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: Target detection, Radar, Signal to noise ratio, Detection and tracking algorithms, Missiles, Filtering (signal processing), Signal detection, Signal processing, Computer simulations, Sensors
In many tracking applications, and particularly those in ballistic
missile defense, one concern involves the continuous tracking of
an object that separates into two objects. Reliable tracking
without track breaks demands early recognition of such a split,
preferably well in advance of the two objects becoming resolvable
by the radar. In previous work, signal processing techniques for
detecting the presence of unresolved objects and angle-of-arrival
estimation for unresolved targets have been developed for
monopulse radars. In this paper, these techniques are reviewed and
extended. Techniques for detecting the presence of unresolved
objects are treated for the case of idealized resolution, in which
all of the energy for a target is returned in a single range
resolution sample or cell. The approaches work solely on monopulse
angle statistics and rely on idealized range resolution. The
requirement for idealized range resolution is relaxed by using
joint statistics with adjacent matched filter returns. The AOA
estimation and detection of the presence of unresolved objects for
non-ideal resolution are then addressed. The performances are
demonstrated using a high fidelity software simulation tool for
target tracking.
KEYWORDS: Detection and tracking algorithms, Target detection, Electroluminescence, Antennas, Data modeling, Radar, Algorithm development, Monte Carlo methods, Signal to noise ratio, Statistical analysis
A key assumption in monopulse based angle-of-arrival (AOA) estimators is that at most one return from a single object is present in each range cell, or equivalently in each sample of the matched filter output. These algorithms break down if the data consists of merged measurements-multiple target returns contained in the same range cell. The proposed technique makes use of data from a three channel monopulse radar to estimate the AOA of two targets from merged measurements. Specifically, the technique capitalizes on the structure of squint beams in conjunction with multiple range samples to resolve the multiple targets. The paper focuses on the development of the new algorithm along with results from computer simulations that demonstrate its viability.
To illustrate the utility of this technique to target tracking problems, comparative Monte Carlo results of performance of a tracker with the new technique and conventional monopulse AOA estimates are provided.
KEYWORDS: Sensors, Error analysis, System on a chip, Filtering (signal processing), Radar, Sensor fusion, Detection and tracking algorithms, Monte Carlo methods, Electronic filtering, Motion models
A tracklet is the estimate of a target state or track that is equivalent to an estimate based only a few measurements. Typically, tracklets are considered to reduce the communications costs between sensors and remote global or fusion trackers. The literature includes several methods for computing tracklets. Some of the methods compute tracklets from measurements, while others compute tracklets from the sensor-level tracks. Some of the methods ignore or omit process noise from the modeling, while others methods attempt to address the presence of process noise. The tracking of maneuvering targets requires the inclusion of process noise. When a tracklet that was developed for nonmaneuvering targets (i.e., no process noise) is used for tracking maneuvering targets, the errors of the tracklet will be somewhat cross-correlated with data from other sensors for the same target, and it is referred to as a quasi-tracklet. Due to some important practical considerations, the impact of maneuvering targets on the performance of tracklets has not been thoroughly addressed in the literature. An investigation that includes the critical practical considerations requires computer simulations with realistic target maneuvers and pertinent evaluation criteria (i.e., computation of errors). In this paper, some of the practical issues concerning the use of tracklets for tracking maneuvering targets are discussed, and the results from a simulation study of the impact of target maneuvers on tracking with tracklets are given. The study considered a fusion tracker receiving tracklets from multiple sensors at dispersed locations and targets maneuvering with either random accelerations or deterministic maneuvers. Tracklets from measurements and tracklets from tracks were studied. Since process noise was added to sensor and fusion trackers to account for target maneuvers, the tracklet methods studied are technically quasi-tracklets. A novel technique is used to compare the performance of tracklets for targets maneuvering randomly with that for targets performing deterministic maneuvers.
Since the time and energy of phased array radars are under great demand in modern combat systems, methods that conserve those resources are very important. Two opportunities for conserving radar resources that have not been fully exploited when tracking closely-spaced objects with currently deployed systems are revisit time selection (i.e., time to make a measurement) and beam boresight placement. While these two functions are somewhat coupled, this paper addresses only the problem of beam pointing. Previously, a methodology for track management for phased array radars hinged on the concept of organizing tracks into, so called, dwell groups that included closely-spaced targets that could be illuminated with a single beam. Pointing angle for a dwell group was determined using a geometry-based approach. While the geometry-based approach was useful in improving the entire track management function, it was known to be sub-optimal in that the detection characteristics of the targets were not considered. This paper addresses an improved methodology for assigning membership in dwell groups and selecting dwell pointing angles.
Covariance consistency is a critical element of a robust target tracking system. Target maneuvers and measurement origin uncertainty pose significant challenges to a tracking algorithm achieving covariance consistency. The Interacting Multiple Model (IMM) estimator is a nearly consistent estimator for tracking maneuvering targets. While the Probabilistic Data Association Filter (PDAF) achieves covariance consistency for a single target in presence of false alarms, achieving covariance consistency while tracking multiple closely-spaced targets is an open presence of false alarms, achieving covariance consistency while tracking multiple closely-spaced targets is an open issue. When using an unique assignment technique for associating measurements-to-track association probabilities are unity for each measurement-track pair. This processing of the measurements results in poor covariance consistency for closely-spaced targets. In this paper, the use of approximate association probabilities for each measurement-to-track pair is proposed for the unique assignments and included in the track filter processing of the measurement to enhance the covariance consistency for closely-spaced targets.
In this paper, two modifications are made to the derivation of the PDAF: one replaces the Poisson distributed false alarms with a binomial distribution, the other involves the assumed distribution of the angular measurements associated with false alarms. The Binomial distribution better fits the kind of data typically seen in radar because the track gate typically involves a small number of candidate range cells. The second modification is founded on the assumption that the angle-of-arrival estimates are produced with monopulse techniques. Previous work has modeled the false measurements as being uniformly distributed in the uncertainty volume of the track gate, while a more accurate approach recognizes that the angle components of the false alarms are better modeled as Gaussian perturbations about beam center.
A new method of track management for a phased array radar is proposed to simplify the data association and improve the allocation of radar resources. The tracks are organized into Association Groups and Dwell Groups. Association Groups are used for course gating when associating new measurement data with existing tracks, while Dwell Groups are used to efficiently schedule the next dwell on closely-spaced targets. By considering only closely-spaced tracks in the same Association Group, a form of coarse gating is inherently done to cull candidate tracks that are unlikely to associate with a measurement from a dwell to illuminate all of its members. A Dwell Group contains tracks that are spaced sufficiently to allow one dwell to illuminate all of its members. Dwell groups lay the foundation for more systematic approaches to optimal allocation of the radar resources. Simulation results are presented to illustrate the new technique.
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