Variances of the predicted state in the steady state for a three‐dimensional radar tracking using a linear filter

Abstract

AbstractWe explain a tracking method that uses a linear filter to estimate the true values of the position and the velocity with the target position as the radar observation. One representative example is a Kalman filter for three‐dimensional space. The α‐β filter with its easily analyzed performance is widely used in one‐dimensional space. In a tracking method, the tracking precision must be evaluated when sufficient time has elapsed since the initial calculation, that is, in the steady state. The equation for calculating the variance of the errors in the predicted position in the steady state has been reported for radar observations of a constant‐velocity linear motion target by an α‐β filter. In addition, a Kalman filter can obtain the variance of the errors in the predicted position in the steady state by the Riccatti equation. In this case, however, a premise is the presence of drive noise that indicates the ambiguity of the motion model. There is no equation for calculating the variance of the errors in the predicted position in the steady state for the radar observations of a constant‐velocity linear motion target. In this paper, we present an equation for calculating the covariance matrix of the prediction errors in the steady state of the position and velocity for the radar observations of the constant‐velocity linear motion target in a 3D spatial linear filter. The results calculated in this paper present an extension of a conventional α‐β filter. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 87(12): 68–77, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.10186