Tracking of Maneuvering Ballistic Missiles by Designing a Multiple Model Adaptive Estimator (MMAE) to Estimating the Unknown Ballistic Coefficient

Document Type : Original Article

Authors

1 Master's degree, Electrical and Computer Faculty, Malek Ashtar University of Technology, Tehran, Iran

2 Associate Professor.Communication Department, Electrical and Computer Faculty, MalekAshtar University of Technology. Tehran. Iran

3 PhD student, Electrical and Computer Faculty, Malek Ashtar University of Technology, Tehran, Iran

Abstract

Ballistic missiles(BM) are one of the most important threats, which have three flight stages: Boost, Ballistic and Re-Entry. The important issue in BM tracking is the lack of prior information about its shape and size, which shows itself in a parameter called the ballistic coefficient(β); But the most challenging issue is the change in the size and direction of the acceleration vector or the so-called "maneuvering" of the BM in the phase of re-entry into the Earth's atmosphere, which is modeled as a change in the β parameter and practically makes it impossible to track the BM. The estimation of this parameter can be done with two approaches: using a single Kalman filter with a ballistic dynamic model and a high update rate, the advantage of which is the simplicity of implementation and estimates the continuous changes of β, or the use of interactive multiple models (IMM), which are more complex compared to the first approach, but it can also model discrete and instantaneous β changes with a low update rate. The IMM transition probability matrix shows the probability of occurrence of each filter compared to other filters; In this article, an innovative model of IMM called Multiple Model Adaptive Estimator (MMAE) is presented, whose transition probability matrix indicates the independence of the probability of occurrence of each filter compared to other filters and minimizes the delay of moving between models in the estimation filter bank. In this model, it is shown that a maneuver with acceleration close to 3g is modeled as 1/2β, and if a suitable filter is designed for such a maneuver, the path estimation error is significantly reduced. The simulation results show that the MMAE filter bank has an error of less than 2kg/m^2 in estimating the unknown ballistic coefficient and the time of the maneuver.

Keywords

Radar
Volume 11, Issue 2
Autumn and Winter
January 2024

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History

  • Receive Date: 19 August 2023
  • Revise Date: 09 October 2023
  • Accept Date: 06 December 2023
  • Publish Date: 22 December 2023

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