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• Acknowledgments.Acronyms.List of algorithms.Introduction.PART I INTRODUCTORY MATERIAL.1 Linear systems theory.1.1 Matrix algebra and matrix calculus.1.1.1 Matrix algebra.1.1.2 The matrix inversion lemma.1.1.3 Matrix calculus.1.1.4 The history of matrices.1.2 Linear systems.1.3 Nonlinear systems.1.4 Discretization.1.5 Simulation.1.5.1 Rectangular integration.1.5.2 Trapezoidal integration.1.5.3 RungeKutta integration.1.6 Stability.1.6.1 Continuous-time systems.1.6.2 Discretetime systems.1.7 Controllability and observability.1.7.1 Controllability.1.7.2 Observability.1.7.3 Stabilizability and detectability.1.8 Summary.Problems.Probability theory.2.1 Probability.2.2 Random variables.2.3 Transformations of random variables.2.4 Multiple random variables.2.4.1 Statistical independence.2.4.2 Multivariate statistics.2.5 Stochastic Processes.2.6 White noise and colored noise.2.7 Simulating correlated noise.2.8 Summary.Problems.3 Least squares estimation.3.1 Estimation of a constant.3.2 Weighted least squares estimation.3.3 Recursive least squares estimation.3.3.1 Alternate estimator forms.3.3.2 Curve fitting.3.4 Wiener filtering.3.4.1 Parametric filter optimization.3.4.2 General filter optimization.3.4.3 Noncausal filter optimization.3.4.4 Causal filter optimization.3.4.5 Comparison.3.5 Summary.Problems.4 Propagation of states and covariances.4.1 Discretetime systems.4.2 Sampled-data systems.4.3 Continuous-time systems.4.4 Summary.Problems.PART II THE KALMAN FILTER.5 The discrete-time Kalman filter.5.1 Derivation of the discrete-time Kalman filter.5.2 Kalman filter properties.5.3 One-step Kalman filter equations.5.4 Alternate propagation of covariance.5.4.1 Multiple state systems.5.4.2 Scalar systems.5.5 Divergence issues.5.6 Summary.Problems.6 Alternate Kalman filter formulations.6.1 Sequential Kalman filtering.6.2 Information filtering.6.3 Square root filtering.6.3.1 Condition number.6.3.2 The square root time-update equation.6.3.3 Potter's square root measurement-update equation.6.3.4 Square root measurement update via triangularization.6.3.5 Algorithms for orthogonal transformations.6.4 U-D filtering.6.4.1 U-D filtering: The measurement-update equation.6.4.2 U-D filtering: The time-update equation.6.5 Summary.Problems.7 Kalman filter generalizations.7.1 Correlated process and measurement noise.7.2 Colored process and measurement noise.7.2.1 Colored process noise.7.2.2 Colored measurement noise: State augmentation.7.2.3 Colored measurement noise: Measurement differencing.7.3 Steady-state filtering.7.3.1 a-P filtering.7.3.2 a-P-y filtering.7.3.3 A Hamiltonian approach to steady-state filtering.7.4 Kalman filtering with fading memory.7.5 Constrained Kalman filtering.7.5.1 Model reduction.7.5.2 Perfect measurements.7.5.3 Projection approaches.7.5.4 A pdf truncation approach.7.6 Summary.Problems.8 The continuous-time Kalman filter.8.1 Discrete-time and continuous-time white noise.8.1.1 Process noise.8.1.2 Measurement noise.8.1.3 Discretized simulation of noisy continuous-time systems.8.2 Derivation of the continuous-time Kalman filter.8.3 Alternate solutions to the Riccati equation.8.3.1 The transition matrix approach.8.3.2 The Chandrasekhar algorithm.8.3.3 The square root filter.8.4 Generalizations of the continuous-time filter.8.4.1 Correlated process and measurement noise.8.4.2 Colored measurement noise8.5 The steady-state continuous-time Kalman filter8.5.1 The algebraic Riccati equation.8.5.2 The Wiener filter is a Kalman filter.8.5.3 Duality.8.6 Summary.Problems.9 Optimal smoothing.9.1 An alternate form for the Kalman filter.9.2 Fixed-point smoothing.9.2.1 Estimation improvement due to smoothing.9.2.2 Smoothing constant states.9.3 Fixed-lag smoothing.9.4 Fixed-interval smoothing.9.4.1 Forward-backward smoothing.9.4.2 RTS smoothing.9.5 Summary.Problems.10 Additional topics in Kalman filtering.10.1 Verifying Kalman filter performance.10.2 Multiple-model estimation.10.3 Reduced-order Kalman filtering.10.3.1 Anderson's approach to reduced-order filtering.10.3.2 The reduced-order Schmidt-Kalman filter.10.4 Robust Kalman filtering.10.5 Delayed measurements and synchronization errors.10.5.1 A statistical derivation of the Kalman filter.10.5.2 Kalman filtering with delayed measurements.10.6 Summary.Problems.PART III THE H, FILTER.11 The H, filter.11.1 Introduction.11.1.1 An alternate form for the Kalman filter.11.1.2 Kalman filter limitations.11.2 Constrained optimization.11.2.1 Static constrained optimization.11.2.2 Inequality constraints.11.2.3 Dynamic constrained optimization.11.3 A game theory approach to H, filtering.11.3.1 Stationarity with respect to xo and wk.11.3.2 Stationarity with respect to 2 and y.11.3.3 A comparison of the Kalman and H, filters.11.3.4 Steady-state H, filtering.11.3.5 The transfer function bound of the H, filter.11.4 The continuous-time H, filter.11.5 Transfer function approaches.11.6 Summary.Problems.12 Additional topics in H, filtering.12.1 Mixed KalmanIH, filtering.12.2 Robust Kalman/H, filtering.12.3 Constrained H, filtering.12.4 Summary.Problems.PART IV NONLINEAR FILTERS.13 Nonlinear Kalman filtering.13.1 The linearized Kalman filter.13.2 The extended Kalman filter.13.2.1 The continuous-time extended Kalman filter.13.2.2 The hybrid extended Kalman filter.13.2.3 The discrete-time extended Kalman filter.13.3 Higher-order approaches.13.3.1 The iterated extended Kalman filter.13.3.2 The second-order extended Kalman filter.13.3.3 Other approaches.13.4 Parameter estimation.13.5 Summary.Problems.14 The unscented Kalman filter.14.1 Means and covariances of nonlinear transformations.14.1.1 The mean of a nonlinear transformation.14.1.2 The covariance of a nonlinear transformation.14.2 Unscented transformations.14.2.1 Mean approximation.14.2.2 Covariance approximation.14.3 Unscented Kalman filtering.14.4 Other unscented transformations.14.4.1 General unscented transformations.14.4.2 The simplex unscented transformation.14.4.3 The spherical unscented transformation.14.5 Summary.Problems.15 The particle filter.15.1 Bayesian state estimation.15.2 Particle filtering.15.3 Implementation issues.15.3.1 Sample impoverishment.15.3.2 Particle filtering combined with other filters.15.4 Summary.Problems.Appendix A: Historical perspectives.Appendix B: Other books on Kalman filtering.Appendix C: State estimation and the meaning of life.References.Index.
• (source: Nielsen Book Data)

Presents a bottom-up approach that enables readers to master and apply the latest techniques in state estimation. This book offers the best mathematical approaches to estimating the state of a general system. The author presents state estimation theory clearly and rigorously, providing the right amount of advanced material, recent research results, and references to enable the reader to apply state estimation techniques confidently across a variety of fields in science and engineering. While there are other textbooks that treat state estimation, this one offers special features and a unique perspective and pedagogical approach that speed learning. Straightforward, bottom-up approach begins with basic concepts and then builds step by step to more advanced topics for a clear understanding of state estimation. Simple examples and problems that require only paper and pen to solve lead to an intuitive understanding of how theory works in practice. MATLAB[registered]-based source code that corresponds to examples in the book, available on the author's Web site, enables readers to recreate results and experiment with other simulation setups and parameters. Armed with a solid foundation in the basics, readers are presented with a careful treatment of advanced topics, including unscented filtering, high order nonlinear filtering, particle filtering, constrained state estimation, reduced order filtering, robust Kalman filtering, and mixed Kalman/H? filtering. Problems at the end of each chapter include both written exercises and computer exercises. Written exercises focus on improving the reader's understanding of theory and key concepts, whereas computer exercises help readers apply theory to problems similar to ones they are likely to encounter in industry. A solutions manual is available for instructors. With its expert blend of theory and practice, coupled with its presentation of recent research results, "Optimal State Estimation" is strongly recommended for undergraduate and graduate-level courses in optimal control and state estimation theory. It also serves as a reference for engineers and science professionals across a wide array of industries. A solutions manual is available upon request from the Wiley editorial board.
(source: Nielsen Book Data)

• Chapter 1. The Science of Biogeography 1 1.1. Introduction 1 1.2. Island biogeography 3 1.3. Influence factors for biogeography 6
• Chapter 2. Biogeography and Biological Optimization 11 2.1. A mathematical model of biogeography 11 2.2. Biogeography as an optimization process 16 2.3. Biological optimization 19 2.3.1. Genetic algorithms 19 2.3.2. Evolution strategies 20 2.3.3. Particle swarm optimization 21 2.3.4. Artificial bee colony algorithm 22 2.4. Conclusion 23
• Chapter 3. A Basic BBO Algorithm 25 3.1. BBO definitions and algorithm 25 3.1.1. Migration 26 3.1.2. Mutation 27 3.1.3. BBO implementation 27 3.2. Differences between BBO and other optimization algorithms 35 3.2.1. BBO and genetic algorithms 35 3.2.2. BBO and other algorithms 36 3.3. Simulations 37 3.4. Conclusion 44
• Chapter 4. BBO Extensions 45 4.1. Migration curves 45 4.2. Blended migration 49 4.3. Other approaches to BBO 51 4.4. Applications 56 4.5. Conclusion 59
• Chapter 5. BBO as a Markov Process 61 5.1. Markov definitions and notations 61 5.2. Markov model of BBO 72 5.3. BBO convergence 79 5.4. Markov models of BBO extensions 90 5.5. Conclusions 99
• Chapter 6. Dynamic System Models of BBO 103 6.1. Basic notation 103 6.2. Dynamic system models of BBO 105 6.3. Applications to benchmark problems 119 6.4. Conclusions 122
• Chapter 7. Statistical Mechanics Approximations of BBO 123 7.1. Preliminary foundation 123 7.2. Statistical mechanics model of BBO 128 7.2.1. Migration 128 7.2.2. Mutation 134 7.3. Further discussion 141 7.3.1. Finite population effects 141 7.3.2. Separable fitness functions 142 7.4. Conclusions 143
• Chapter 8. BBO for Combinatorial Optimization 145 8.1. Traveling salesman problem 147 8.2. BBO for the TSP 148 8.2.1. Population initialization 148 8.2.2. Migration in the TSP 150 8.2.3. Mutation in the TSP 157 8.2.4. Implementation framework 159 8.3. Graph coloring 163 8.4. Knapsack problem 165 8.5. Conclusion 167
• Chapter 9. Constrained BBO 169 9.1. Constrained optimization 170 9.2. Constraint-handling methods 172 9.2.1. Static penalty methods 172 9.2.2. Superiority of feasible points 173 9.2.3. The eclectic evolutionary algorithm 174 9.2.4. Dynamic penalty methods 174 9.2.5. Adaptive penalty methods 176 9.2.6. The niched-penalty approach 177 9.2.7. Stochastic ranking 178 9.2.8. -level comparisons 178 9.3. BBO for constrained optimization 179 9.4. Conclusion 185
• Chapter 10. BBO in Noisy Environments 187 10.1. Noisy fitness functions 188 10.2. Influence of noise on BBO 190 10.3. BBO with re-sampling 193 10.4. The Kalman BBO 196 10.5. Experimental results 199 10.6. Conclusion 201
• Chapter 11. Multi-objective BBO 203 11.1. Multi-objective optimization problems 204 11.2. Multi-objective BBO 211 11.2.1. Vector evaluated BBO 211 11.2.2. Non-dominated sorting BBO 213 11.2.3. Niched Pareto BBO 216 11.2.4. Strength Pareto BBO 218 11.3. Real-world applications 223 11.3.1. Warehouse scheduling model 223 11.3.2. Optimization of warehouse scheduling 229 11.4. Conclusion 231
• Chapter 12. Hybrid BBO Algorithms 233 12.1. Opposition-based BBO 234 12.1.1. Opposition definitions and concepts 234 12.1.2. Oppositional BBO 236 12.1.3. Experimental results 238 12.2. BBO with local search 240 12.2.1. Local search methods 240 12.2.2. Simulation results 245 12.3. BBO with other EAs 247 12.3.1. Iteration-level hybridization 247 12.3.2. Algorithm-level hybridization 250 12.3.3. Experimental results 254 12.4. Conclusion 256 Appendices 259 Appendix A. Unconstrained Benchmark Functions 261 Appendix B. Constrained Benchmark Functions 265 Appendix C. Multi-objective Benchmark Functions 289 Bibliography 309 Index 325.
• (source: Nielsen Book Data)

Evolutionary computation algorithms are employed to minimize functions with large number of variables. Biogeography-based optimization (BBO) is an optimization algorithm that is based on the science of biogeography, which researches the migration patterns of species. These migration paradigms provide the main logic behind BBO. Due to the cross-disciplinary nature of the optimization problems, there is a need to develop multiple approaches to tackle them and to study the theoretical reasoning behind their performance. This book explains the mathematical model of BBO algorithm and its variants created to cope with continuous domain problems (with and without constraints) and combinatorial problems.
(source: Nielsen Book Data)