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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