KEYWORDS: Error analysis, Mahalanobis distance, Monte Carlo methods, Matrices, Data fusion, Digital filtering, Sensors, Statistical analysis, Computer simulations, Data processing
The primary components of a target track are the estimated state vector and its error variance-covariance matrix (or simply the covariance). The estimated state indicates the location and motion of the target. The track covariance should indicate the uncertainty or inaccuracy of the state estimate. The covariance is computed by the track processor and may or may not realistically indicate the inaccuracy of the state estimate. Covariance Consistency is the property that a computed variance-covariance matrix realistically represents the covariance of the actual errors of the estimate. The computed covariance of the state estimation error is used in the computations of the data association processing function; consequently, degraded track consistency causes misassociations (correlation errors) that can substantially degrade track performance. The computed covariance of the state estimation error is also used by downstream functions, such as the network-level resource management functions, to indicate the accuracy of the target state estimate. Hence, degraded track consistency can mislead those functions and the war fighter about how accurate each target track is. In the past, far more attention has been given to improving the accuracy of the estimated target state than in improving the track covariance consistency. This paper addresses the importance and analyzes properties of covariance consistency. Monte Carlo simulation results illustrate the characteristics of covariance consistency and the performance with some simple methods for improving covariance consistency.
The real world presents a much messier tracking environment than the usual pristine world of tracking simulations. In particular, simulations often do not properly account for the presence of CSOs in the vicinity of the objects being tracked, thereby producing potentially misleading results. CSOs have several nasty effects on trackers, which, if not mitigated, may result in show-stopping surprises when attempting to use a tracker operationally. This paper will describe and quantify some of the limitations that CSOs impose on single sensor and/or multisensor trackers. These limitations include delaying the expected time that a given object can be confidently resolved, interfering with the ability to asso-ciate objects between sensors properly, contaminating track files with spurious signature information, and forcing some form of cluster tracking to be employed. Analytic predictions of these limitations, based on local object density over time, will be presented, backed up by various Monte Carlo simulations. A more robust metric is proposed to allow the prediction of a more operationally meaningful probability of correct target association in a multisensor environment.
KEYWORDS: Data fusion, Sensors, Monte Carlo methods, Motion models, Data processing, Sensor fusion, Statistical analysis, Defense and security, Signal processing, Data modeling
Adding new sensor metric information into a data fusion process does not always improve performance and can sometimes produce poorer results. References 1 and 2 used examples to show that - in some instances and contrary to expectation - adding new information resulted in poorer rather than improved performance, even though the information itself was correct. Correct is being used here to describe data that may be in error because of sensor deficiencies but whose error characteristics are accurately described and known to the fusion process. In other words, the fusion process is not being lied to be misrepresentation of the data quality. In this sense, an individual data point may be inaccurate, but the fusion process is capable of properly weighting that point in an optimal sensors that its statistical inaccuracy does not damage the final product any more than a data point from a better sensor that has less statistical inaccuracy. In a multiple-sensor fusion process, these kinds of result have been cited as reasons for not using data from poorer quality sensors for fear of diluting the performance of the better quality sensors. This paper explores the counterintuitive findings for these referenced examples and evaluates under what conditions lesser quality sensor or sensor that mistakenly overestimate their own data quality should be allowed to contribute to a sensor fusion process.
The uncertainty in the time of ballistic missile transition from boost to coast phase poses significant problems to tracking sensors. The Interacting Multiple-Model (IMM) filter monitors this transition through the application of two Kalman filters, whose inputs and outputs are weighted by computed probabilities that the missile is in boost or coast phase. The ability of IMM to produce accurate tracks early in the midcourse phase is compared with that for simpler models that use a 'nearest neighbor' approach to determine the best fit to sensor measurements. Track output -- state vectors and error covariance matrices -- are handed off in the post-boost phase to midcourse sensors, which propagate tacks using either centralized measurement fusion or tracklets; that is, tracks computed so that their errors are not cross-correlated with those from other tracks of the same target.
KEYWORDS: Sensors, Signal processing, Data processing, Data modeling, Optical resolution, Image resolution, Monte Carlo methods, Infrared sensors, Signal detection, Target designation
This paper documents an analytical effort that looks at the expectation of being able to resolve individual members of a cluster of objects as a function of the parameters of time after deployment, the number and distribution of objects in the cluster, their relative separation velocities, sensor resolution capability, and the shape of the cluster -- essentially local object density. Multiple methods of modeling object clusters were investigated and found to be equivalent in their results. A simple set of equations has been derived that fits modeled data over a wide range of the parameter variations. For N objects in a cluster of average density equals d objects per resolution cell; R approximately equals N (DOT) e-d equals the expected number of objects resolved, and P approximately equals (N - R)/d equals the expected number of subclusters perceived. For uniform cluster densities, d is inversely proportional to time squared, and a method is shown for calculating d for non-uniform cluster densities. In addition, an approximately constant relationship between the number of objects perceived and the number of resolved objects is shown; R approximately equals P2/N. Several applications of these relationships which are of interest to the Strategic Defense Initiative (SDI) are examined, including the `Cheshire Cat Effect' wherein the number of perceived objects as a function of resolution and sensor sensitivity is discussed. In addition, system level implications of the effects of target density during boost phase and during the cluster tracking phase of mid-course are covered. The behavior of large numbers of clusters in a threat tube is examined and characterized as the individual clusters overlap each other as they expand and form a `supercluster.' An equilibrium limit of resolution possible within a `supercluster' is shown.
Conference Committee Involvement (4)
Signal and Data Processing of Small Targets 2007
28 August 2007 | San Diego, California, United States
Signal and Data Processing of Small Targets 2006
18 April 2006 | Orlando (Kissimmee), Florida, United States
Signal and Data Processing of Small Targets 2005
2 August 2005 | San Diego, California, United States
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