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Questions and Answers
What does the signal-to-noise ratio (SNR) quantify?
What does the signal-to-noise ratio (SNR) quantify?
Why is having a good SNR critical to obtaining reliable parameter estimates?
Why is having a good SNR critical to obtaining reliable parameter estimates?
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?
Which parameter estimates depend on the signal-to-noise ratio (SNR)?
Which parameter estimates depend on the signal-to-noise ratio (SNR)?
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What contributes to overfitting of a model?
What contributes to overfitting of a model?
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When does overfitting occur?
When does overfitting occur?
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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?
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Which parameter can be uniquely estimated out of 𝒃𝟏, 𝒃𝟐 and 𝒃𝟑?
Which parameter can be uniquely estimated out of 𝒃𝟏, 𝒃𝟐 and 𝒃𝟑?
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What does overfitting occur due to?
What does overfitting occur due to?
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What does having a good SNR enable for parameter estimation?
What does having a good SNR enable for parameter estimation?
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Parametric models are characterized by a large number of parameters.
Parametric models are characterized by a large number of parameters.
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Non-parametric models require a priori knowledge for estimation.
Non-parametric models require a priori knowledge for estimation.
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Convolution models are examples of non-parametric models.
Convolution models are examples of non-parametric models.
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Non-parametric models have a specific structure and order.
Non-parametric models have a specific structure and order.
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Parametric models can be estimated with minimal a priori knowledge.
Parametric models can be estimated with minimal a priori knowledge.
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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.
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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.
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The impulse response model is an example of a parametric model.
The impulse response model is an example of a parametric model.
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Non-parametric models are characterized by fewer parameters.
Non-parametric models are characterized by fewer parameters.
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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.
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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.
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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.
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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.
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Dynamic models have limited applicability compared to steady-state models.
Dynamic models have limited applicability compared to steady-state models.
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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.
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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.
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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.
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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).
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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.
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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.
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