Three-axis Inertial Measurement Unit

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blockType: SubSystem

Path in the library:

/Aerospace/GNC/Navigation/Three-axis Inertial Measurement Unit

Description

The block Three-axis Inertial Measurement Unit is a combination of accelerometer and gyroscope. For a description of the equations, see blocks Three-axis Gyroscope and Three-axis Accelerometer.

Ports

Input

# A_b (m/s²) — actual accelerations
`vector 1 to 3

Details

Actual accelerations in the coupled axes in m/s²^ given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# ω (rad/s) — angular velocities
`vector 1 to 3

Details

Angular velocities in the coupled axes in rad/s, given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# dω/dt — angular accelerations
`vector 1 to 3

Details

Angular accelerations in the coupled axes in rad/s²^ given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# CG (m) — centre of gravity location
`vector 1 to 3

Details

The position of the centre of gravity in m given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# g (m/s²) — free-fall acceleration
`vector 1 to 3

Details

Free-fall acceleration in coupled axes in m/c²^, given as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

Output

# A_meas (m/s²) — measured accelerations
`vector 1 to 3

Details

Measured accelerations from the accelerometer in m/c², returned as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

# ω_meas (rad/s) — measured angular velocities
`vector 1 to 3

Details

Measured angular velocities in rad/s, returned as a three-element vector.

Data types	`Float64`.
Complex numbers support	No

Parameters

Main

# IMU location: — location of the inertial measurement unit

Details

Location of the inertial measurement unit, the reference frame is the same as the one used for entering the centre of mass.

Default value	`[0.0 0.0 0.0]`
Program usage name	`imu`
Tunable	No
Evaluatable	Yes

# Update rate: — refresh rate

Details

The update frequency of the inertial measurement unit.

Default value	`0.0`
Program usage name	`i_Ts`
Tunable	No
Evaluatable	Yes

Accelerometer

# Second-order dynamics for accelerometer — Second-order dynamics for accelerometer

Details

Select this check box to take second-order dynamic effects into account when processing accelerometer data.

Default value	`true (switched on)`
Program usage name	`dtype_a`
Tunable	No
Evaluatable	Yes

# Accelerometer natural frequency (rad/sec): — accelerometer natural frequency

Details

The natural frequency of the accelerometer, given by a scalar, in rad/s.

Default value	`190.0`
Program usage name	`w_a`
Tunable	No
Evaluatable	Yes

# Accelerometer damping ratio: — accelerometer damping factor

Details

Accelerometer damping coefficient given as a dimensionless scalar quantity.

Dependencies

To use this parameter, select the checkbox next to the parameter. Second-order dynamics for accelerometer

Default value	`0.707`
Program usage name	`z_a`
Tunable	No
Evaluatable	Yes

# Accelerometer scale factor and cross-coupling: — Accelerometer scaling factors and cross-couplings

Details

Accelerometer scaling factors and cross-couplings, specified by a 3 by 3 matrix, to introduce distortions between the accelerometer axes and the related axes of the object, and to scale the accelerations along the axes.

Default value	`[1 0 0; 0 1 0; 0 0 1]`
Program usage name	`a_sf_cc`
Tunable	No
Evaluatable	Yes

# Accelerometer measurement bias: — Accelerometer systematic error

Details

Systematic errors of the accelerometer in the axes, given as a three-element vector.

Default value	`[0 0 0]`
Program usage name	`a_bias`
Tunable	No
Evaluatable	Yes

# Accelerometer upper limit: — maximum value of accelerometer accelerations

Details

The maximum value of accelerometer accelerations specified by a scalar.

Default value	`Inf`
Program usage name	`a_sat1`
Tunable	No
Evaluatable	Yes

# Accelerometer lower limit: — minimum accelerometer acceleration value

Details

The minimum value of accelerometer accelerations specified by a scalar.

Default value	`-Inf`
Program usage name	`a_sat2`
Tunable	No
Evaluatable	Yes

Gyroscope

# Second-order dynamics for gyroscope — second-order dynamics for a gyroscope

Details

Select this check box to include second-order dynamic effects when processing gyroscope data.

Default value	`true (switched on)`
Program usage name	`dtype_g`
Tunable	No
Evaluatable	Yes

# Gyro natural frequency (rad/sec): — natural frequency of the gyroscope

Details

The natural frequency of the gyroscope.

Dependencies

To use this parameter, select the checkbox to use it Second-order dynamics for gyroscope

Default value	`190.0`
Program usage name	`w_g`
Tunable	No
Evaluatable	Yes

# Gyro damping ratio: — gyro damping factor

Details

The damping coefficient of the gyroscope.

Dependencies

To use this parameters, tick the checkbox Second-order dynamics for gyroscope

Default value	`0.707`
Program usage name	`z_g`
Tunable	No
Evaluatable	Yes

# Gyro scale factors and cross-coupling: — scaling factors and gyroscope cross-couplings

Details

The scaling factors and cross-couplings of the gyroscope, given as a 3 by 3 matrix, allow the gyroscope to be deflected from the body axes and the accelerations to be scaled along the body axes.

Default value	`[1 0 0; 0 1 0; 0 0 1]`
Program usage name	`g_sf_cc`
Tunable	No
Evaluatable	Yes

# Gyro measurement bias: — gyroscope measurement error

Details

Systematic measurement errors in the gyroscope axes.

Default value	`[0 0 0]`
Program usage name	`g_bias`
Tunable	No
Evaluatable	Yes

# G-sensitive bias: — acceleration sensitivity

Details

The maximum change in angular velocity caused by linear acceleration is given as a three-element vector in rad/s per unit of free-fall acceleration .

Default value	`0.0`
Program usage name	`g_sen`
Tunable	No
Evaluatable	Yes

# Gyro upper limit: — maximum value of gyroscope angular velocities

Details

Maximum value of angular velocities specified by scalar.

Default value	`Inf`
Program usage name	`g_sat1`
Tunable	No
Evaluatable	Yes

# Gyro lower limit: — minimum value of gyroscope angular velocities

Details

Minimum value of angular velocities specified by scalar.

Default value	`-Inf`
Program usage name	`g_sat2`
Tunable	No
Evaluatable	Yes

Noise

# Noise on — white noise

Details

To add white noise to the gyroscope and accelerometer readings, select this check box.

Default value	`false (switched off)`
Program usage name	`i_rand`
Tunable	No
Evaluatable	Yes

# Noise seeds for accelerometer: — white noise generator seed values for accelerometer

Details

Seed values of the white noise generator for accelerometer, specified as a three-element vector.

Dependencies

To use this parameters, select the checkbox Noise on.

Default value	`[23093 23094 23095]`
Program usage name	`a_seeds`
Tunable	No
Evaluatable	Yes

# Noise power for accelerometer: — noise power for accelerometer

Details

The height of the power spectral density (PSD) of white noise for each axis of the accelerometer, given as a three-element vector.

Dependencies

To use this parameter, select the Noise on checkbox.

Default value	`[0.001 0.001 0.001]`
Program usage name	`a_pow`
Tunable	No
Evaluatable	Yes

# Noise seeds for gyroscope — seed values of the white noise generator for the gyroscope

Details

Seed values of the white noise generator for the gyroscope, specified as a three-element vector.

Dependencies

To use this parameters, set the checkbox Noise on.

Default value	`[23096 23097 23098]`
Program usage name	`g_seeds`
Tunable	No
Evaluatable	Yes

# Noise power for gyroscope: — noise power for gyroscope

Details

The height of the power spectral density (PSD) of white noise for each axis of the gyroscope, given as a three-element vector.

Dependencies

To use this parameters, select the checkbox Noise on.

Default value	`[0.0001 0.0001 0.0001]`
Program usage name	`g_pow`
Tunable	No
Evaluatable	Yes

Literature

Rogers, R. M., Applied Mathematics in Integrated Navigation Systems, AIAA Education Series, 2000.