Abstract
Certain difficulties in path forecasting and filtering problems are based in the initial hypothesis of estimation and filtering techniques. Common hypotheses include that the system can be modeled as linear, Markovian, Gaussian, or all at one time. Although, in many cases, there are strategies to tackle problems with approaches that show very good results, the associated engineering process can become highly complex, requiring a great deal of time or even becoming unapproachable. To have tools to tackle complex problems without starting from a previous hypothesis but to continue to solve classic challenges and sharpen the implementation of estimation and filtering systems is of high scientific interest. This paper addresses the forecast–filter problem from deep learning paradigms with a neural network architecture inspired by natural language processing techniques and data structure. Unlike Kalman, this proposal performs the process of prediction and filtering in the same phase, while Kalman requires two phases. We propose three different study cases of incremental conceptual difficulty. The experimentation is divided into five parts: the standardization effect in raw data, proposal validation, filtering, loss of measurements (forecasting), and, finally, robustness. The results are compared with a Kalman filter, showing that the proposal is comparable in terms of the error within the linear case, with improved performance when facing non-linear systems.
Highlights
Many problems in engineering and research require or are based in forecasting or filtering parameters along time, understood by forecasting the predicted values for future times in the sequence
We proposed to approach the joint problem as forecasting-filtering trajectories without assuming a hypothesis of linear, Markovian, or Gaussian behaviors, based only on supervised information and in only one processing stage to build the estimator xk+1 from the available observations, zk, zk−1, . . . zk− L based on a model built with representative training data
Starting from the structure proposed in [19], focused on the benefits in front of regression problems of each one the layers and proven performance in uniform rectilinear motion (URM) paths, we propose an algorithm in Algorithm 2 to increase the depth of the encoder and decoder to adapt the results in front of other paths that are likely more complex in learning terms compared with URM paths
Summary
Many problems in engineering and research require or are based in forecasting or filtering parameters along time, understood by forecasting the predicted values for future times in the sequence. One of the principal landmarks in stochastic observer theory is the optimal stochastic estimators formulation or Kalman filter (KF) [4,5,6] These estimators are based in the state space systems and different versions, such as extended KF (EKF) [7,8,9], unscented KF (UKF) [10,11], or robust KF (RKF) [12], generalize its use with nonlinear Gaussian problems as shown in Afshari et al [3]. While Kalman seeks to minimize its covariance based on prior assumptions, a deep neural network does not assume any of Kalman’s assumptions but attempts to adapt its hidden dynamics to the training data independently of their distribution or the dynamical relationship between them This neural network flexibility provides an opportunity to generalize estimation and filtering problems under artificial intelligence paradigms.
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