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Top1. Introduction
Nonlinear filtering issues exist in many aspects including statistical signal processing and engineering, such as communication, radar tracking, sonar ranging, and target tracking. System estimation in nonlinear discrete-time stochastic systems has become an important field of study for many researchers owing to its wide range of applications in various fields. Problems with Doppler-Bearing tracking (DBT) have been studied over many years for its tremendous importance in the assessment of signal processing, such as observer tracking using passive sonar. In this research paper the research introduces sequential Bayesian estimation methods employing bearings and frequency measurements for nonlinear dynamic stochastic systems. Standard nonlinear filtering estimates are points in the determining measurement space which are affected by the additive measurement noise of a known probability density function (pdf).
Underwater tracking of the target is to determine its path from the observations obtained solely from the signals originated by the target (Doucet et al., 2001; Nardone & Aidala, 1981; Ockeloen & Willemsen, 1982). The originating signals may be from the noise generated by the machinery or reverberations due to the motion of target. These signals are identified when the signal energy is increased beyond an ambient level in certain direction. In most occasions, the energy obtained is of broadband frequency, but at some occasions, the energy spectrum might have tonals. Whenever the target emits these tonals harmonically, Doppler shift can be detected at the observer. These Doppler shifts are utilized in enhancing the precision while estimating Target Motion Parameters (TMP).Analysing TMP using bearing angle as well as Doppler shifts is commonly termed as DBT.
Particle Filter (PF) methods also recently emerged as one of the effective tools for numerically overcoming complex and dynamic system estimation problems involving higher nonlinearities (Fu & Jia, 2010; Rao et al., 2014; Ristic et al., 2004; Simon, 2006). PF methodology is estimated by a set of random samples to the posterior state pdf. Accuracy in PF mainly depends on number of particles and the recommendation functions used for the sampling of significance. The degree of uncertainty is high in available measurements which leads to high computational complexity. So, it takes a large number of particles to reduce the complexity problems.
The two long-standing problems in PF are referred as sample degeneracy and impoverishment. The performance of ðlter improvement in terms of accuracy, robustness and convergence is noted (Vinoth Kumar et al., 2020). In signal processing application non-linear filtering is widely used for many engineering applications. PF improves the estimation accuracy in terms of computational of conditional probability density given in state. PF suffers from curse of dimensionality due to its complexity and computational. Optimal solution for sample degeneracy is to move the particles in good position in the present state space. Computation of flow of particles will be done by inducing the flow of probability density from the prior to posterior. Resampling deals with the degeneracy problem by getting rid of the particles with very small weights (Jagan et al., 2017; Paul et al., 2017; Zhao, 2014). So, the new problem is introduced which is known as sample impoverishment. At the time of resampling particles with large weights are likely to be drawn multiple times whereas particles with small weights are not likely to be drawn. At the time of resampling step diversity of the particles will tend to decrease.
In Bayesian method of approximating the probability of posterior samples distribution, PF utilizes a set of samples that are weighted according to their probability of distribution, called particles. The target’s state pdf can be approximated at any time period using these particles. In PF, the accuracy in sample approximation increases with increase in the number of particles utilised. PF is the ideal nonlinear and non-Gaussian filter that provides optimal solution. As PF approximates the nonlinearities in the process using many particles, the computational complexity is also high for PF. However, this issue is subsided using processors with high computational efficiency.