Inertial sensor analysis tools.
The analysis module provides classes and methods to:
- calculate Allan deviation (the standard method of characterizing random error in inertial sensors)
- fit parametric models to Allan deviation data
Classes:
| Name | Description |
|---|---|
AllanDeviation |
Allan deviation (variance) analysis of random noise. |
NoiseModel |
Noise parameters to include when fitting Allan deviation model. |
Allan deviation (variance) analysis of random noise.
Allan deviation (or it's square, Allan variance) is a standard technique for analysis of random noise sources in inertial sensors. See Standards [05] and [06] for further details.
This class provides methods to calculate Allan deviation and its estimated accuracy. It also provides methods to extract best-fit parameters from an Allan deviation signal.
Methods:
| Name | Description |
|---|---|
calculate |
Calculate the Allan deviation of a uniformly sampled signal. |
fit_model |
Fit standard noise parameters to an Allan deviation signal. |
classmethod
¶
Calculate the Allan deviation of a uniformly sampled signal.
The Allan deviation is a statistical measure used in characterizing random processes in time domain signals. It is calculated as the standard deviation of a sliding window of time averages across a signal, with the window varying from a minimum value of a single sample up to a maximum of half the duration of the signal (the Nyquist frequency). Each window covers a "cluster" of data points of a fixed length (given that the signal is uniformly sampled in time).
Allan deviation (or its square, Allan variance) is the standard method for characterizing noise in inertial sensors. The function returns the fully overlapping Allan deviation as defined in Section C.1. of Standard [05]. See also Reference [20] for further details.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
measurement
|
Measurement
|
Measurement object containing the sensor data to analyze. This should be uniformly sampled time series data. The results will be calculated independently for each channel. |
required |
num_clusters
|
int
|
Number of logarithmically spaced cluster sizes to return. Must be at least 1. Default = 100. |
100
|
Returns:
| Name | Type | Description |
|---|---|---|
tau |
NDArray
|
Averaging time (in seconds) corresponding to each Allan deviation output. Tau is logarithmically spaced from a minimum <= the sample period to a <= the Nyquist frequency (half the sample rate). |
allan_deviation |
NDArray
|
An estimate of the Allan deviation of the input signal. |
allan_deviation_deviation |
NDArray
|
An estimate of the standard deviation of the Allan deviation. |
classmethod
¶
fit_model(
model: NoiseModel,
tau: ArrayLike,
allan_deviation: ArrayLike,
allan_deviation_deviation: ArrayLike | None = None,
) -> NDArray
Fit standard noise parameters to an Allan deviation signal.
Find the coefficients of quantization (Q), random walk (N), bias instability (B), rate random walk (K), and rate ramp (R) noises that best fit the Allan deviation data (in the weighted least squares sense). See calculate to calculate the required inputs from sensor measurements.
See Standard [05], Section C.1 and Reference [20] & Reference [29] for further details. Note: this procedure is optimal in the sense of Reference [29] when the model is correctly specified.
The resulting model parameters can then be used in IMU, gyro, and accelerometer specifications.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
model
|
NoiseModel
|
NoiseModel specifying which coefficients to include in the least squares model fit. |
required |
tau
|
ArrayLike
|
Averaging time (in seconds) corresponding to each Allan deviation input. |
required |
allan_deviation
|
ArrayLike
|
Allan deviation. |
required |
allan_deviation_deviation
|
ArrayLike | None
|
Optional estimate of the standard deviation of the Allan deviation. If None, all inputs will be weighted equally. |
None
|
Returns:
| Name | Type | Description |
|---|---|---|
noise_parameters |
NDArray
|
Array of up to 5 noise parameters [Q, N, B, K, R]. Units will be compatible with the units of the input Allan deviation. If model excludes some parameters, the included parameters will be returned in the order shown. Negative coefficients will be truncated to 0.0. This typically indicates insufficient data and/or a mis-specified model. |
Raises:
| Type | Description |
|---|---|
ValueError
|
Model does not include any coefficients to fit. |
dataclass
¶
NoiseModel(
*,
fit_quantization: bool = True,
fit_random_walk: bool = True,
fit_bias_instability: bool = True,
fit_rate_random_walk: bool = True,
fit_rate_ramp: bool = True,
)
Noise parameters to include when fitting Allan deviation model.
Specify which noise parameters to include when fitting a least-squares model to Allan deviation data.
Attributes:
| Name | Type | Description |
|---|---|---|
fit_quantization |
bool
|
Include angle (gyro) or velocity (accelerometer) quantization terms in |
fit_random_walk |
bool
|
Include angle (gyro) or velocity (accelerometer) random walk terms in |
fit_bias_instability |
bool
|
Include angular rate (gyro) or acceleration (accelerometer) bias |
fit_rate_random_walk |
bool
|
Include angular rate (gyro) or acceleration (accelerometer) random walk |
fit_rate_ramp |
bool
|
Include angular rate (gyro) or acceleration (accelerometer) ramp |
class-attribute
instance-attribute
¶
fit_quantization: bool = True
Include angle (gyro) or velocity (accelerometer) quantization terms in the Allan deviation model.
class-attribute
instance-attribute
¶
fit_random_walk: bool = True
Include angle (gyro) or velocity (accelerometer) random walk terms in the Allan deviation model.
class-attribute
instance-attribute
¶
fit_bias_instability: bool = True
Include angular rate (gyro) or acceleration (accelerometer) bias instability terms in the Allan deviation model.