) have attracted a lot of attentions. In order to obtain the better representation, a novel method called projection representation-based classification (PRC) is proposed for image recognition in this paper. PRC is based on a new mathematical model. This model denotes that the "ideal projection" of a sample point x on the hyper-space H may be gained by iteratively computing the projection of x on a line of hyper-space H with the proper strategy. Therefore, PRC is able to iteratively approximate the "ideal representation" of each subject for classification. Moreover, the discriminant PRC (DPRC) is further proposed, which obtains the discriminant information by maximizing the ratio of the between-class reconstruction error over the within-class reconstruction error. Experimental results on five typical databases show that the proposed PRC and DPRC are effective and outperform other state-of-the-art methods on several vision recognition tasks.