## 1 Introduction  
Kalmam Filter (KF) was conceptualised for use in a linear system. In a nonlinear filter, Extended KF (EKF) requires Jacobian mappings, which can be computationally intensive if the vector measurement is high. However, limitations in computer processing may be a problem [1,2]. In brief, an EKF can estimate a highly non-stationary data series, with a known state space model incorporated along with EKF [3].  
[PERSON] _et al._ explained that Particle Filter (PF) has received much attention in various fields over the past decades [4]. The basic principle of PF is to use a set of weighted samples, also known as particles, to approximate the posterior probability of a time-varying signal of interest, given related observations. PFs generalize traditional KFs and can be applied to nonlinear and non-Gaussian state-space models. Similar to EKF, the PF algorithm is a two-state approach, _i.e._, prediction and correction; and is a technique for implementing recursive Bayesian filters by Monte Carlo sampling. In summary, PF represents the posterior density using a set of random particles with associated weights and requires a large number of particles. The most common applications of PFs are in the areas of image processing and segmentation, model selection, tracking and navigation, channel estimation, blind equalization, positioning in wireless networks, biochemistry, economics, finance, geosciences, immunology, materials science, pharmacology, and toxicology. Theoretically, the advantages of PF over EKF are in the representation of nonlinear functions because optimal estimation also uses nonlinear non-Gaussian state-space models [5, 6, 7].  
In 1996, [PERSON] and [PERSON] [8] developed a posteriori algorithm for analysing nonlinear and nonstationary datasets using EMD, which is known as the Hilbert-Huang transform (HHT). It was applied in many applications such as bioinformatics [6,7], signal processing [5,8,9], geophysics [10,11], and finance [8,9,12]. It was claimed that the HHT model could replace the narrow-band filter technique proposed by [PERSON], when Fourier analysis was a vital tool for signal detections in the early days. EMD is based on the local time scale of the signal, which is decomposed using a sifting process [13,14]. The principle of Wavelet Transform (WT) is that an input signal is split into various small waves, which are compact or are functions with finite length. In recent years, a few studies have used a method that combines EMD and WT to reduce nonlinear, nonstationary signals such as electrocardiography (ECG) signals. However, there is no end solution to determine the stop criteria of the EMD process. A comparison of WT and HHT shows that both have similar time and frequency distributions using amplitude as the common axis, where the analytical results for WT indicate a number of deficiencies such as harmonics and small spikes in the frequency scale. Thus, WT may not be suitable for the analysis and capture of large volumes of data [15].  
This paper presents a new novel digital filter termed \"aIMF\" which is a derivative of EMD. The aIMF algorithm is used to reduce a noise associated with nonlinear nonstationary time series data sets (exchange rates). To verify the performance of the proposed aIMF digital filter, we compare it with WT, EKF and PF. The result shows the aIMF algorithm outperforms those mentioned filters. Section 2 presents theoretical considerations of EMD, aIMF, WT, EKF and PF. The simulation and results including robustness test are presented in Section 3, whereas conclusion and discussion are in Section 4.