The exhaustive list of topics in System (Process) Identification Problems in which we provide Help with Homework Assignment and Help with Project is as follows:
- System Identification
- Models of Discrete-Time LTI Systems - Convolution equation.
- Difference equations
- Transfer functions
- State-space models
- Discretization
- Sampling and Hold operations
- Sampling theorem.
- Non-parametric models - impulse response, step response and frequency response models.
- Disturbance models - random processes, representation of stationary processes, white-noise process, auto-covariance function (ACF), ARMA models.
- Parametric model structures - ARX, ARMAX, OE, Bj and PEM - structures.
- Linear Regression - Least Squares estimates
- Statistical properties of LS Estimates.
- Weighted Least Squares, Recursive Least Squares, Maximum Likelihood Estimation.
- Estimation of non-parametric models - impulse / step response coefficients, frequency response models.
- Estimation of parametric models - notions of prediction and simulation, predictors for parametric models, prediction-error methods, Instrumental Variable method.
- Model Structure Selection and Diagnostics - estimation of delay and order, residual checks, properties of parameter estimates, model validation.
- Experimental Design - input design for identification, notion of persistent excitation, identifiability.
- Subspace Identification - classical and innovations forms, free and structured parametrizations.
- Least squares estimation, extended observability matrix, order determination through singular-value decomposition.
- Case studies and topics for further study.