Impact Point Prediction of Small Ballistic Munitions with an Interacting Multiple Model Estimator Steve Conover a , J. Clayton Kerce a , George Brown a , Lisa Ehrman a , and David Hardiman b a Georgia Tech Research Institute, Atlanta, GA 30332 b Aviation and Missile RDEC, AMSRD-AMR-SG-CT, Huntsville, AL ABSTRACT The interacting multiple model (IMM) estimator, which mixes and blends results of multiple filters according to their mode probabilities, is frequently used to track targets whose motion is not well-captured by a single model. This paper extends the use of an IMM estimator to computing impact point predictions (IPPs) of small ballistic munitions whose motion models change when they reach transonic and supersonic speeds. Three approaches for computing IPPs are compared. The first approach propagates only the track from the most likely mode until it impacts the ground. Since this approach neglects inputs from the other modes, it is not desirable if multiple modes have near-equal probabilities. The second approach for computing IPPs propagates tracks from each model contained in the IMM estimator to the ground independent of each other and combines the resulting state estimates and covariances on the ground via a weighted sum in which weights are the model probabilities. The final approach investigated here is designed to take advantage of the computational savings of the first without sacrificing input from any of the IMM’s modes. It fuses the tracks from the models together and propagates the fused track to the ground. Note that the second and third approaches reduce to the first if one of the models has a mode probability of one. Results from all three approaches are compared in simulation. Keywords: Interacting Multiple Model, Impact Point Prediction 1. INTRODUCTION The interacting multiple model (IMM) estimator , which mixes and blends results of multiple filters according to their mode probabilities, is frequently used to track targets whose motion is not well-captured by a single model [1,2,3,4]. This paper examines the use of an IMM estimator in computing impact point predictions (IPPs) for small ballistic munitions whose motion models vary at subsonic, transonic, and supersonic speeds. Such munitions exhibit variable drag characteristics depending on the mach regime the projectile occupies, and the rate of change of drag with Mach number is generally largest in the transonic regime. The approach taken in this paper is to model projectile motion in the tracker with two types of dynamics, further assigning a high process noise and low process noise filter for each of these types of dynamics. The desire in breaking out these types of dynamic models is to capture well behaved drag characteristics in the supersonic and subsonic regimes, while allowing enough model uncertainty in the transonic regime to maintain a good track. The first dynamic model, the A-filter (acceleration-filter), assumes ideal point mass motion under the influence of gravity, drag, and a constant acceleration; the second filter considered here will be referred to as the B-filter (ballistic-filter), and includes only dynamic accelerations arising from gravity and drag along the velocity component of the projectile center of mass. The A-filter acceleration is included to model the cross range motion observed in spin stabilized projectiles, while the B-filter models a fin stabilized projectile. Three approaches for computing IPP estimates are compared. The first approach propagates only the track from the most likely mode until it impacts the ground. Since this approach neglects inputs from the other modes, it may not be desirable if multiple modes have near-equal probabilities, since the average of two equally likely models can be better then either one independently. The second approach for computing IPPs propagates tracks from each model contained in the IMM estimator to the ground independent of each other and combines the resulting state estimates and covariances on the ground via a weighted sum in which weights are the model probabilities. The third approach is designed to take advantage of the computational savings of the first without sacrificing input from any of the IMM’s modes. It fuses the tracks from the models together and propagates the fused track to the ground. Note that the second