Forward/backward prediction solution for adaptive noisy FIR filtering

An important and hard problem in signal processing is the estimation of parameters in the presence of observation noise.In this paper, adaptive finite impulse response （FIR） filtering with noisy input-output data is considered and two developed bias compensation least squares （BCLS） methods are proposed.By introducing two auxiliary estimators, the forward output predictor and the backward output predictor are constructed respectively.By exploiting the statistical properties of the cross-correlation function between the least squares （LS） error and the forward/backward prediction error, the estimate of the input noise variance is obtained; the effect of the bias can thereafter be removed.Simulation results are presented to illustrate the good performances of the proposed algorithms.

Quantum Operator Model for Data Analysis and Forecast

A new dynamic model identification method is developed for continuous-time series analysis and forward prediction applications. The quantum of data is defined over moving time intervals in sliding window coordinates for compressing the size of stored data while retaining the resolution of information. Quantum vectors are introduced as the basis of a linear space for defining a Dynamic Quantum Operator (DQO) model of the system defined by its data stream. The transport of the quantum of compressed data is modeled between the time interval bins during the movement of the sliding time window. The DQO model is identified from the samples of the real-time flow of data over the sliding time window. A least-square-fit identification method is used for evaluating the parameters of the quantum operator model, utilizing the repeated use of the sampled data through a number of time steps. The method is tested to analyze, and forward-predict air temperature variations accessed from weather data as well as methane concentration variations obtained from measurements of an operating mine. The results show efficient forward prediction capabilities, surpassing those using neural networks and other methods for the same task.

Total Transmission from Deep Learning Designs

Total transmission plays an important role in efficiency improvement and wavefront control,and has made great progress in many applications,such as the optical film and signal transmission.Therefore,many traditional physical methods represented by transformation optics have been studied to achieve total transmission.However,these methods have strict limitations on the size of the photonic structure,and the calculation is complex.Here,we exploit deep learning to achieve this goal.In deep learning,the data-driven prediction and design are carried out by artificial neural networks(ANNs),which provide a convenient architecture for large dataset problems.By taking the transmission characteristic of the multi-layer stacks as an example,we demonstrate how optical materials can be designed by using ANNs.The trained network directly establishes the mapping from optical materials to transmission spectra,and enables the forward spectral prediction and inverse material design of total transmission in the given parameter space.Our work paves the way for the optical material design with special properties based on deep learning.