An Adaptive IMM Estimator for Aircraft Tracking Emil Semerdjiev 1 Ludmila Mihaylova 1

to compute the overall estimate. When the range of the expected control parameter is wide, however, IMM needs a large number of models to provide consistent estimation. One promising solution to this problem is to use variable-structure estimation algorithms [5-7]. An alternative, nontrivial solution is proposed in this paper. It requires a minimal number of models (one for rectilinear motion, one for right turn and one for left turn) to cover the range of all possible target maneuvers. The proposed adaptive IMM algorithm estimates the difference between the control parameter assumed in the current model and its real value. The method has been applied at first for marine targets tracking in [10], where the range of the control parameter is very narrow. To cover the very wide respective range for air targets an additional adaptation mechanism is applied. It is concerned with the IMM transition probabilities and the fudge factor and the noise covariance matrices of the maneuvering models. The algorithm’s performance is evaluated by Monte Carlo simulations and the effectiveness is illustrated by a comparison with 3and 5-model standard IMM algorithm versions.
where
Pi ,k / k = Pi ,k / k −1 − Ki ,k S i K i' ,k , (12) $i ,k / k and x $i ,k / k −1 are the filtered and the where x
ˆi given by: predicted estimates of x k ; f i = ∂f i ∂x
Proc. 1999 International Conf. on Information Fusion, Silicon Valley, CA, USA, July 1999
& = gnT , v
&= ϕ
∗ N
− gn ∗ N
/ v,
$ i ,k / k −1 = f x $ i ,k −1/ k −1 , n ∗ x N i ,k − 1 ,
xk = ( X k
Yk
ϕk
γ i and S i ,k are the filter residual process and its
1 0 $ fi x = 0 0 0
$i,k / k −1 $ i ,k / k −1cosϕ 0 Tv $i ,k / k −1 $ i ,k / k −1sinϕ 1 − Tv 0 0 0 1 0 0 −
2. Aircraft Models
The target motion is described in the horizontal plane xOy by the commonly used model [8]:
& = V sin ϕ , X & = V cos ϕ , Y
1 Partially supported by the Bulgarian National Science Fund - Contract No. I-808/98. * Supported by ONR via Grant N00014-97-1-0570, NSF via Grant ECS-9734285, and LEQSF via Grant (1996-99)-RD-A32.
1. Introduction
In recent years the design of reliable and effective multiple-model (MM) algorithms for maneuvering target tracking is a subject of extensive research (see e.g., [1-7]). These algorithms are used to overcome problems caused by structural and parametric uncertainties. The Interacting Multiple-Model (IMM) algorithm is the most commonly used MM estimation algorithm among them. The lack of knowledge about the target’s control parameters is overcome in it by introducing a set of fixed control parameters. This set is expected to cover the range of possible parameter changes. A set of models represents the system behavior in each fixed control value. Kalman filters based on these models are running in parallel and their estimates are finally fused [1-3, 6]
$i ,k / k −1 Tsinϕ $i ,k / k −1 Tcosϕ ∗ $∗ Tg nNi + ∆ n Ni ,k / k −1
(
)
$i2,k / k −1 v 1 0
ቤተ መጻሕፍቲ ባይዱ Tg $i ,k / k −1 v 0 1 0 0
presence of unknown control parameters n N and
ˆ x
n∗ N ,k
= n N ,k sin γ k , γ k = arc cos( 1 / n N ,k ) ;
v k ) should be estimated in the
'
k is the current discrete time; T is the radar sampling interval. The state vector
$ i ,k / k −1 , γ i ,k = y k − Hi x
(
)
(7) (8)
Pi ,k / k −1 = φ i f i x Pi ,k −1 / k −1 f i x
( )
'
+ Qi ,k ,
(9) (10) (11)
S i ,k = H i Pi ,k / k −1 H i' + R ,
where n = n N sin γ , γ = arc cos( 1 / n N ) ; (X, Y) are aircraft mass center coordinates, V and ϕ are aircraft velocity and heading, n N and nT are normal and tangential g-load factors (NLF and TLF), γ is roll angle; g = 9.81 is the load factor. The respective discrete-time model has the form
Proc. 1999 International Conf. on Information Fusion, Silicon Valley, CA, USA, July 1999
An Adaptive IMM Estimator for Aircraft Tracking
Emil Semerdjiev 1 Ludmila Mihaylova 1 X. Rong Li ∗
Abstract–An adaptive Interacting Multiple-Model (IMM) estimator using a small number of models is proposed for maneuvering aircraft tracking. It estimates the difference between the true target control parameter and the value currently used in the IMM models to improve the estimator’s performance. The algorithm performance is compared with the performance of a standard IMM estimator for some maneuver scenarios via Monte Carlo simulations. Key Words: target tracking, IMM, adaptive estimation