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The performance of a redundant strapdown inertia! navigation system in the normal mode, failure mode, and reconfiguration mode is characterized by a single figure-of-merit representing the probability of mission success. A sensitivity matrix derived from a linearized error analysis relates attitude, position, and velocity errors to initial condition errors as well as inertial sensor static and dynamic errors. The implementation of state vector updates is described. Numerical results are presented for an orbit insertion mission. INEARIZED error analyses have frequently been used to obtain a statistical characterization of navigation system performance.lj2 This paper presents a rigorous extension of these techniques to the analysis of the performance .of an aided redundant strapdown inertial navigation system. The formulation of this analysis in terms of the sensitivity of state errors to error sources provides considerable insight into the performance of the redundant system in the normal mode (i.e., in the absence of failures), as well as in any of the operational modes resulting from failures or from failure detection and identification (FDI) decisions which affect the sensor configuration. The design of redundant aided inertial navigation systems affords numerous opportunities to tradeoff system elements in an effort to satisfy performance objectives under various design constraints. The use of the linearized analysis described in this paper in combination with an analysis of FDI performance3 provides the quantitative results which make intelligent tradeoffs possible. The for- mulation of the analysis is sparing of computer resources and inexpensive to use once it has been implemented. The elements of the sensitivity matrices represent the sensitivity of system performance to each of the individual error sources or sensor failures which are modeled as deterministic constants. Using these sensitivity matrices, the statistics of the state errors (or their estimates) can be determined from the statistics of the error sources (or their estimates) at any time. The effects of error sources which are properly modeled as random processes can be evaluated by reformulating the analysis as a conventional covariance analysis4 or by com- puting their effects separately and adding them to the covariance of the state errors obtained from the sensitivity analysis. In the authors' experiences,5 the random errors which are characteristic of navigation quality inertial sensors seldom contribute significantly to overall system performance when all other error sources are considered. Navaid updates are formulated in terms of their effect on the statistics of the error sources rather than in terms of their effect on the sensitivities. This results in a computationally efficient evaluation of the extent to which navigation system performance can be improved, and the effects of system failures mitigated, through the use of navaids. The failure sensitivities, which are computed in the linearized analysis, establish the levels of failures which significantly degrade system performance. These levels represent design requirements for the FDI system. Once the FDI system is designed, the analysis of navigation system performance can be combined with an analysis of FDI per- formance to choose FDI thresholds which maximize the probability of success of the system.6 The remainder of the paper is divided into two major sections. The first section presents the analysis. The recursive equations used to propagate the sensitivity matrices along a nominal trajectory are developed, and the equations used to update the statistics of the state errors are derived. The modifications of these results to account for system failures are then discussed. The second section presents results for an aided redundant strapdown inertial navigation system consisting of five gyros and five accelerometers in a conical array. Star-sensor and ranging measurements are included to indicate the effects of navaid updates on system performance in normal and failure modes. |
