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Long term integration, defined as integration along paths through multiple resolvable volumes, can significantly increase moving target detection sensitivity in clutter. Physically, this improvement comes primarily from the ability to smooth over and thus reduce clutter spatial variations that are responsible for its "spiky" statistical behavior. A secondary improvement comes from increased ability to smooth over aspect-dependent target fluctuations. However, since target motion is not known, increased complexity results from the need to implement multiple hypothesized integration paths. Implementation complexity depends on integration duration, spatial resolution, bounds on target speed and maneuverability, and the subsequent path mismatch losses. The current analysis focuses on point defense using a predetermined set of constant radial velocity paths that do not cross fixed beam patterns; i.e., simple "range walks". The integration across resolvable volumes is perlormed noncoherently, although coherent integration can take place within resolvable volumes. Thus, coherent integration across resolvable volumes is not considered. The K-density spatial variation clutter model is used, where the pulse to pulse temporal fluctuation is a correlated complex Gaussian random process whose "local" mean varies independently from scan to scan according to a gamma density. Although any form of coherent processing can be included, an MTI filter is used explicitly. Although propagation effects are not considered, long term integration should provide an additional detection sensitivity improvement by increased ability to smooth over these fluctuations. Starting with conventional integration in a single resolvable volume, detection performance is determined using a novel approximation that involves finding the equivalent number of statistically independent returns before square law detection. This allows the results of Marcum and Swerling to be modified and used as conditional probabilities in a numerical integration. The approximation also makes the long term noncoherent integration problem numerically tractable using density cumulants in a generalized Laguerre series. In a tradeoff where the number of pulses coherently integrated per dwell, the scan revisit rate, and the number of dwells noncoherently integrated all vary according to a fixed radar resource constraint, results show that transmitting the shortest dwells possible, including MTI fill pulses, yields optimum results. Although this depends on the scenario, for close-in point defense in spiky sea clutter this implies that clutter and target smoothing advantages offered by long term noncoherent integration outweigh greater SIR buildup offered by increased coherent integration within a resolvable volume. A final comparison with this scenario shows that long term integration increases SIR sensitivity by about 10 dB over conventional cumulative detection, allowing a shipboard horizon scanning system to detect -30 dBsm subsonic sea-skimmers with d=°•9 Pf=l 0-6 at 10 km range in sea state 4.
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