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Preface | p. v |
Random Signals Background | p. 1 |
Probability and Random Variables: A Review | p. 3 |
Random Signals | p. 3 |
Intuitive Notion of Probability | p. 4 |
Axiomatic Probability | p. 5 |
Random Variables | p. 8 |
Joint and Conditional Probability, Bayes Rule and Independence | p. 9 |
Continuous Random Variables and Probability Density Function | p. 13 |
Expectation, Averages, and Characteristic Function | p. 15 |
Normal or Gaussian Random Variables | p. 18 |
Impulsive Probability Density Functions | p. 22 |
Joint Continuous Random Variables | p. 23 |
Correlation, Covariance, and Orthogonality | p. 26 |
Sum of Independent Random Variables and Tendency Toward Normal Distribution | p. 28 |
Transformation of Random Variables | p. 32 |
Multivariate Normal Density Function | p. 37 |
Linear Transformation and General Properties of Normal Random Variables | p. 40 |
Limits, Convergence, and Unbiased Estimators | p. 43 |
A Note on Statistical Estimators | p. 46 |
Mathematical Description of Random Signals | p. 57 |
Concept of a Random Process | p. 57 |
Probabilistic Description of a Random Process | p. 60 |
Gaussian Random Process | p. 62 |
Stationarity, Ergodicity, and Classification of Processes | p. 63 |
Autocorrelation Function | p. 65 |
Crosscorrelation Function | p. 68 |
Power Spectral Density Function | p. 70 |
White Noise | p. 75 |
Gauss-Markov Processes | p. 77 |
Narrowband Gaussian Process | p. 81 |
Wiener or Brownian-Motion Process | p. 83 |
Pseudorandom Signals | p. 86 |
Determination of Autocorrelation and Spectral Density Functions from Experimental Data | p. 90 |
Sampling Theorem | p. 95 |
Linear Systems Response, State-Space Modeling, and Monte Carlo Simulation | p. 105 |
Introduction: The Analysis Problem | p. 105 |
Stationary (Steady-State) Analysis | p. 106 |
Integral Tables for Computing Mean-Square Value | p. 109 |
Pure White Noise and Bandlimited Systems | p. 110 |
Noise Equivalent Bandwidth | p. 111 |
Shaping Filter | p. 113 |
Nonstationary (Transient) Analysis | p. 114 |
Note on Units and Unity White Noise | p. 118 |
Vector Description of Random Processes | p. 121 |
Monte Carlo Simulation of Discrete-Time Processes | p. 128 |
Summary | p. 130 |
Kalman Filtering and Applications | p. 139 |
Discrete Kalman Filter Basics | p. 141 |
A Simple Recursive Example | p. 141 |
The Discrete Kalman Filter | p. 143 |
Simple Kalman Filter Examples and Augmenting the State Vector | p. 148 |
Marine Navigation Application with Multiple-Inputs/Multiple-Outputs | p. 151 |
Gaussian Monte Carlo Examples | p. 154 |
Prediction | p. 159 |
The Conditional Density Viewpoint | p. 162 |
Re-cap and Special Note On Updating the Error Covariance Matrix | p. 165 |
Intermediate Topics on Kalman Filtering | p. 173 |
Alternative Form of the Discrete Kalman Filter - the Information Filter | p. 173 |
Processing the Measurements One at a Time | p. 176 |
Orthogonality Principle | p. 178 |
Divergence Problems | p. 181 |
Suboptimal Error Analysis | p. 184 |
Reduced-Order Suboptimality | p. 188 |
Square-Root Filtering and U-D Factorization | p. 193 |
Kalman Filter Stability | p. 197 |
Relationship to Deterministic Least Squares Estimation | p. 198 |
Deterministic Inputs | p. 201 |
Smoothing and Further Intermediate Topics | p. 207 |
Classification of smoothing Problems | p. 207 |
Discrete Fixed-Interval Smoothing | p. 208 |
Discrete Fixed-Point Smoothing | p. 212 |
Discrete Fixed-Lag Smoothing | p. 213 |
Adaptive Kalman Filter (Multiple Model Adaptive Estimator) | p. 216 |
Correlated Process and Measurement Noise for the Discrete Filter-Delayed-State Filter Algorithm | p. 226 |
Decentralized Kalman Filtering | p. 231 |
Difficulty with Hard-Bandlimited Processes | p. 234 |
The Recursive Bayesian Filter | p. 237 |
Linearization, Nonlinear Filtering, and Sampling Bayesian Filters | p. 249 |
Linearization | p. 249 |
The Extended Kalman Filter | p. 257 |
"Beyond the Kalman Filter" | p. 260 |
The Ensemble Kalman Filter | p. 262 |
The Unscented Kalman Filter | p. 265 |
The Particle Filter | p. 269 |
The "Go-Free" Concept, Complementary Filter, and Aided Inertial Examples | p. 284 |
Introduction: Why Go Free of Anything? | p. 284 |
Simple GPS Clock Bias Model | p. 285 |
Euler/Goad Experiment | p. 287 |
Reprise: GPS Clock-Bias Model Revisited | p. 289 |
The Complementary Filter | p. 290 |
Simple Complementary Filter: Intuitive Method | p. 292 |
Kalman Filter Approach-Error Model | p. 294 |
Kalman Filter Approach-Total Model | p. 296 |
Go-Free Monte Carlo Simulation | p. 298 |
INS Error Models | p. 303 |
Aiding with Positioning Measurements-INS/DME Measurement Model | p. 307 |
Other Integration Considerations and Concluding Remarks | p. 309 |
Kalman Filter Applications to the GPS and Other Navigation Systems | p. 318 |
Position Determination with GPS | p. 318 |
The Observables | p. 321 |
Basic Position and Time Process Models | p. 324 |
Modeling of Different Carrier Phase Measurements and Ranging Errors | p. 330 |
GPS-Aided Inertial Error Models | p. 339 |
Communication Link Ranging and Timing | p. 345 |
Simultaneous Localization and Mapping (SLAM) | p. 348 |
Closing Remarks | p. 352 |
Laplace and Fourier Transforms | p. 365 |
The Continuous Kalman Filter | p. 371 |
Index | p. 379 |
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