By Farrell, Jay
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Extra resources for Aided Navigation
INTRODUCTION 12 • What are properties of the optimal estimator? • To what form of model does the optimal estimator apply? • What model structural properties are required for an optimal estimator to exist? • How can the navigation problem be manipulated into a suitable form? • How is the performance of the estimator analyzed? • How can the performance analysis methods be used to analyze system design tradeoﬀs? 1 and previous discussion of this section motivates discussion of several topics critical to the design and analysis of aided navigation systems.
3 Stochastic Processes By their senior year at college, most students are fairly comfortable with modeling continuous-time deterministic systems. The idea that we integrate acceleration to ﬁnd velocity and integrate velocity to ﬁnd position is now rather innate. However, for many readers derivation and analysis of stochastic models remains somewhat esoteric. 1, the model has (at least) three stochastic variables: ω1 , b and ωb . In fact, we will see that any quantities 14 CHAPTER 1. INTRODUCTION computed from these variables will also be stochastic variables.
A linearized model is developed for the navigation error state vector. The goal for this step is to obtain a set of linear diﬀerential equations with inputs that are deﬁned by stochastic processes with known statistics. This model is the basis for the subsequent two steps. 5. A state estimator is designed to stabilize the error state system. 1. METHOD OVERVIEW 11 6. The system performance is analyzed. The design objective is to provide an optimal estimate of x for the given set of sensors. Additionally, the designer is often interested in performing quantitative analysis to answer questions such as: • What values of f1 and f2 are necessary to achieve a speciﬁed performance?
Aided Navigation by Farrell, Jay