30 Questions
What does the signal-to-noise ratio (SNR) quantify?
The relative contributions of deterministic excitation and random variations
Why is having a good SNR critical to obtaining reliable parameter estimates?
To minimize the impact of noise on parameter estimation
What is the relationship between the output y[k] and the input u[k] of a system?
$y_k = b1 u_k + b0$
Which parameter estimates depend on the signal-to-noise ratio (SNR)?
$b1$ and $b0$
What contributes to overfitting of a model?
Over-specifying the complexity of the deterministic portion
When does overfitting occur?
When the model is trained to capture the 'local' features of the data
What happens if a significant portion of the variations in the measurement is due to noise?
$u[k]$ weakens in its contribution to parameter estimation
Which parameter can be uniquely estimated out of 𝒃𝟏, 𝒃𝟐 and 𝒃𝟑?
$b1$ and $b0$
What does overfitting occur due to?
'Local' features of the data
What does having a good SNR enable for parameter estimation?
Minimizes noise in measurement
Parametric models are characterized by a large number of parameters.
False
Non-parametric models require a priori knowledge for estimation.
False
Convolution models are examples of non-parametric models.
True
Non-parametric models have a specific structure and order.
False
Parametric models can be estimated with minimal a priori knowledge.
False
The distinction between non-parametric and parametric models is based on the number of unknowns.
False
An impulse response model assumes no assumption about the 'structure' of the model.
True
The impulse response model is an example of a parametric model.
False
Non-parametric models are characterized by fewer parameters.
False
All discrete-time linear time-invariant systems can be described by the difference equation.
True
The model 𝑦[𝑘, ො 𝜃] = 𝜃1 𝜃2 𝑢[𝑘] is globally identifiable at all points in the space.
False
If the model is re-parametrized in terms of a single parameter 𝛽 = 𝜃1 𝜃2, then the model becomes identifiable at all points in the space.
True
The consistency of an estimator is also known as the asymptotic property of the estimator.
True
Dynamic models have limited applicability compared to steady-state models.
False
Model identifiability depends on the experimental conditions and the existence of a unique mapping between the model and the parameters being estimated.
True
Non-parametric models require a large amount of a priori knowledge for estimation.
False
Re-parametrization of a model from a higher-dimensional to a lower-dimensional parameter space can worsen identifiability for that model.
False
The sinusoidal input 𝑢[𝑘] = sin(2𝜋(0.1)𝑘) is applied to the system, resulting in the output 𝑦[𝑘] = 𝑏1 sin(𝜔0 𝑘 − 𝜑) + 𝑏2 sin(𝜔0 𝑘 − 2𝜑) + 𝑏3 sin(𝜔0 𝑘 − 3𝜑).
True
It is possible to uniquely recover 𝑏1, 𝑏2, and 𝑏3 from 𝑏ሖ1 and 𝑏ሖ3 when a sinusoid of single frequency is applied to the system.
False
With a sinusoid of single frequency, all three explanatory variables 𝑢[𝑘 − 1], 𝑢[𝑘 − 2], and 𝑢[𝑘 − 3] are unique.
False
Explore the methods for estimating continuous-time models from discrete-time data, and understand the categorization of models into static and dynamic models. Learn about the differences between static models, which relate instantaneous quantities, and dynamic models, which account for delayed inputs.
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