## Dynamic Systems Models: New Methods of Parameter and State EstimationThis monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamics or biological sequence analysis. The technical material is illustrated by the use of worked examples and methods for training the algorithms are included. Dynamic Systems Models provides researchers in aerospatial engineering, bioinformatics and financial mathematics (as well as computer scientists interested in any of these fields) with a reliable and effective numerical method for nonlinear estimation and solving boundary problems when carrying out control design. It will also be of interest to academic researchers studying inverse problems and their solution. |

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### Contents

1 | |

2 Basis of the Method of Polynomial Approximation | 19 |

3 Polynomial Approximation and Optimization of Control | 29 |

4 Polynomial Approximation Technique Applied to Inverse VectorFunction | 45 |

5 Identification of Parameters of Nonlinear Dynamic Systems Smoothing Filtration Forecasting of State Vectors | 71 |

6 Estimating Status Vectors from Sight Angles | 109 |

7 Estimating the Parameters of Stochastic Models | 125 |

8 Designing Motion Control to a Target Point of Phase Space | 169 |

The Algorithm for Identifying the Parameters of an Aircraft | 187 |

### Other editions - View all

Dynamic Systems Models: New Methods of Parameter and State Estimation Josif A. Boguslavskiy No preview available - 2014 |

Dynamic Systems Models: New Methods of Parameter and State Estimation Josif A. Boguslavskiy No preview available - 2015 |

Dynamic Systems Models: New Methods of Parameter and State Estimation Josif A Boguslavskiy No preview available - 2018 |

### Common terms and phrases

accuracy aerodynamic aircraft algebraic equations algorithm-estimator angles approximation algorithm approximation errors assume Bayesian Boguslavskiy boundary value problem calculated Chap coefficients components of vector computational process conditional expectation conditional expectation vector construct coordinates corresponding covariance matrix cube defined determined differential equations dimensionality q distribution dynamic system equal error covariance matrix estimation error covariance estimation vector follows formula function given implemented initial conditions instant integer inverse J(YN Kalman filter linear combinations matrix Q maximum likelihood measure Monte Carlo method MPA algorithm multipolynomial numerical integration optimal parallelepiped parameter vector points polynomial approximation technique priori data priori domain priori region priori statistical random variables random vector recurrent algorithm relative errors relative estimation errors root vector root-mean-square sense RSFF algorithm second statistical moments solution solving status vector stochastic theorem uniformly unknown parameters vector components vector V(d vector YN vector-function zero