A new IMM algorithm using fixed coefficients filters (fastIMM) Dahmani Mohammed à , Keche Mokhtar, Ouamri Abdelaziz, Meche Abdelkrim University of Science and Technology USTO-MB, B.P 1505, El M’Naouar - Bir el Djir- Oran, Algeria article info Article history: Received 7 July 2009 Accepted 21 October 2009 Keywords: Kalman filtering IMM Tracking Fixed coefficient filter abstract In this paper we present an new approach based on two filters ab and abg using Interacting Multiples Models (IMM) design instead of a Kalman filter second and third order for the tracking a single maneuver target. The comparison between the proposed filter and the IMM improves the computing time amount about 60% while having a high accuracy. & 2009 Elsevier GmbH. All rights reserved. 1. Introduction Target tracking and predicting is realized in track while scan systems, which are sampled data filters, based on previously observed positions containing measurement noise. The perfor- mance of these filters is function of their noise smoothing behavior and their transient system response. A filter developed in the mid 1950s, the ab tracker, is popular because of its simplicity and consequently inexpensive computational require- ments. This permits its use in limited power capacity applications’ like passive sono-buoys. The ab filter performance has been analyzed by Sklansky [1]. Particularly in radar applications, having a single model to capture the dynamics of a system (target) is not enough, and therefore algorithms based on several models (modes) may be necessary for tracking the behavior of un-predictable target. The Interacting Multiples Models (IMM) is such an algorithm. In this algorithm several filters are run in parallel, each filter matching a specific model for the target’s dynamic. A particularity of the IMM is that these models interact. The state estimates and their covariances, obtained from different filters, are computed and combined to form the overall state estimate and its covariance. To reduce the complexity, the filters used in the proposed IMM algorithm are the ab and abg filters. We here after describe these filters before showing how they are incorporated into the IMM algorithm. 2. ab and abc filter 2.1. ab filter The ab filter is probably the most extensively applied fixed coefficient filter. It may be viewed as the steady state second order Kalman filter. This filter is defined by the following [2,3]: ^ xðkÞ¼ x p ðkÞþ aðx 0 ðkÞx p ðkÞÞ ð1Þ ^ vðkÞ¼ ^ vðk1Þþ b T ðx 0 ðkÞx p ðkÞÞ ð2Þ x p ðk þ 1Þ¼ ^ xðkÞþ T ^ vðkÞ ð3Þ where ^ xðkÞ is the coordinate of the smoothed (estimated) target’s position, x 0 ðkÞ is the coordinate of the measured target’s position at the kth scan, x p ðkÞ is the coordinate of the predicted target’s position at the k th scan, ^ vðkÞ is the smoothed target’s velocity at the kth scan, T is the radar scan time or the sample interval, and a; b are the fixed coefficients filter parameters. Finally, the usual initialization procedure is x p ð1Þ¼ ^ x ð0Þ and ^ vð0Þ¼ 0 ð4Þ and ^ vð1Þ¼ ½ ^ x ð1Þ ^ x ð0Þ T ð5Þ According to [4], the ab estimator is optimal the two coefficients a; b verify the following equation: b ¼ a 2 2a ð6Þ Further details on the steady state of the second order Kalman filter can be found in [5]. Contents lists available at ScienceDirect journal homepage: www.elsevier.de/aeue Int. J. Electron. Commun. (AEU ¨ ) 1434-8411/$ - see front matter & 2009 Elsevier GmbH. All rights reserved. doi:10.1016/j.aeue.2009.11.009 à Corresponding author. E-mail address: dahmani@univ-usto.dz (M. Dahmani). Int. J. Electron. Commun. (AEU ¨ ) 64 (2010) 1123–1127