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Tracking in Several Real-World Scenarios, 2016, 156p

  • Two-point differencing using the unbiased measurement conversion from polar to Cartesian coordinates was used in the initialization of the other filters[7].
[7] Y. Bar-Shalom, X.-R. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation. New York: Wiley, 2001.

Comparison of Single-point and Two-point Difference Track Initiation Algorithms Using Position Measurements

MALLICK Mahendra, 2008 [Download]

  • 트랙초기화(Track initiation)는 추적의 필수 요소이지만 중요성에 비해 연구가 많이 이루어 지지 않았다. Track initiation is an essential component of all tracking algorithms, but one that has received little attention.

  • 움직임이 일정한 물체의 추적에는 칼만필터를 사용하는것이 일반적으로 좋다. For situations where the dynamic and measurement models are linear and appropriate Gaussianity and independence assumptions hold, it is well-known that the Kalman filter (KF) is optimal in the minimum mean squared error sense [1−2].

  • 하지만 이런 좋은 결과를 위해서는 요구 사항들이 있다. However, this result requires that

  • the mean of the initial state estimate is equal to the mean of the initial state,

  • and its associated error covariance matrix is equal to the true initial covariance.

  • 실제 적용시에는 이상적으로는 잘못된 초기화도 수정(=제거)되지만 이를 보장 할수는 없다. In practice, this is rarely the case. Ideally, any initial transients introduced by incorrect initialization will quickly be eliminated, but this cannot be guaranteed.

  • 이러한 에러의 영향에 대한 연구가 [3-5]에서 이루어 졌고 최근에는 타겟 추적에 초점을 연구 되었다[6]. The effect of such errors on Kalman filters for general problems have been examined in [3 − 5] and more recently, with a focus on target tracking, in [6].

타겟 추적 문제와 관련된 몇가지 고려 사항들이 더 있다. There are additional factors to be considered for target tracking problems.

  • 실생활에서 Radar 추적의 측정치는 2D에서는 거리, 방위각이며, 3D에서는 거리, 방위가, 고도이다. In real-world radar tracking problems,the measurements are range and azimuth in the 2D case,and range, azimuth, and elevation in the 3D case.

  • Unbiased position measurements and associated measurement covariances can be derived from these radar measurements [7] ,

  • but the associated measurement errors are no longer Gaussian.

  • For the ground target tracking problem using the ground moving target indicator (GMTI) radar sensor,

  • the 3D position of a target can be estimated using the GMTI range andazimuth measurements, sensor position, and terrain data [8] .

  • 비디오 추적문제에서도 비슷한 상황이 발생 한다. A similar situation occurs in the video tracking problem.

The 3D position of a ground target can be estimated usingthe target centroid pixel location, intrinsic and extrinsic camera parameters, and terrain data [9] .

Similarly, the errors in the 3D position estimate of the target for the GMTI and video tracking problems are not Gaussian.

  • 이런 비가우시안 속성으로 인해서 필터 성능에 영향을 미치고 잠재적으로 초기에러 확산을 야기 한다. This lack of Gaussianity will also have an impact on the performance of the filter and can potentially exacerbate any initialization errors.
  • [10]에서 이를 증빙하였다. This is demonstrated in [10], which considers the problem of target tracking with long range radars.

본 논문에서는 두개의 트랙 초기화 알고리즘을 비교 하였다. In this paper, we compare two track initiation algorithms,

  • the single-point (SP) method [11−12] and
  • the two-point difference (TPD) method [2] , using position-only measurements in 1D, 2D, or 3D.

본 논문에서는 타겟의 움직음은 고정된 속도라고 가정 하였다. We assume that the target motion is described by the nearly constant velocity model(NCVM) [2] .

  • SP: Then, the SP algorithm initiates the track using the first position measurement and sets the velocity components to zero.

  • The maximum possible speed of the target is used, in addition to the measurement covariances, to initialize the associated covariance matrix [11−12] .

  • A KF is then used to process subsequent position measurements.

  • TDP : In contrast, the TPD algorithm [2] uses information on the first two measurements alone to initialize the filter.

  • This estimate represents the maximum likelihood estimatefor Gaussian position errors.

We demonstrate numerically that the SP method has a smaller mean square error matrix (MSEM) than the TPD for a 3D radar target tracking problem.

We conjecture that this result holds analytically.

We analytically show that, if the process noise approaches zero and the maximum speed of a target used to initialize the velocity variance approaches infinity, then the SP algorithm reduces to the TPD algorithm.