Bearing-only 2D maneuvering target tracking using smart interacting multiple model filter

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Abstract

In this paper, along with reviewing and analyzing the maneuvering target tracking model, the multiple-model Interacting Multiple Model algorithm is used to solve the maneuvering target tracking problem in the presence of measurement noise. In addition, for reliable estimation another method is proposed, which uses higher-order Markov models to describe the system behavior precisely. It means that the previous two models are used to predict the next model of target in order to present a more better algorithm than the first-order IMM algorithm. In this approach, two models are employed. For each model Extended Kalman Filter is used to randomly estimate states of the target. The final estimation of the maneuvering target consists of these two models. Final target estimation is obtained from a weighted sum of all state estimates. In addition, target tracking is presented with two modes for noise measurement: one is an adaptive method and the other is an assignment of an integer amount considering problem circumstances. In the end, the results are compared.

Introduction

Target tracking is one of the most important tools in surveillance, supervision, and guidance systems, which are used in radar, sonar [1], [2], and telescope systems, optical, infrared sensors, autonomous robots, and mobile networks [3], [4], [5]. The main objective of target tracking is to obtain the position, velocity, and acceleration of targets [6]. The main challenge in these systems is extracting target motion information based on noise observations. Target tracking is highly regarded in terms of increasing radars' accuracy and position forecasting especially tracking of targets with high maneuverability. Dynamics of target motion comes along with high complexities, nonlinear nature, the existence of uncertainties and various system noises. This makes us/researchers to use various nonlinear filters, including the Kalman filter, quasi-monte Carlo methods, intelligent target tracking methods using neural networks, fuzzy logic in the past few years [7], [8], [9], [10]. The purpose of estimation theory is to estimate the states of a random system based on inaccurate observations.

Different methods have been described for state estimation. One of them is an estimation based on the Bayesian hypothesis. Gaussian filters are a special category of the Bayesian method that works based on the system model and the assumption of having Gaussian noise [11], [12], [13], [14]. If the system behavior consists of different models, multi-model methods are used for state estimation. In Bayesian estimation problems, the ultimate goal is to estimate a random vector in case the observations are available. In dynamic systems, state estimation using Extended Kalman Filter is one of the popular methods in research fields [15]. In [16] Bearing-Only Tracking problem is represented with IMM Filter and Partial Filter. Pseudo-Linear Kalman Filter (PDF) has also been used in Bear-Only tracking method in [17].

Kalman Filters work based on system model and measurement, so a motion model is needed to track the target. To select an appropriate measurement noise covariances, some references such as [18] or [19], implemented adaptive method using Sage Husa recursive method based on the criterion of maximum similarity and the adaptive method using fuzzy approach, respectively. But the result of the simulations of the present paper for a maneuvering target shows that due to the high volume of calculations and the very small changes that are observed, the estimation process depending on the situation is more appropriate. Reference [20] with the assumption of knowing measurement noise had proposed a method for time-invariant linear systems in which the system noise covariance was well estimated. In target tracking If the target speed range can be determined, the noise covariance of the target states can be approximated. For maneuvering target, different structures are presented that here a target motion in two-dimensional coordination is examined [21]. And using two models in the IMM method which, in each model the EKF1 is used, the random target motion model is estimated. To ensure observability of maneuvering target considering a maneuverable observation source with sinusoidal motion is used [22], [23], [24], [25]. The innovations of this article are as follows:

  • •

    using the second-order Markov model instead of the second-order IMM filter which leads to the use of sampler models and better result

  • •

    Integration of BOT method and second-order Markov chain using nonlinear IMM Filter

  • •

    The adaptive approach used for measurement noise is compared with the integer amount estimate method for calculation of measurement noise covariance

The second section explains the second-order IMM model and the correlation that governs it.

In section three, tracking the target using BOT is explained and how it is possible to track the target just by hearing that. Section 4 describes correlation in the maneuverable model. In section five, an example of a number related to a maneuverable target and how to track the target by selecting noise covariance and performed simulations are given. Section 6 describes the results obtained in this study.

Section snippets

Second-order IMM model

Multi-modal algorithms are used for a system with different models. In some systems under certain circumstances, the system model changes with time and is transferred from one type to another. A well-known example of this type of system is the motion model of an object in physical coordinates, in particular, it includes the target tracking problem and predicting the target trajectory. As mentioned earlier, in target motion modeling there are various methods and calculations that lead to the

BOT target tracking

Target tracking is classified into active and inactive types depending on the observer's type. One of the most important tasks of inactive observers is to detect the transmitted signals from the target, followed by detecting the distance and direction of target motion. A conventional method in passive measurement is to detect the direction of the received wave, which indicates the angle or direction between the observer and the target. Tracking based on this type of measurement is known as BOT

Maneuvering model

In the maneuverable model, the target has acceleration, unlike the constant speed mode. According to Fig. 2, in this model, the target has two independent accelerations in the direction tangent to the trajectory and in the direction perpendicular to it. Which respectively are in line with two single vectors e→n,e→t. In the time period dt, the target travels from point p to path ds and reaches point p′. The target has a V‾ velocity vector at point p, which is tangent to the path, and a V‾

Numerical example

It is assumed that in the initial position the target (8 km, -10 km) is moving at a constant speed (3.9 m / s, 5 m / s). After 2000 seconds, the target maneuvers with ω=0.003rad/s angular velocity, and then continues to move at a constant velocity. Then maneuvers with ω=−0.005rad/s angular velocity in 6000 seconds, and this maneuver lasts up to 8000 seconds.

The EKF equations also require the calculation of ∂h(x)/∂x.∂h(x)∂x=[∂h∂x∂h∂x˙∂h∂y∂h∂y˙] As mentioned, the observer move should be chosen in

Conclusion

In this paper, target tracking was performed for the maneuverable model in two dimensions with BOT method and using IMM filter. One of the most important things in this article, in addition to proper target tracking using BOT method, is the use of the second-order Markov model, which leads to the adaptation of the transition matrix model. There are various methods for adapting covariances such as fuzzy method, invention sequence, MIT rule and etc. Which according to the efficiency and volume of

CRediT authorship contribution statement

Mohsen Ebrahimi: Software, Writing – Original Draft, Writing – Review & Editing, Visualization, Project administration. Mahdi Ardeshiri: Term, Writing – Original Draft, Supervision. Sedigheh Alaie Khangha: Writing – Original Draft, Writing – Review & Editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Mohsen Ebrahimi received the M.Sc. degree in electrical engineering from Shahrood University of Technology, Shahrood, Iran, in 2010. Areas of his research interests include adaptive control, robust control, fractional calculus and machine learning algorithms. He has conducted projects in IoT and Intelligent buildings field.

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    Mohsen Ebrahimi received the M.Sc. degree in electrical engineering from Shahrood University of Technology, Shahrood, Iran, in 2010. Areas of his research interests include adaptive control, robust control, fractional calculus and machine learning algorithms. He has conducted projects in IoT and Intelligent buildings field.

    Mahdi Ardeshiri received the PhD degree in electrical engineering from Shahrood University of Technology, Shahrood, Iran. He carried out projects in target tracking, intelligent control and autonomous cars.

    Sedigheh Alaie Khanghah received the B.Sc. degree in electrical engineering Azarbaijan Shahid Madani University, Tabriz, Iran, in 2007. She served as a railway signaling engineer in Iran railway industry.

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