Deep learning technology provides novel solutions for increasingly complex target tracking requirements. For traditional target tracking models, the movement of the target need to be simulated by a predefined mathematical model. However, it is extremely difficult to obtain sufficient information in advance, which makes it challenging to track changeable and noisy trajectories in a timely and precise manner. A deep learning framework is constructed for automatic trajectory tracking based on learning the dynamic laws of motion, called DeepGTT. Specifically, a trajectory generator and a trajectory mapper were designed to standardise trajectory data and construct trajectory mapping, which enable the long short-term memory-based tracking network to learn general dynamic laws. Then, to discuss the interpretability of the model, the mechanism of the deep learning framework is considered and a memory factor matrix is defined. Finally, extensive experiments are conducted on various weak manoeuvring and manoeuvring scenarios to evaluate the algorithm. Experimental results demonstrate that the DeepGTT algorithm remarkably improves accuracy and efficiency compared with most conventional algorithms and state-of-the-art methods. In addition, interpretability experiments qualitatively prove that the tracking network can perceive dynamic laws when estimating the target state.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

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The cost functions and their performances of direct position determination (DPD) methods in the presence of multipath propagation are investigated. We first establish a general DPD (GDPD) model in the presence of multi-path propagation and point out that the existing cost functions cannot get the emitter positions correctly because of the singularity of the manifold matrix in a multipath propagation scenario. Eight cost functions are developed for the GDPD model and formulated in a unified subspace fitting (USF)based framework, which provides insight into their algebraic and asymptotic relations. Moreover, we derive the closed-form expressions of the asymptotic distributions of the estimation errors, which are optimized by those cost functions. Besides, the optimal cost function for achieving an optimal asymptotic performance is derived based on the optimization theory. Finally, the numerical simulations and Cramér-Rao lower bound are provided to verify the analytical results and show that: 1) the cost functions which work well in the singlepath DPD model cannot find the emitters correctly in a multipath scenario; 2) the signal subspace fitting cost functions and noise subspace fitting cost functions, which are proposed in this paper, find the emitters accurately in the multipath propagation scenarios; 3) the optimal-weighted-subspace-fitting cost function holds the best asymptotic performance under the USF framework; and 4) the asymptotic performance of a multiple dimension cost function is better than a 1D cost function.

ARC (Advance-retreat course) analysis is a theoretical analysis and method on socioeconomic development. The main point of ARC is that any economic development behavior will face various pressure coming from environment, that is to say, human beings can actively devise and implement his own economic development strategies, and on the other hand integrative environment formed by all kinds of objective factors can not only passively receive human's choices but aslo human behaviors by the pressure or resistance caused by mankind's behavior. Such dynamic game between human beings and environment is quite different from traditional game problems. Basing on the frame of advance-retreat course (F. Dai, et al, 2007), this paper devises an explanatory model of enterprise development considering environmental pressure according to the basic characteristics of enterprise, develops an analytic model for general advance-retreat course, proves that the solution of the course exists, presents a general method to solve the solution, proposes a series of practical strategies on industry growth control, and particularly draws the important conclusion that faster growing speed will lead to economic growth ending earlier. Finally, the empirical analysis explains ARC to be effective in describing economic growth process, and the controlling strategies for keeping on growth in US economy are given.

The remarkable success of deep learning technologies has provided new ideas for solving complex tracking problems. It is difficult for traditional algorithms to directly estimate the trajectory vector and target class from the received signal due to the limitation of modelling ability, which causes inevitable information loss. Moreover, existing algorithms suffer severe performance degradation when dealing with problems that are difficult to mathematically model in advance, such as highly nonlinear observations and manoeuvring scenarios. To address these issues, we propose a deep learning algorithm for joint direct tracking and classification (DeepDTC), which is a novel direct tracking framework. Specifically, we construct a convolutional neural network (CNN)‐based signal processing component to capture observation features, and a Transformer‐based trajectory tracking component to capture the features of target state and identity. Meanwhile, in signal processing component, we design an attribute network to learn auxiliary knowledge features. Finally, we construct a multi‐task learning network to connect these components and estimate trajectory vectors and target classes simultaneously. Our algorithm takes the transformer with attention mechanism as the core network, which is highly scalable and suitable for introducing various auxiliary knowledge. The comparison experiments with traditional methods demonstrate the effectiveness and advancement of the proposed algorithm. The comparative experiments with the single‐task model show that DeepDTC can further improve the tracking accuracy by utilising the learnt classification information.