Safety critical estimation applications require quantification of integrity risk, which is the probability of the state estimate error exceeding predefined bounds of acceptability. Integrity risk can only be evaluated when the state estimate error probability density function is precisely known, necessitating stochastic models that exactly describe measurement noise and disturbance inputs. Uncertainty in these models directly results in inaccurate assessments of integrity risk. This dissertation develops the first implementable methods to upper bound integrity risk when the autocorrelation functions of stochastic inputs reside between upper and lower bounding functions.
The first part of this work considers real-valued estimation applications that use the Kalman filter or batch weighted least squares estimator. Explicit relations are developed between the estimate error variance and autocorrelation functions using a new generalized covariance matrix derived in this dissertation. From these expressions, two methods are provided to upper bound integrity risk. The first method enables fast computation of a conservative bound, and the second method produces the minimum upper bound via semi-definite optimization.
Mixed real/integer estimation applications utilizing integer bootstrapping are the focus of the second part of this work. The integrity risk bound is formally defined as the global solution to a non-convex optimization problem over a polytope. Determination of the polytopic region is difficult, and two bounding approaches are initially developed for a circumscribing hyper-rectangular feasible region. Using an innovative method to define the polytope together with linear programming, a third method is derived to upper bound integrity risk over the true polytopic feasible region.
|School:||Illinois Institute of Technology|
|School Location:||United States -- Illinois|
|Source:||DAI-B 76/01(E), Dissertation Abstracts International|
|Subjects:||Aerospace engineering, Mechanical engineering|
|Keywords:||Colored Noise, Estimation Theory, Kalman Filter, Mixed integer Estimation, Stochastic Systems, Uncertain Systems|
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