Nonlinear Regression Models
The linear regression model in Eq. (3.14) can be generalized to a nonlinear model: where fis a (n × 1)-vector of smooth functions of m variables.
LS estimation of prequires the minimization of the following objective function: The function \\({\\mathcal {S}}({{\\boldsymbol {p}}})\\) can be minimized with any of the methods discussed in Sect. 3.1.
The o.
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Prediction Step
The state vector and its covariance matrix are propagated to the next instance using the system equation Eq. (3.26) and linear error propagation:
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State Space Models
A dynamic or state space model describes the state of an object in space or time, such as a rocket or a charged particle [9].
The state usually changes continuously, but is assumed to be of interest only at discrete instances in the present context.
These instances are labeled with indices from 0, the initial state, to n, the final state.
The state.
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Update Step
The updated state vector is the weighted mean of the predicted state vector and the observation mk.
There are two equivalent ways to compute the update.
The first one uses the gain matrix Kk: The second one is a multivariate weighted mean: The update step has an associated chi-square statistic χk2, which can be computed from the predicted residual .
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What are the statistical methods used in statistics?
Such statistical methods include, from the simplest to the most sophisticated:
- Doubling or tripling of the absolute number of cases over a given time period
This method, although simple, is crude because it does not take into consideration the number of cases on which the increase is calculated.
,
What is numerical methods & engineering statistics for Chemical Engineers?
This course provides an introduction to numerical methods andengineering statistics for chemical engineers.
Students learn to usecomputer models and statistics to understand engineering systems.
Thefocus of numerical methods is translating engineering problems intonalgorithms and implementing them in a spreadsheet or programminglanguage.
,
What is the difference between numerical methods and statistics?
Numerical methods, as said above, are techniques to approximate Mathematical procedures.
On the other hand, statistics is the study and manipulation of data, including:
- ways to gather
- review
- analyze
- draw conclusions from the given data
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Where can I find a course on numerical statistics?
View the course online:
- whitead
github.io/
numerical_stats/ Course Description This course provides an introduction to
numerical methods andengineering
statistics for chemical engineers.
Students learn to usecomputer models and
statistics to understand engineering systems.
