Autonomous driving has received a great deal of attention in the automotive industry and is often seen as the future of transportation. The development of autonomous driving technology has been greatly accelerated by the growth of end-to-end machine learning techniques that have been successfully used for perception, planning, and control tasks. An important aspect of autonomous driving planning is knowing how the environment evolves in the immediate future and taking appropriate actions. An autonomous driving system should effectively use the information collected from the various sensors to form an abstract representation of the world to maintain situational awareness. For this purpose, deep learning models can be used to learn compact latent representations from a stream of incoming data. However, most deep learning models are trained end-to-end and do not incorporate any prior knowledge (e.g., from physics) of the vehicle in the architecture. In this direction, many works have explored physics-infused neural network (PINN) architectures to infuse physics models during training. Inspired by this observation, we present a Kalman filter augmented recurrent neural network architecture to learn the latent representation of the traffic flow using front camera images only. We demonstrate the efficacy of the proposed model in both imitation and reinforcement learning settings using both simulated and real-world datasets. The results show that incorporating an explicit model of the vehicle (states estimated using Kalman filtering) in the end-to-end learning significantly increases performance.

In this article, we show that solving the system of linear equations by manipulating the kernel and the range space is equivalent to solving the problem of least squares error approximation. This establishes the ground for a gradient-free learning search when the system can be expressed in the form of a linear matrix equation. When the nonlinear activation function is invertible, the learning problem of a fully-connected multilayer feedforward neural network can be easily adapted for this novel learning framework. By a series of kernel and range space manipulations, it turns out that such a network learning boils down to solving a set of cross-coupling equations. By having the weights randomly initialized, the equations can be decoupled and the network solution shows relatively good learning capability for real world data sets of small to moderate dimensions. Based on the structural information of the matrix equation, the network representation is found to be dependent on the number of data samples and the output dimension.

The learning problem in machine intelligence has been traditionally formulated as an optimization task where an error metric is minimized. In the system of linear equations, becauseit is difficulttohave anexact match between thesamplesizeand the number of model parameters, an approximation is often sought-after according to the primal solution space or the dual solution space in the least error sense. Such an optimization, particularly one that is based on minimizing the least squares error, has been a popular choice due to its simplicity and tractability in analysis and implementation. The approach is predominant in engineering applications as evident from its pervasive adoption in statistical and network learning. Attributed to the computational effectiveness of the backpropagation algorithm running on the then limited hardware (see e.g.,[1, 2, 3, 4, 5]) and the theoretical establishment of the mapping capability (see e.g., [6, 7, 8, 9]), the multilayer neural networks were once a popular tool for research and applications in the 1980s.