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| Preface | |
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| Random Signals Background | |
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| Probability and Random Variables: A Review | |
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| Random Signals | |
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| Intuitive Notion of Probability | |
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| Axiomatic Probability | |
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| Random Variables | |
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| Joint and Conditional Probability, Bayes Rule and Independence | |
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| Continuous Random Variables and Probability Density Function | |
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| Expectation, Averages, and Characteristic Function | |
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| Normal or Gaussian Random Variables | |
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| Impulsive Probability Density Functions | |
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| Joint Continuous Random Variables | |
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| Correlation, Covariance, and Orthogonality | |
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| Sum of Independent Random Variables and Tendency Toward Normal Distribution | |
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| Transformation of Random Variables | |
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| Multivariate Normal Density Function | |
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| Linear Transformation and General Properties of Normal Random Variables | |
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| Limits, Convergence, and Unbiased Estimators | |
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| A Note on Statistical Estimators | |
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| Mathematical Description of Random Signals | |
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| Concept of a Random Process | |
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| Probabilistic Description of a Random Process | |
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| Gaussian Random Process | |
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| Stationarity, Ergodicity, and Classification of Processes | |
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| Autocorrelation Function | |
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| Crosscorrelation Function | |
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| Power Spectral Density Function | |
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| White Noise | |
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| Gauss-Markov Processes | |
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| Narrowband Gaussian Process | |
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| Wiener or Brownian-Motion Process | |
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| Pseudorandom Signals | |
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| Determination of Autocorrelation and Spectral Density Functions from Experimental Data | |
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| Sampling Theorem | |
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| Linear Systems Response, State-Space Modeling, and Monte Carlo Simulation | |
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| Introduction: The Analysis Problem | |
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| Stationary (Steady-State) Analysis | |
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| Integral Tables for Computing Mean-Square Value | |
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| Pure White Noise and Bandlimited Systems | |
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| Noise Equivalent Bandwidth | |
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| Shaping Filter | |
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| Nonstationary (Transient) Analysis | |
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| Note on Units and Unity White Noise | |
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| Vector Description of Random Processes | |
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| Monte Carlo Simulation of Discrete-Time Processes | |
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| Summary | |
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| Kalman Filtering and Applications | |
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| Discrete Kalman Filter Basics | |
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| A Simple Recursive Example | |
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| The Discrete Kalman Filter | |
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| Simple Kalman Filter Examples and Augmenting the State Vector | |
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| Marine Navigation Application with Multiple-Inputs/Multiple-Outputs | |
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| Gaussian Monte Carlo Examples | |
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| Prediction | |
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| The Conditional Density Viewpoint | |
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| Re-cap and Special Note On Updating the Error Covariance Matrix | |
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| Intermediate Topics on Kalman Filtering | |
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| Alternative Form of the Discrete Kalman Filter - the Information Filter | |
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| Processing the Measurements One at a Time | |
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| Orthogonality Principle | |
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| Divergence Problems | |
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| Suboptimal Error Analysis | |
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| Reduced-Order Suboptimality | |
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| Square-Root Filtering and U-D Factorization | |
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| Kalman Filter Stability | |
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| Relationship to Deterministic Least Squares Estimation | |
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| Deterministic Inputs | |
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| Smoothing and Further Intermediate Topics | |
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| Classification of smoothing Problems | |
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| Discrete Fixed-Interval Smoothing | |
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| Discrete Fixed-Point Smoothing | |
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| Discrete Fixed-Lag Smoothing | |
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| Adaptive Kalman Filter (Multiple Model Adaptive Estimator) | |
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| Correlated Process and Measurement Noise for the Discrete Filter-Delayed-State Filter Algorithm | |
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| Decentralized Kalman Filtering | |
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| Difficulty with Hard-Bandlimited Processes | |
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| The Recursive Bayesian Filter | |
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| Linearization, Nonlinear Filtering, and Sampling Bayesian Filters | |
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| Linearization | |
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| The Extended Kalman Filter | |
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| "Beyond the Kalman Filter" | |
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| The Ensemble Kalman Filter | |
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| The Unscented Kalman Filter | |
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| The Particle Filter | |
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| The "Go-Free" Concept, Complementary Filter, and Aided Inertial Examples | |
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| Introduction: Why Go Free of Anything? | |
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| Simple GPS Clock Bias Model | |
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| Euler/Goad Experiment | |
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| Reprise: GPS Clock-Bias Model Revisited | |
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| The Complementary Filter | |
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| Simple Complementary Filter: Intuitive Method | |
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| Kalman Filter Approach-Error Model | |
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| Kalman Filter Approach-Total Model | |
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| Go-Free Monte Carlo Simulation | |
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| INS Error Models | |
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| Aiding with Positioning Measurements-INS/DME Measurement Model | |
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| Other Integration Considerations and Concluding Remarks | |
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| Kalman Filter Applications to the GPS and Other Navigation Systems | |
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| Position Determination with GPS | |
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| The Observables | |
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| Basic Position and Time Process Models | |
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| Modeling of Different Carrier Phase Measurements and Ranging Errors | |
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| GPS-Aided Inertial Error Models | |
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| Communication Link Ranging and Timing | |
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| Simultaneous Localization and Mapping (SLAM) | |
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| Closing Remarks | |
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| Laplace and Fourier Transforms | |
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| The Continuous Kalman Filter | |
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| Index | |