how to generate barcode using c#.net OVERVIEW OF PART I: THEORY in Software

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12 OVERVIEW OF PART I: THEORY
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however, the user of the vehicle is interested in knowing the vehicle state (ie, position and velocity) in the Earth reference frame The vehicle frame is attached to and rotates with the vehicle The Earth frame is attached to and rotates with the Earth Because the vehicle is free to translate and rotate with respect to the Earth, the vehicle and Earth frames can arbitrarily translate and rotate with respect to each other Therefore, the navigation system must maintain accurate estimates of the quantities necessary to allow transformation of variables between these reference frames De nition of various important reference frames and transformations between rotating reference frames is addressed in 2
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Deterministic Systems
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The kinematics of the vehicle naturally evolve in continuous-time Therefore, the analysis and design process typically begins with the development of a continuous-time kinematic model for the vehicle Various continuoustime model formats exist The majority of this text will focus on the state space model format Since navigation systems and optimal estimators are conveniently implemented in discrete-time on a computer, we will require discrete-time equivalent state space models of continuous-time systems To accommodate modeling of sensor alignment and calibration parameters, it may be desirable to augment the vehicle state variables with additional alignment and calibration variables In the simple example in Section 11, p and v are the vehicle model states and b is a sensor calibration parameter If we are able to estimate this parameter accurately, then the estimated value can be removed from the sensed quantity to produce a more accurate estimate of the acceleration a: a(t) = a(t) + b(t), which could be used in the mechanization equations instead of the raw sensor output a 3 will review various important concepts related to continuous and discrete-time dynamic systems Since all engineering students take ordinary di erential equations, physics, and some dynamics courses, the underlying concepts should be familiar; however, not all such courses are formulated within the state variable framework Therefore, the two main goals of that chapter are to review state space analysis and state estimation
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Stochastic Processes
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By their senior year at college, most students are fairly comfortable with modeling continuous-time deterministic systems The idea that we integrate acceleration to nd velocity and integrate velocity to nd position is now rather innate However, for many readers derivation and analysis of stochastic models remains somewhat esoteric Even in the simple example in Section 11, the model has (at least) three stochastic variables: 1 , b and b In fact, we will see that any quantities
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CHAPTER 1 INTRODUCTION
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computed from these variables will also be stochastic variables Therefore, accurate stochastic system modeling and analysis is critical to navigation system design Accurate characterization of model and variable properties and analysis of their a ect on the system de nes the analysis of the overall system performance When purchasing or designing sensors, the designer naturally searches for the best sensors that t within the project budget However, any use of an adjective such as best requires further consideration of its de nition in this context For example, for the acceleration sensor, the best sensor would have no noise (ie, 1 (t) = 0) and no bias (ie, b(t) = 0); however, this is typically not possible under application conditions Instead, thermal uctuations and component variation will cause both quantities to be nonzero To surpass the competition, each sensor manufacturer has the incentive to remove, to the extent possible, all the predictable components of sensor error (eg, nonlinearities, temperature dependent characteristics) Therefore, the remaining sensor error is non-deterministic and will be accommodated within the navigation system design by stochastic process modeling and state estimation Knowing this, the sensor manufacturer designs the sensor so that the characteristics that de ne the random nature of the sensor are time-invariant Also, the sensor manufacturer will typically supply the parameters that quantify the stochastic nature of the sensor A brief discussion of sensor speci cations is presented in Section 492 4 discusses the various topics from the theory of random variables and stochastic processes that must be understood for the design and analysis of navigation systems This discussion includes de nitions of basic stochastic process concepts, discussion of dynamic systems with stochastic inputs, de nition of various stochastic process models that regularly appear in navigation systems, and discussion of the time variation of the mean and variance of the state of a linear stochastic state space system 4 concludes with a discussion of state estimation as it relates to linear stochastic state space systems and the characterization of their state estimation accuracy through covariance analysis The example of Section 111 is considered again in Section 493-494 using the quantitative methods of 4
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