In estimating the state of thrusting/ballistic endoatmospheric projectiles for the end purpose of impact point
prediction (IPP), the total observation time, the wind effect and the sensor accuracy significantly affect the IPP
performance. First the tracker accounting for the wind effect is presented. Following this, based on the multiple
interacting multiple model (MIMM) estimator developed recently, a sensitivity study of the IPP performance with
respect to the total observation time, the wind (strength and direction) and the sensor accuracy is presented.
This paper presents a multiple interacting multiple model (MIMM) procedure to estimate the state of thrusting/
ballistic projectiles in the atmosphere for the purpose of impact point prediction (IPP). Given a very short
time span of observations, the strong interaction between drag and thrust in the dynamic model, in the sense of
ambiguity in the estimation, significantly affects the estimation performance and the final IPP accuracy. This
leads to the need to use an MIMM estimator with various initial drag coefficient estimates. The modes of each
IMM estimator are for the thrusting and the ballistic phases and different extended Kalman filters (EKF) are
used as the mode-matched filters with different dimension states. A novel unbiased mixing procedure for an IMM
estimator is introduced to deal with state estimates with unequal dimensions, as is the case for the thrusting and
ballistic models. The IPP is carried out at the end of the observation period by using the most probable mode
of the selected IMM estimator, the latter being the one with the highest likelihood in the MIMM approach.
Proc. SPIE. 7698, Signal and Data Processing of Small Targets 2010
KEYWORDS: Sensors, Data processing, Signal processing, Quantization, Electronic filtering, Spherical lenses, Atmospheric modeling, Filtering (signal processing), Process modeling, Current controlled current source
This paper presents an interacting multiple model (IMM) based procedure to estimate the state of thrusting
ballistic projectiles in the atmosphere for the purpose of impact point prediction (IPP). The modes of the IMM
estimator are for the thrusting and the ballistic phases and different extended Kalman filters (EKF) are used as
the mode-matched filters with different dimension states. The IPP is achieved by using the IMM-predicted most
probable mode at the mid-point of the trajectory.
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
This paper considers three nonlinear estimation algorithms for impact point prediction (IPP) of ballistic
targets. The paper assumes measurements are available from a 3D surveillance radar or phased array
radar over some portion of the ballistic trajectory. The ballistic target (BT) is tracked using an extended
Kalman filter (EKF), an unscented Kalman filter (UKF), and a particle filter (PF). With the track estimate
as an initial condition, the equations of motion for the BT are integrated to obtain a prediction of the
impact point. This paper compares the performance of the EKF, UKF, and a particular choice of PF
for impact point prediction. The traditional Extended Kalman Filter equations are based on a first-order
Taylor series approximation of the nonlinear transformations (expanded about the latest state estimate).
Both the Unscented Kalman Filter and the Particle Filter allow nonlinear systems to be modeled without
prior linearizion. The primary focus of the analysis presented in this paper is comparing the performance
and accuracy of the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), and the chosen
Particle Filter implementation for impact point prediction. The three filtering techniques are compared to
the theoretical Cramer-Rao lower bounds (CRLB) of estimation error.