Aircraft Tracking Using Particle Filtering and Monopulse
An important research area for multi-function radar, such as MPAR, is improved target
tracking, particularly for highly maneuvering targets.
For tactical targets, maneuvering
implies that the object possess significant accelerations along one or more of their respective
velocity vectors.
Figure 4 depicts data recorded at the NWRT in conjunction with BCI, in September, 2005. In the study of real world dynamic systems or data analysis, it is often required to estimate the unknown quantities based on some given measurements. State space models are used to approximate real world phenomena as systems, where the states (either observable or not) represent the internal variable that governs how the system evolves with time. In this framework, estimating the unknown quantities can be formulated in the problem of state estimation.
Figure 4 depicts data recorded at the NWRT in conjunction with BCI, in September, 2005. In the study of real world dynamic systems or data analysis, it is often required to estimate the unknown quantities based on some given measurements. State space models are used to approximate real world phenomena as systems, where the states (either observable or not) represent the internal variable that governs how the system evolves with time. In this framework, estimating the unknown quantities can be formulated in the problem of state estimation.
Figure 4a: Detections of airport traffic at the OKC airport and vicinity, as measured by the NWRT on September 15, 2005.
Figure 4b: Same as Figure 4a but for the date on September 19, 2005.
For this experiment, detections were
made within a 90 degree sector, looking towards the airport. The set of concentric
circles denote distances in units of kilometers away from the radar.
In state estimation, Kalman filtering is widely used when the model is linear and the
additive noise is Gaussian. In the real world, however, systems are more complex, typically
involving nonlinear and non-Gaussian elements. Estimating the states of such systems is
a difficult problem and, in general, the optimal solution cannot be expressed in a closed
form. Usually, if the system under study is nonlinear, an extended Kalman filter (EKF)
can provide a suboptimal solution.
This approach is based on linearizing the system about
certain states, then applying a Kalman filter to the linearized model. There exist some
deficiencies associated with the application of EKF.
- large errors may result from linearization.
- it is often nontrivial to derive the Jacobian matrices, which may result in implementation difficulties.
- the EKF is not generally applicable to non-Gaussian noise.
More recently, particle filtering techniques have received increasing attention
[Djuric et al., 2003;
Gustafsson, 2002].
The basic idea of the particle filter is to approximate the
probability density function (PDF) of the system state by a set of weighted random samples
(also called particles).
Within a sequential framework, the particles and their weights are
propagated through the system and updated whenever the most recent measurements are
received. Given the nature of sequential importance sampling and the Monte Carlo approach,
particle filtering has emerged as a superior alternative to the traditional nonlinear filtering
methods.
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Research in Progress
Correlating Detections Into Viable Tracks
Using a set of valid PAR detections, we
propose to use a trajectory correlator to assign specific paths to the moving targets.
This work will begin by leveraging on the previous measurements of BCI presented in
Figure 4 and anticipates new PAR experiments to be conducted as needed. Using
the PAR difference channel capability,
these measurements will
be compared to traditional monopulse techniques.
Development of Track-While-Scan (TWS) Algorithm
In the multi-function mode of
operation, it is undesirable to dedicate the entire radar system to tracking a single
target. We propose to develop a track-while-scan (TWS) algorithm, which could be
used with PAR.
Given the current limitations, however, we intend to use a combination
of numerical simulations and full volumetric scan data to complete this task. The TWS
system will maintain the search function, while a bank of particle filters will perform the
tracking functions. The TWS system will be designed to be capable of automatically
tracking many targets simultaneously. The TWS system will use range, angle, Doppler
and elevation gates in order to discriminate targets from one another.
Hypothesis Formulation for Beam Steering Computer
Particle filtering, combined with
beam multiplexing, will provide the optimum strategy
for dwell assignments at time t + Δt, for a given time t. These dwell assignments
will be used to develop a close-loop system for optimum beam scanning and resource
allocation for simultaneous target tracking and weather surveillance.
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