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Accuracy
Underwater Launch
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| Background |
| The accuracy of submarine-launched ballistic missiles has been assessed for all generations of the Fleet Ballistic Missile, but the requirement for high accuracy for the Trident II (D5) weapon system brought with it a requirement to have greater confidence in that assessment. The Trident Accuracy Program was introduced to develop the instrumentation, methodology, and expertise to enable APL to provide the Navy with accuracy estimates whose uncertainty could be quantified -- even for scenarios that are not fully explored in any test program. |
| Flight testing has always been an integral part of any assessment of the performance (accuracy, reliability, and readiness) of the Fleet Ballistic Missile accuracy but until the Trident Accuracy Program, the accuracy analysis consisted primarily of measuring the misses from the target and computing sample statistics. Flight test programs were designed to reflect expected tactical usage as much as possible, but there were test limitations that were necessitated by considerations of cost and flight test safety: in particular, limited areas from which flight tests could be launched and limited ranges for trajectories. |
| The New Approach - Test Instrumentation, Error Estimation, Model Prediction |
| The first aspect of the new approach introduced by the Trident Accuracy Program was to introduce new flight test instrumentation to allow accuracy assessment at a more fundamental level - even down to the level of specific accelerometer and gyroscope errors for the missile. The use of satellites for estimating the position of an object (viz., submarines on patrol) was first developed at APL and this capability was extended to allow the estimation of the position and velocity of a missile in flight. The Satellite Tracking (SATRACK) instrumentation and processing forms the heart of the new instrumentation employed in this new approach; the full set of flight test accuracy instrumentation is shown in the chart below.
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This test instrumentation makes possible the second aspect of the Trident Accuracy Program: the estimation of individual errors that contribute to a total system miss. Data from each accuracy test is analyzed using some variant of a Kalman filter. Within the filters are the detailed models of both the system and instrumentation for each subsystem. This data is combined with prior information generally developed and maintained by contractors responsible for various parts of the system under test. This prior information is necessary for single test processing, given the incomplete observability of error sources. The outputs of the filter provide a basis for understanding particular realizations of system and subsystem behavior. Analysis results provide insight into the sources and causes of inaccuracy.
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The instrumentation-based data is also used in the third new approach introduced by this program: the generation and use of an error model to provide estimates of system accuracy - with quantified confidence. The results of multiple tests (the outputs of the Kalman filters) serve as input to the cumulative parameter estimation process; however, all prior information relative to the error models is removed so that the estimated accuracy is derived solely from the data. Although error models for ballistic missiles had been used before this program, they were never directly derived from weapon system test results. Previous models were validated or (or more often, invalidated) by comparison to the inherently limited flight test results, but the new approach allowed the model to be estimated - and allowed the generation of formal confidence bounds in those estimates.
The process figure here depicts notationally how this analysis is accomplished. |

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This process solves the highly nonlinear equations for the means, variances, and Markov parameters that characterize the overall system accuracy performance. In addition, uncertainties in the parameter estimates are calculated so that we have a quantitative measure of our confidence in the solution. The ultimate desired product is a performance prediction for the system under tactical, not test, conditions. Here we rely on models of the tactical gravity and weather environment developed from data and instrumentation. These models, along with deterministic simulations of the system, are then used to “propagate” the fundamental model parameter estimates and uncertainties to the domain of interest—system accuracy at the target. |
| Contributions |
The Trident II Accuracy Evaluation Program has contributed to the success of the Trident Weapon System in several important ways:
· Instrumentation Requirements and Test Planning - models and simulations of accuracy evaluation supported rigorous quantitative trade-off studies.
· Accuracy Understanding - has provided unprecedented understanding of and confidence in system performance.
· System Improvements - improved models provide better system performance by way of embedded system software through the calculation of system gains used when processing guidance stellar sightings or reentry body fuze information, which relies on an accurate characterization of system performance. The calibration of reentry body release parameters has been improved by knowledge gained from onboard inertial instrumentation.
· Accommodation of Testing Cutbacks - instrumentation and a rigorous analytical approach required less testing to achieve the desired initial confidence and also reduced follow-on testing of the deployed system.
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