Chaotic time series prediction using wavelet transform and multi-model hybrid method

In order to further improve the prediction accuracy of the chaotic time series and overcome the defects of the single model, a multi-model hybrid model of chaotic time series is proposed. First, the Discrete Wavelet Transform (DWT) is used to decompose the data and obtain the approximate coefficients (low-frequency sequence) and detailed coefficients (high-frequency sequence) of the sequence. Secondly, phase space reconstruction is performed on the decomposed data. Thirdly, the chaotic characteristics of each sequence are judged by correlation integral and Kolmogorov entropy. Fourthly, in order to explore the deeper features of the time series and improve the prediction accuracy, a sequence of Volterra adaptive prediction models is established for the components with chaotic characteristics according to the different characteristics of each component. For the components without chaotic characteristics, a JGPC prediction model without chaotic feature sequences is established. Finally, the multi-model fusion prediction of the above multiple sequences is carried out by the LSTM algorithm, and the final prediction result is obtained through calculation, which further improves the prediction accuracy. Experiments show that the multi-model hybrid method of Volterra-JGPC-LSTM is more accurate than other comparable models in predicting chaotic time series

An approach for parameter estimation of combined CPPM and LFM radar signal

AbstractIn this paper, the problem of parameter estimation of the combined radar signal adopting chaotic pulse position modulation (CPPM) and linear frequency modulation (LFM), which can be widely used in electronic countermeasures, is addressed. An approach is proposed to estimate the initial frequency and chirp rate of the combined signal by exploiting the second-order cyclostationarity of the intra-pulse signal. In addition, under the condition of the equal pulse width, the pulse repetition interval (PRI) of the combined signal is predicted using the low-order Volterra adaptive filter. Simulations demonstrate that the proposed cyclic autocorrelation Hough transform (CHT) algorithm is theoretically tolerant to additive white Gaussian noise. When the value of signal noise to ratio (SNR) is less than −4dB, it can still estimate the intra-pulse parameters well. When SNR=−3dB, a good prediction of the PRI sequence can be achieved by the Volterra adaptive filter algorithm, even only 100 training samples

A Hybrid Approach of Traffic Flow Prediction Using Wavelet Transform and Fuzzy Logic

The rapid development of urban areas and the increasing size of vehicle fleets are causing severe traffic congestions. According to traffic index data (Tom Tom Traffic Index 2016), most of the larger cities in Canada placed between 30th and 100th most traffic congested cities in the world. A recent research study by CAA (Canadian Automotive Association) concludes traffic congestions cost drivers 11.5 million hours and 22 million liters of fuel each year that causes billions of dollars in lost revenues. Although for four decades’ active research has been going on to improve transportation management, statistical data shows the demand for new methods to predict traffic flow with improved accuracy. This research presents a hybrid approach that applies a wavelet transform on a time-frequency (traffic count/hour) signal to determine sharp variation points of traffic flow. Datasets in between sharp variation points reveal segments of data with similar trends. These sets of data, construct fuzzy membership sets by categorizing the processed data together with other recorded information such as time, season, and weather. When real-time data is compared with the historical data using fuzzy IF-THEN rules, a matched dataset represents a reliable source of information for traffic prediction. In addition to the proposed new method, this research work also includes experiment results to demonstrate the improvement of accuracy for long-term traffic flow prediction

The Kolmogorov mapping theorem in signal processing

Since the publication in 1957 of the work of Andrei Kolmogorov 181 in mapping a function of multiple variables by means functions of a single variable, many mathematicians and engineers try , with different degree of success and not without controversy 1191. to find the direct application of it to multiple extremes problems, rooting of multivariate polynomials, neural networks and pattern recognition. This paper revisits the theorem from the optic of a generalised architecture for signal processing 1281. It is envisaged the high potential of the theorem to handle either linear or non-linear processing problems. A specific implementation following the main guide-lines of the theorem is reported, as well as some preliminary results concerning the design, implementation and performance of non-linear systems. The applications cover non linear transmission channels for communications, instantaneous companders and prediction of chaotic series.Peer ReviewedPostprint (published version