Podcast
Questions and Answers
What does the signal-to-noise ratio (SNR) quantify?
What does the signal-to-noise ratio (SNR) quantify?
- The true response of the system
- The overfitting of the model
- The output y[k] and the input u[k] of a system
- The relative contributions of deterministic excitation and random variations (correct)
Why is having a good SNR critical to obtaining reliable parameter estimates?
Why is having a good SNR critical to obtaining reliable parameter estimates?
- To strengthen the contribution of the input u[k]
- To minimize the overfitting of the model
- To minimize the impact of noise on parameter estimation (correct)
- To explain variations in the output y[k]
What is the relationship between the output y[k] and the input u[k] of a system?
What is the relationship between the output y[k] and the input u[k] of a system?
- $y_k = b1 u_k + b0$ (correct)
- $y_k = b1 u_k - b0$
- $y_k = b1 - b0 u_k$
- $y_k = b1 + b0 u_k$
Which parameter estimates depend on the signal-to-noise ratio (SNR)?
Which parameter estimates depend on the signal-to-noise ratio (SNR)?
What contributes to overfitting of a model?
What contributes to overfitting of a model?
When does overfitting occur?
When does overfitting occur?
What happens if a significant portion of the variations in the measurement is due to noise?
What happens if a significant portion of the variations in the measurement is due to noise?
Which parameter can be uniquely estimated out of 𝒃𝟏, 𝒃𝟐 and 𝒃𝟑?
Which parameter can be uniquely estimated out of 𝒃𝟏, 𝒃𝟐 and 𝒃𝟑?
What does overfitting occur due to?
What does overfitting occur due to?
What does having a good SNR enable for parameter estimation?
What does having a good SNR enable for parameter estimation?
Parametric models are characterized by a large number of parameters.
Parametric models are characterized by a large number of parameters.
Non-parametric models require a priori knowledge for estimation.
Non-parametric models require a priori knowledge for estimation.
Convolution models are examples of non-parametric models.
Convolution models are examples of non-parametric models.
Non-parametric models have a specific structure and order.
Non-parametric models have a specific structure and order.
Parametric models can be estimated with minimal a priori knowledge.
Parametric models can be estimated with minimal a priori knowledge.
The distinction between non-parametric and parametric models is based on the number of unknowns.
The distinction between non-parametric and parametric models is based on the number of unknowns.
An impulse response model assumes no assumption about the 'structure' of the model.
An impulse response model assumes no assumption about the 'structure' of the model.
The impulse response model is an example of a parametric model.
The impulse response model is an example of a parametric model.
Non-parametric models are characterized by fewer parameters.
Non-parametric models are characterized by fewer parameters.
All discrete-time linear time-invariant systems can be described by the difference equation.
All discrete-time linear time-invariant systems can be described by the difference equation.
The model 𝑦[𝑘, ො 𝜃] = 𝜃1 𝜃2 𝑢[𝑘] is globally identifiable at all points in the space.
The model 𝑦[𝑘, ො 𝜃] = 𝜃1 𝜃2 𝑢[𝑘] is globally identifiable at all points in the space.
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.
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.
The consistency of an estimator is also known as the asymptotic property of the estimator.
The consistency of an estimator is also known as the asymptotic property of the estimator.
Dynamic models have limited applicability compared to steady-state models.
Dynamic models have limited applicability compared to steady-state models.
Model identifiability depends on the experimental conditions and the existence of a unique mapping between the model and the parameters being estimated.
Model identifiability depends on the experimental conditions and the existence of a unique mapping between the model and the parameters being estimated.
Non-parametric models require a large amount of a priori knowledge for estimation.
Non-parametric models require a large amount of a priori knowledge for estimation.
Re-parametrization of a model from a higher-dimensional to a lower-dimensional parameter space can worsen identifiability for that model.
Re-parametrization of a model from a higher-dimensional to a lower-dimensional parameter space can worsen identifiability for that model.
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).
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).
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.
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.
With a sinusoid of single frequency, all three explanatory variables 𝑢[𝑘 − 1], 𝑢[𝑘 − 2], and 𝑢[𝑘 − 3] are unique.
With a sinusoid of single frequency, all three explanatory variables 𝑢[𝑘 − 1], 𝑢[𝑘 − 2], and 𝑢[𝑘 − 3] are unique.
Flashcards are hidden until you start studying
