Recent Advances in Computer Scienceand Communications Hazem H. Osman *,1 , Ismail A. Ismail 2 , Ehab Morsy 3 and Hamid M. Hawidi 4 1 Department of Mathematics, Faculty of Science, Suez Canal University, Cairo, Egypt; 2 Faculty of Computers and In- formatics, October 6 University, Cairo, Egypt; 3 Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, Egypt; 4 Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia, Egypt Abstract: Background: Kalman filter and its variants had achieved great success in many applica- tions in the field of technology. However, the kalman filter is under heavy computations burden. Under big data, it becomes pretty slow. On the other hand, the computer industry has now entered the multicore era with hardware computational capacity increased by adding more processors (cores) on one chip, the sequential processors will not be available in near future, so we should have to move to parallel computations Objective: This paper focuses on how to make Kalman Filter faster on multicore machines and im- plementing the parallel form of Kalman Filter equations to denoise sound wave as a case study. Method: Splitting the all signal points into large segments of data and applying equations on each segment simultaneously. After that, we merge the filtered points again in one large signal Results: Our Parallel form of Kalman Filter can achieve nearly linear speed-up. Conclusion: Through implementing the parallel form of Kalman Filter equations on the noisy sound wave as a case study and using various numbers of cores, it is found that a kalman filter al- gorithm can be efficiently implemented in parallel by splitting the all signal points into large seg- ments of data and applying equations on each segment simultaneously. A R T I C L E H I S T O R Y Received: May 20, 2019 Revised: September 12, 2019 Accepted: March 20, 2020 DOI: 10.2174/2666255813999200806161813 Keywords: Optimal state estimation, kalman filter, sound model and kalman filter, parallel computations, sound wave. 1. INTRODUCTION The signal filters were originally seen as circuits or sys- tems with frequency selection behaviors. The development of filtering techniques went on and more sophisticated filters were introduced, such as e.g. Chebychev and Butterworth filters, which gave means of shaping the frequency charac- teristics of the filter in a more systematic design procedure. During this stage, the filtering was mainly considered from this frequency-domain point of view. By the introduction of the Wiener-Kolmogorov filter [1, 2], statistical ideas were incorporated into the field of filter- ing and statistical properties of the signal, rather than the frequency content, were utilized to select what to filter out. Besides the use of frequency The idea of the Wiener-Kolmogorov filter is to minimize the mean square error between the estimated signal and the *Address correspondence to this author at the Department of Mathematics, Faculty of Science, Suez Canal University, Cairo, Egypt; E-mail: hhelal_online@yahoo.com true signal. Thus an optimality criterion was introduced in this case and it became possible to state whether a filter was optimal in some specific sense. Further steps in the devel- opment of filters were taken by Emil Rudolph Kalman by the introduction of the famous Kalman filter that, in contrast to the Wiener and Kolmogorov filters, applies to nonstationary processes (online). Kalman filter is a linear state estimator, which is an op- timal recursive data processing algorithm. The word “Opti- mal” means that it minimizes errors in some respect and “Recursive” means, unlike certain data processing concepts, that the Kalman filter does not require all previous data to be kept in storage but a small proportion of the previous data and reprocessed it every time a new measurement is taken. The applications of the Kalman filter are numerous such as Noise Cancellation, Tracking Objects, System Identifica- tion, Navigation and Economics etc. [3, 4] The practical implementation of the Kalman filtering with a huge number  of variables requires an expensive operational time. The arithmetic operations required for im- plementing the Kalman filter with  state variables can be 2666-2566/21 $65.00+.00 © 2021 Bentham Science Publishers Send Orders for Reprints to reprints@benthamscience.net 2828 Recent Advances in Computer Science and Communications, 2021, 14, 2828-2835 RESEARCH ARTICLE Implementing the Kalman Filter Algorithm in Parallel Form: Denoising Sound Wave as a Case Study