This study uses simulated data from a set of two-band sensors and a set of three-band sensors. There are dozens of warheads and numerous decoys simulated (several decoys for each warhead). For a large part of the scenario, the objects are so close that individual targets cannot be resolved by the sensors, even though a single object's infrared signature could readily be detected. In those cases, multiple objects are seen as a single object, with the summed intensity of several objects. A BODE discrimination technique, which fits a quadratic and a sinusoid to the infrared time histories, is used to attempt to distinguish the warheads from the decoys. The average coefficients of the curve fit, along with their covariances, are used as features which describe the two object sets (warheads and decoys). Warheads and decoys can be readily distinguished once objects are far enough apart so that no multiple objects are mistaken as single objects. But when a cluster of objects appears as one object on the sensor focal plane, it is apparently impossible to tell whether or not a warhead is present in the cluster.
This study considers a satellite-mounted sensor in a 1000-km circular orbit. The sensor is initially placed North, South, East, or West of a ballistic target, at a variety of initial ranges from 500 km to over 3000 km. The initial angle between the sensor and target velocity vectors is varied, from near zero degrees to roughly 180 degrees, in steps of 30 degrees. The tracking algorithm used is a standard Kalman filter. The track errors as a function of track time for several track data rates (once every 2 to 20 seconds) are examined. The error is defined to be the maximum eigenvalue of the covariance matrix. Both the current covariance matrix and the matrix propagated to impact are studied. The study is done for a variety of angular measurement errors, from one microradian to over 100 microradians. The best tracking performance seldom occurs when the target and sensor velocity vectors are crossing, as might be intuitively expected. The track error is very nearly linear with angular error. While increasing the data rate improves tracking performance, doubling the data rate does not improve performance nearly as much as doubling the total track time. The tracking performance does not automatically degrade with inithi range, as might be expected. Once a good track is obtained, further updates to the track can be very infrequent (less than once per 100 seconds), and the track will still improve steadily with time. Stereo tracking, as might be expected, offers dramatically better results than mono tracking.
This paper examines the focal plane for the proposed Brilliant Pebbles sensor. Each Pebble is designed to be autonomous -- to locate and identify thrusting targets, determine which it can reach, and to attempt to intercept the closest target. Tracking a booster is not possible with a single sensor, so each Pebble identifies targets by comparing the measured intensity histories with those for known targets. The proposed focal plane has a large dead space between detectors. The detected target intensity thus varies dramatically as the target moves across the focal plane, even when the target intensity is a constant. Intensity measurements can thus be extremely inaccurate. The effect is studied for several fill factors, from 100% down to 50%, the approximate fill factor for the proposed system. Knowing the precise position of the blur spot on the detector helps to compensate for this effect. One method, which estimates position using intensities from adjacent detectors, is shown. But this method's value declines as the fill factor decreases. Furthermore, the method can only work when the detector response as a function of target position is known precisely. The effect of the focal plane design on separation of closely-spaced objects (CSOs) is derived. Several cases are shown in which multiple targets, separated by substantial fractions of a detector width, are indistinguishable from a single target. The effect of changing the fill factor is also demonstrated. As the fill factor decreases, the effect worsens. Proposed changes to the sensor design include increasing the fill factor and/or defocussing the blur spot. Results are shown for various combinations of these parameters.
This study considers a satellite-mounted sensor in a 1000-km circular orbit. The sensor is initially placed north, south, east, or west of a ballistic target, at a variety of initial ranges from 500 km to over 3000 km. The initial angle between the sensor and target velocity vectors is varied, from near zero degrees to roughly 180 deg, in steps of 30 deg. The tracking algorithm used is a standard Kalman filter. The track errors as a function of track time for several track data rates are examined. The error is defined to be the maximum eigenvalue of the covariance matrix. Both the current covariance matrix and the matrix propagated to impact are studied. The study is done for a variety of angular measurement errors, from one microradian to over 100 microradians. The best tracking performance seldom occurs when the target and sensor velocity vectors are crossing, as might be intuitively expected. The track error is very nearly linear with angular error. While increasing the data rate improves tracking performance, doubling the data rate does not improve performance nearly as much as doubling the total track time. Once a good track is obtained, further updates to the track can be very infrequent and the track will still improve steadily with time.
The focal plane examined has a small fill factor; in other words, there is a large dead space between detectors. From the size of the blur spot, one can calculate the fraction of the target energy, from a point source, which is detectable. This fraction is a function of the position of the center of the blur spot. As a result, the detected target intensity varies dramatically as the target moves across the focal plane, even when the target intensity is a constant. Intensity measurements can thus be extremely inaccurate. The effect is studied for several fill factors, from 100% down to 50%,the approximate fill factor for the proposed system. The effect can be compensated for if the precise position of the blur spot on the detector is known. One method, which estimates that position using intensities from adjacent detectors, is shown. This method's value, unfortunately, declines as the fill factor decreases. Furthermore, the method can only work when the detector response as a function of target position is known precisely. The effect of the focal plane design on separation of closely-spaced objects (CSOs) is then derived. Several cases are shown in which multiple targets, separated by substantial fractions of a detector width, are indistinguishable from a single target. The effect of changing the fill factor is also demonstrated. As the fill factor decreases, the effect worsens. Proposed changes to the sensor design include increasing the fill factor and/or defocussing the blur spot. Results are shown for various combinations of these parameters.
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