imuSensor
IMU simulation model
Description
The imuSensor
System object™ models receiving data from an inertial measurement unit (IMU). You can specify
the reference frame of the block inputs as the NED
(North-East-Down) or
ENU
(East-North-Up) frame by using the
ReferenceFrame
argument.
To model an IMU:
Create the
imuSensor
object and set its properties.Call the object with arguments, as if it were a function.
To learn more about how System objects work, see What Are System Objects?
Creation
Syntax
Description
returns a System object, IMU
= imuSensorIMU
, that computes an inertial measurement unit reading
based on an inertial input signal. IMU
has an ideal accelerometer and
gyroscope.
IMU = imuSensor(
returns an
'accel-gyro'
)imuSensor
System object with an ideal accelerometer and gyroscope. imuSensor
and
imuSensor('accel-gyro')
are equivalent creation syntaxes.
IMU = imuSensor(
returns an
'accel-mag'
)imuSensor
System object with an ideal accelerometer and magnetometer.
IMU = imuSensor(
returns an
'accel-gyro-mag'
)imuSensor
System object with an ideal accelerometer, gyroscope, and magnetometer.
IMU = imuSensor(___,"ReferenceFrame",
returns an RF
)imuSensor
System object that computes an inertial measurement unit reading relative to the reference
frame RF
.
IMU = imuSensor(___,
sets one or more properties using name-value arguments in addition to any of the previous
input arguments.Name=Value
)
Input Arguments
RF
— Reference frame of sensor inputs
'NED'
(default) | 'ENU'
Reference frame of the sensor inputs, specified as either 'NED'
(North-East-Down) or 'ENU'
(East-North-Up).
Note
If you choose the NED reference frame, specify the sensor inputs in the NED reference frame. Additionally, the sensor models the gravitational acceleration as [0 0 9.81] m/s2.
If you choose the ENU reference frame, specify the sensor inputs in the ENU reference frame. Additionally, the sensor models the gravitational acceleration as [0 0 −9.81] m/s2.
Data Types: char
| string
Properties
Unless otherwise indicated, properties are nontunable, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
release
function unlocks them.
If a property is tunable, you can change its value at any time.
For more information on changing property values, see System Design in MATLAB Using System Objects.
IMUType
— Type of inertial measurement unit
'accel-gyro'
(default) | 'accel-mag'
| 'accel-gyro-mag'
Type of inertial measurement unit, specified as a 'accel-gyro'
,
'accel-mag'
, or 'accel-gyro-mag'
.
The type of inertial measurement unit specifies which sensor readings to model:
'accel-gyro'
–– Accelerometer and gyroscope'accel-mag'
–– Accelerometer and magnetometer'accel-gyro-mag'
–– Accelerometer, gyroscope, and magnetometer
You can specify IMUType
as a value-only argument during creation
or as a Name,Value
pair.
Data Types: char
| string
SampleRate
— Sample rate of sensor (Hz)
100
(default) | positive scalar
Sample rate of the sensor model in Hz, specified as a positive scalar.
Data Types: single
| double
Temperature
— Temperature of IMU (oC)
25
(default) | real scalar
Operating temperature of the IMU in degrees Celsius, specified as a real scalar.
When the object calculates temperature scale factors and environmental drift noises, 25 oC is used as the nominal temperature.
Tunable: Yes
Data Types: single
| double
MagneticField
— Magnetic field vector in local navigation coordinate system (μT)
[27.5550 -2.4169 -16.0849]
(default) | three-element real-valued vector
Magnetic field vector in microtesla, specified as a three-element row vector in the local navigation coordinate system.
The default magnetic field corresponds to the magnetic field at latitude zero, longitude zero, and altitude zero.
Tunable: Yes
Data Types: single
| double
Accelerometer
— Accelerometer sensor parameters
accelparams
object (default)
Accelerometer sensor parameters, specified by an accelparams
object.
Tunable: Yes
Gyroscope
— Gyroscope sensor parameters
gyroparams
object (default)
Gyroscope sensor parameters, specified by a gyroparams
object.
Tunable: Yes
Magnetometer
— Magnetometer sensor parameters
magparams
object (default)
Magnetometer sensor parameters, specified by a magparams
object.
Tunable: Yes
RandomStream
— Random number source
'Global stream'
(default) | 'mt19937ar with seed'
Random number source, specified as a character vector or string:
'Global stream'
–– Random numbers are generated using the current global random number stream.'mt19937ar with seed'
–– Random numbers are generated using the mt19937ar algorithm with the seed specified by theSeed
property.
Data Types: char
| string
Seed
— Initial seed
67
(default) | nonnegative integer scalar
Initial seed of an mt19937ar random number generator algorithm, specified as a real, nonnegative integer scalar.
Dependencies
To enable this property, set RandomStream
to
'mt19937ar with seed'
.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
Usage
Syntax
Description
[
generates accelerometer and gyroscope readings from the acceleration and angular
velocity inputs.accelReadings
,gyroReadings
] = IMU(acc
,angVel
)
This syntax is only valid if IMUType
is set to
'accel-gyro'
or 'accel-gyro-mag'
.
[
generates accelerometer and gyroscope readings from the acceleration, angular velocity,
and orientation inputs.accelReadings
,gyroReadings
] = IMU(acc
,angVel
,orientation
)
This syntax is only valid if IMUType
is set to
'accel-gyro'
or 'accel-gyro-mag'
.
[
generates accelerometer and magnetometer readings from the acceleration and angular
velocity inputs.accelReadings
,magReadings
] = IMU(acc
,angVel
)
This syntax is only valid if IMUType
is set to
'accel-mag'
.
[
generates accelerometer and magnetometer readings from the acceleration, angular
velocity, and orientation inputs.accelReadings
,magReadings
] = IMU(acc
,angVel
,orientation
)
This syntax is only valid if IMUType
is set to
'accel-mag'
.
[
generates accelerometer, gyroscope, and magnetometer readings from the acceleration and
angular velocity inputs.accelReadings
,gyroReadings
,magReadings
] = IMU(acc
,angVel
)
This syntax is only valid if IMUType
is set to
'accel-gyro-mag'
.
[
generates accelerometer, gyroscope, and magnetometer readings from the acceleration,
angular velocity, and orientation inputs.accelReadings
,gyroReadings
,magReadings
] = IMU(acc
,angVel
,orientation
)
This syntax is only valid if IMUType
is set to
'accel-gyro-mag'
.
Input Arguments
acc
— Acceleration of IMU in local navigation coordinate system
(m/s2)
N-by-3 matrix
Acceleration of the IMU in the local navigation coordinate system, specified as a real, finite N-by-3 array in meters per second squared. N is the number of samples in the current frame. Do not include the gravitational acceleration in this input since the sensor models gravitational acceleration by default.
To specify the orientation of the IMU sensor body frame with respect to the local
navigation frame, use the orientation
input argument.
Data Types: single
| double
angVel
— Angular velocity of IMU in local navigation coordinate system (rad/s)
N-by-3 matrix
Angular velocity of the IMU in the local navigation coordinate system, specified
as a real, finite N-by-3 array in radians per second.
N is the number of samples in the current frame. To specify the
orientation of the IMU sensor body frame with respect to the local navigation frame,
use the orientation
input argument.
Data Types: single
| double
orientation
— Orientation of IMU in local navigation coordinate system
N-element quaternion column vector | 3-by-3-by-N-element rotation matrix
Orientation of the IMU with respect to the local navigation coordinate system,
specified as a quaternion
N-element column vector or a 3-by-3-by-N
rotation matrix. Each quaternion
or rotation matrix represents a frame
rotation from the local navigation coordinate system to the current IMU sensor body
coordinate system. N is the number of samples in the current
frame.
Data Types: single
| double
| quaternion
Output Arguments
accelReadings
— Accelerometer measurement of IMU in sensor body coordinate system
(m/s2)
N-by-3 matrix
Accelerometer measurement of the IMU in the sensor body coordinate system, specified as a real, finite N-by-3 array in meters per second squared. N is the number of samples in the current frame.
Data Types: single
| double
gyroReadings
— Gyroscope measurement of IMU in sensor body coordinate system (rad/s)
N-by-3 matrix
Gyroscope measurement of the IMU in the sensor body coordinate system, specified as a real, finite N-by-3 array in radians per second. N is the number of samples in the current frame.
Data Types: single
| double
magReadings
— Magnetometer measurement of IMU in sensor body coordinate system (μT)
N-by-3 matrix (default)
Magnetometer measurement of the IMU in the sensor body coordinate system, specified as a real, finite N-by-3 array in microtelsa. N is the number of samples in the current frame.
Data Types: single
| double
Object Functions
To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named obj
, use
this syntax:
release(obj)
Specific to imuSensor
loadparams | Load sensor parameters from JSON file |
perturbations | Perturbation defined on object |
perturb | Apply perturbations to object |
Examples
Create Default imuSensor
System object
The imuSensor
System object™ enables you to model the data received from an inertial measurement unit consisting of a combination of gyroscope, accelerometer, and magnetometer.
Create a default imuSensor
object.
IMU = imuSensor
IMU = imuSensor with properties: IMUType: 'accel-gyro' SampleRate: 100 Temperature: 25 Accelerometer: [1x1 accelparams] Gyroscope: [1x1 gyroparams] RandomStream: 'Global stream'
The imuSensor
object, IMU
, contains an idealized gyroscope and accelerometer. Use dot notation to view properties of the gyroscope.
IMU.Gyroscope
ans = gyroparams with properties: MeasurementRange: Inf rad/s Resolution: 0 (rad/s)/LSB ConstantBias: [0 0 0] rad/s AxesMisalignment: [3⨯3 double] % NoiseDensity: [0 0 0] (rad/s)/√Hz BiasInstability: [0 0 0] rad/s RandomWalk: [0 0 0] (rad/s)*√Hz NoiseType: "double-sided" BiasInstabilityCoefficients: [1⨯1 struct] TemperatureBias: [0 0 0] (rad/s)/°C TemperatureScaleFactor: [0 0 0] %/°C AccelerationBias: [0 0 0] (rad/s)/(m/s²)
Sensor properties are defined by corresponding parameter objects. For example, the gyroscope model used by the imuSensor
is defined by an instance of the gyroparams
class. You can modify properties of the gyroscope model using dot notation. Set the gyroscope measurement range to 4.3 rad/s.
IMU.Gyroscope.MeasurementRange = 4.3;
You can also set sensor properties to preset parameter objects. Create an accelparams
object to mimic specific hardware, and then set the IMU Accelerometer
property to the accelparams
object. Display the Accelerometer
property to verify the properties are correctly set.
SpecSheet1 = accelparams( ... 'MeasurementRange',19.62, ... 'Resolution',0.00059875, ... 'ConstantBias',0.4905, ... 'AxesMisalignment',2, ... 'NoiseDensity',0.003924, ... 'BiasInstability',0, ... 'TemperatureBias', [0.34335 0.34335 0.5886], ... 'TemperatureScaleFactor', 0.02); IMU.Accelerometer = SpecSheet1; IMU.Accelerometer
ans = accelparams with properties: MeasurementRange: 19.62 m/s² Resolution: 0.00059875 (m/s²)/LSB ConstantBias: [0.4905 0.4905 0.4905] m/s² AxesMisalignment: [3⨯3 double] % NoiseDensity: [0.003924 0.003924 0.003924] (m/s²)/√Hz BiasInstability: [0 0 0] m/s² RandomWalk: [0 0 0] (m/s²)*√Hz NoiseType: "double-sided" BiasInstabilityCoefficients: [1⨯1 struct] TemperatureBias: [0.34335 0.34335 0.5886] (m/s²)/°C TemperatureScaleFactor: [0.02 0.02 0.02] %/°C
Generate IMU Data from Stationary Input
Use the imuSensor
System object™ to model receiving data from a stationary ideal IMU containing an accelerometer, gyroscope, and magnetometer.
Create an ideal IMU sensor model that contains an accelerometer, gyroscope, and magnetometer.
IMU = imuSensor('accel-gyro-mag')
IMU = imuSensor with properties: IMUType: 'accel-gyro-mag' SampleRate: 100 Temperature: 25 MagneticField: [27.5550 -2.4169 -16.0849] Accelerometer: [1x1 accelparams] Gyroscope: [1x1 gyroparams] Magnetometer: [1x1 magparams] RandomStream: 'Global stream'
Define the ground-truth, underlying motion of the IMU you are modeling. The acceleration and angular velocity are defined relative to the local NED coordinate system.
numSamples = 1000; acceleration = zeros(numSamples,3); angularVelocity = zeros(numSamples,3);
Call IMU
with the ground-truth acceleration and angular velocity. The object outputs accelerometer readings, gyroscope readings, and magnetometer readings, as modeled by the properties of the imuSensor
System object. The accelerometer readings, gyroscope readings, and magnetometer readings are relative to the IMU sensor body coordinate system.
[accelReading,gyroReading,magReading] = IMU(acceleration,angularVelocity);
Plot the accelerometer readings, gyroscope readings, and magnetometer readings.
t = (0:(numSamples-1))/IMU.SampleRate; subplot(3,1,1) plot(t,accelReading) legend('X-axis','Y-axis','Z-axis') title('Accelerometer Readings') ylabel('Acceleration (m/s^2)') subplot(3,1,2) plot(t,gyroReading) legend('X-axis','Y-axis','Z-axis') title('Gyroscope Readings') ylabel('Angular Velocity (rad/s)') subplot(3,1,3) plot(t,magReading) legend('X-axis','Y-axis','Z-axis') title('Magnetometer Readings') xlabel('Time (s)') ylabel('Magnetic Field (uT)')
Orientation is not specified and the ground-truth motion is stationary, so the IMU sensor body coordinate system and the local NED coordinate system overlap for the entire simulation.
Accelerometer readings: The z-axis of the sensor body corresponds to the Down-axis. The 9.8 m/s^2 acceleration along the z-axis is due to gravity.
Gyroscope readings: The gyroscope readings are zero along each axis, as expected.
Magnetometer readings: Because the sensor body coordinate system is aligned with the local NED coordinate system, the magnetometer readings correspond to the
MagneticField
property ofimuSensor
. TheMagneticField
property is defined in the local NED coordinate system.
Model Rotating Six-Axis IMU Data
Use imuSensor
to model data obtained from a rotating IMU containing an ideal accelerometer and an ideal magnetometer. Use kinematicTrajectory
to define the ground-truth motion. Fuse the imuSensor
model output using the ecompass
function to determine orientation over time.
Define the ground-truth motion for a platform that rotates 360 degrees in four seconds, and then another 360 degrees in two seconds. Use kinematicTrajectory
to output the orientation, acceleration, and angular velocity in the NED coordinate system.
fs = 100;
firstLoopNumSamples = fs*4;
secondLoopNumSamples = fs*2;
totalNumSamples = firstLoopNumSamples + secondLoopNumSamples;
traj = kinematicTrajectory('SampleRate',fs);
accBody = zeros(totalNumSamples,3);
angVelBody = zeros(totalNumSamples,3);
angVelBody(1:firstLoopNumSamples,3) = (2*pi)/4;
angVelBody(firstLoopNumSamples+1:end,3) = (2*pi)/2;
[~,orientationNED,~,accNED,angVelNED] = traj(accBody,angVelBody);
Create an imuSensor
object with an ideal accelerometer and an ideal magnetometer. Call IMU
with the ground-truth acceleration, angular velocity, and orientation to output accelerometer readings and magnetometer readings. Plot the results.
IMU = imuSensor('accel-mag','SampleRate',fs); [accelReadings,magReadings] = IMU(accNED,angVelNED,orientationNED); figure(1) t = (0:(totalNumSamples-1))/fs; subplot(2,1,1) plot(t,accelReadings) legend('X-axis','Y-axis','Z-axis') ylabel('Acceleration (m/s^2)') title('Accelerometer Readings') subplot(2,1,2) plot(t,magReadings) legend('X-axis','Y-axis','Z-axis') ylabel('Magnetic Field (\muT)') xlabel('Time (s)') title('Magnetometer Readings')
The accelerometer readings indicate that the platform has no translation. The magnetometer readings indicate that the platform is rotating around the z-axis.
Feed the accelerometer and magnetometer readings into the ecompass
function to estimate the orientation over time. The ecompass
function returns orientation in quaternion format. Convert orientation to Euler angles and plot the results. The orientation plot indicates that the platform rotates about the z-axis only.
orientation = ecompass(accelReadings,magReadings); orientationEuler = eulerd(orientation,'ZYX','frame'); figure(2) plot(t,orientationEuler) legend('Z-axis','Y-axis','X-axis') xlabel('Time (s)') ylabel('Rotation (degrees)') title('Orientation')
Model Rotating Six-Axis IMU Data with Noise
Use imuSensor
to model data obtained from a rotating IMU containing a realistic accelerometer and a realistic magnetometer. Use kinematicTrajectory
to define the ground-truth motion. Fuse the imuSensor
model output using the ecompass
function to determine orientation over time.
Define the ground-truth motion for a platform that rotates 360 degrees in four seconds, and then another 360 degrees in two seconds. Use kinematicTrajectory
to output the orientation, acceleration, and angular velocity in the NED coordinate system.
fs = 100;
firstLoopNumSamples = fs*4;
secondLoopNumSamples = fs*2;
totalNumSamples = firstLoopNumSamples + secondLoopNumSamples;
traj = kinematicTrajectory('SampleRate',fs);
accBody = zeros(totalNumSamples,3);
angVelBody = zeros(totalNumSamples,3);
angVelBody(1:firstLoopNumSamples,3) = (2*pi)/4;
angVelBody(firstLoopNumSamples+1:end,3) = (2*pi)/2;
[~,orientationNED,~,accNED,angVelNED] = traj(accBody,angVelBody);
Create an imuSensor
object with a realistic accelerometer and a realistic magnetometer. Call IMU
with the ground-truth acceleration, angular velocity, and orientation to output accelerometer readings and magnetometer readings. Plot the results.
IMU = imuSensor('accel-mag','SampleRate',fs); IMU.Accelerometer = accelparams( ... 'MeasurementRange',19.62, ... % m/s^2 'Resolution',0.0023936, ... % m/s^2 / LSB 'TemperatureScaleFactor',0.008, ... % % / degree C 'ConstantBias',0.1962, ... % m/s^2 'TemperatureBias',0.0014715, ... % m/s^2 / degree C 'NoiseDensity',0.0012361); % m/s^2 / Hz^(1/2) IMU.Magnetometer = magparams( ... 'MeasurementRange',1200, ... % uT 'Resolution',0.1, ... % uT / LSB 'TemperatureScaleFactor',0.1, ... % % / degree C 'ConstantBias',1, ... % uT 'TemperatureBias',[0.8 0.8 2.4], ... % uT / degree C 'NoiseDensity',[0.6 0.6 0.9]/sqrt(100)); % uT / Hz^(1/2) [accelReadings,magReadings] = IMU(accNED,angVelNED,orientationNED); figure(1) t = (0:(totalNumSamples-1))/fs; subplot(2,1,1) plot(t,accelReadings) legend('X-axis','Y-axis','Z-axis') ylabel('Acceleration (m/s^2)') title('Accelerometer Readings') subplot(2,1,2) plot(t,magReadings) legend('X-axis','Y-axis','Z-axis') ylabel('Magnetic Field (\muT)') xlabel('Time (s)') title('Magnetometer Readings')
The accelerometer readings indicate that the platform has no translation. The magnetometer readings indicate that the platform is rotating around the z-axis.
Feed the accelerometer and magnetometer readings into the ecompass
function to estimate the orientation over time. The ecompass
function returns orientation in quaternion format. Convert orientation to Euler angles and plot the results. The orientation plot indicates that the platform rotates about the z-axis only.
orientation = ecompass(accelReadings,magReadings); orientationEuler = eulerd(orientation,'ZYX','frame'); figure(2) plot(t,orientationEuler) legend('Z-axis','Y-axis','X-axis') xlabel('Time (s)') ylabel('Rotation (degrees)') title('Orientation')
%
Model Tilt Using Gyroscope and Accelerometer Readings
Model a tilting IMU that contains an accelerometer and gyroscope using the imuSensor
System object™. Use ideal and realistic models to compare the results of orientation tracking using the imufilter
System object.
Load a struct describing ground-truth motion and a sample rate. The motion struct describes sequential rotations:
yaw: 120 degrees over two seconds
pitch: 60 degrees over one second
roll: 30 degrees over one-half second
roll: -30 degrees over one-half second
pitch: -60 degrees over one second
yaw: -120 degrees over two seconds
In the last stage, the motion struct combines the 1st, 2nd, and 3rd rotations into a single-axis rotation. The acceleration, angular velocity, and orientation are defined in the local NED coordinate system.
load y120p60r30.mat motion fs accNED = motion.Acceleration; angVelNED = motion.AngularVelocity; orientationNED = motion.Orientation; numSamples = size(motion.Orientation,1); t = (0:(numSamples-1)).'/fs;
Create an ideal IMU sensor object and a default IMU filter object.
IMU = imuSensor('accel-gyro','SampleRate',fs); aFilter = imufilter('SampleRate',fs);
In a loop:
Simulate IMU output by feeding the ground-truth motion to the IMU sensor object.
Filter the IMU output using the default IMU filter object.
orientation = zeros(numSamples,1,'quaternion'); for i = 1:numSamples [accelBody,gyroBody] = IMU(accNED(i,:),angVelNED(i,:),orientationNED(i,:)); orientation(i) = aFilter(accelBody,gyroBody); end release(aFilter)
Plot the orientation over time.
figure(1) plot(t,eulerd(orientation,'ZYX','frame')) xlabel('Time (s)') ylabel('Rotation (degrees)') title('Orientation Estimation -- Ideal IMU Data, Default IMU Filter') legend('Z-axis','Y-axis','X-axis')
Modify properties of your imuSensor
to model real-world sensors. Run the loop again and plot the orientation estimate over time.
IMU.Accelerometer = accelparams( ... 'MeasurementRange',19.62, ... 'Resolution',0.00059875, ... 'ConstantBias',0.4905, ... 'AxesMisalignment',2, ... 'NoiseDensity',0.003924, ... 'BiasInstability',0, ... 'TemperatureBias', [0.34335 0.34335 0.5886], ... 'TemperatureScaleFactor',0.02); IMU.Gyroscope = gyroparams( ... 'MeasurementRange',4.3633, ... 'Resolution',0.00013323, ... 'AxesMisalignment',2, ... 'NoiseDensity',8.7266e-05, ... 'TemperatureBias',0.34907, ... 'TemperatureScaleFactor',0.02, ... 'AccelerationBias',0.00017809, ... 'ConstantBias',[0.3491,0.5,0]); orientationDefault = zeros(numSamples,1,'quaternion'); for i = 1:numSamples [accelBody,gyroBody] = IMU(accNED(i,:),angVelNED(i,:),orientationNED(i,:)); orientationDefault(i) = aFilter(accelBody,gyroBody); end release(aFilter) figure(2) plot(t,eulerd(orientationDefault,'ZYX','frame')) xlabel('Time (s)') ylabel('Rotation (degrees)') title('Orientation Estimation -- Realistic IMU Data, Default IMU Filter') legend('Z-axis','Y-axis','X-axis')
The ability of the imufilter
to track the ground-truth data is significantly reduced when modeling a realistic IMU. To improve performance, modify properties of your imufilter
object. These values were determined empirically. Run the loop again and plot the orientation estimate over time.
aFilter.GyroscopeNoise = 7.6154e-7; aFilter.AccelerometerNoise = 0.0015398; aFilter.GyroscopeDriftNoise = 3.0462e-12; aFilter.LinearAccelerationNoise = 0.00096236; aFilter.InitialProcessNoise = aFilter.InitialProcessNoise*10; orientationNondefault = zeros(numSamples,1,'quaternion'); for i = 1:numSamples [accelBody,gyroBody] = IMU(accNED(i,:),angVelNED(i,:),orientationNED(i,:)); orientationNondefault(i) = aFilter(accelBody,gyroBody); end release(aFilter) figure(3) plot(t,eulerd(orientationNondefault,'ZYX','frame')) xlabel('Time (s)') ylabel('Rotation (degrees)') title('Orientation Estimation -- Realistic IMU Data, Nondefault IMU Filter') legend('Z-axis','Y-axis','X-axis')
To quantify the improved performance of the modified imufilter
, plot the quaternion distance between the ground-truth motion and the orientation as returned by the imufilter
with default and nondefault properties.
qDistDefault = rad2deg(dist(orientationNED,orientationDefault)); qDistNondefault = rad2deg(dist(orientationNED,orientationNondefault)); figure(4) plot(t,[qDistDefault,qDistNondefault]) title('Quaternion Distance from True Orientation') legend('Realistic IMU Data, Default IMU Filter', ... 'Realistic IMU Data, Nondefault IMU Filter') xlabel('Time (s)') ylabel('Quaternion Distance (degrees)')
Algorithms
Tip
In the following algorithm description, variables in italic fonts are inputs or outputs
of the imuSensor
object. Variables in bold fonts are properties of the
imuSensor
. Variables in normal fonts are properties of the accelparams
, gyroparams
, or magparams
object.
Accelerometer
The following algorithm description assumes an NED navigation frame. The accelerometer model
uses the ground-truth orientation and acceleration inputs and the imuSensor
and accelparams
properties to model accelerometer readings.
To obtain the total acceleration (totalAcc), the acceleration is preprocessed by negating and adding the gravity constant vector (g= [0; 0; 9.8] m/s2 assuming an NED frame) as:
The acceleration
term is negated to obtain zero
total acceleration readings when the accelerometer is in a free fall. The
acceleration
term is also known as the specific force.
Then the total acceleration is converted from the local navigation frame to the sensor frame using:
If the orientation is input in quaternion form, it is converted to a rotation matrix before processing.
The ground-truth acceleration in the sensor frame, a, passes through the bulk model, which adds axes misalignment and bias:
where ConstantBias is a property of accelparams
, and α1, α2, and α3 are given by the first, second, and third elements of the AxesMisalignment property of accelparams
.
The bias instability drift β1 is modeled as white noise biased and then filtered:
where k is the discrete time step index, BiasInstability is
a property of accelparams
,
w is white noise that follows a normal distribution of mean 0 and
variance of 1. The discrete time step size is the reciprocal of the SampleRate
property. [g1,
g2, …,
gn+1] are the
denominator coefficients specified in the
BiasInstabilityCoefficients
property of the accelparams
object.
[f1,
f2, …,
fm+1] are the
numerator coefficients of the BiasInstabilityCoefficients
property.
n and m are the orders of the denominator and
numerator coefficients, respectively.
White noise drift is modeled by multiplying elements of the white noise random stream by the standard deviation:
where w is white noise that follows a normal
distribution of mean 0 and variance of 1, SampleRate is an
imuSensor
property, and NoiseDensity is an
accelparams
property.
The scale variable s = 2 if the NoiseType
property of the accelparams
object is
double-sided and s = 1 if the NoiseType
property is single-sided.
The random walk drift is modeled by biasing elements of the white noise random stream and then filtering:
where k is the discrete time step index, RandomWalk is a
property of accelparams
, SampleRate is a
property of imuSensor
, w is white noise that follows
a normal distribution of mean 0 and variance of 1. The discrete time step size is the
reciprocal of the SampleRate
property. The scale variable s = 2 if the
NoiseType
property of the accelparams
object is
double-sided and s = 1 if the NoiseType
property is single-sided.
The environmental drift noise is modeled by multiplying the temperature difference from a standard with the temperature bias:
where Temperature is a property of imuSensor
, and TemperatureBias is a property of accelparams
. The constant 25 corresponds to a standard temperature.
The temperature scale factor error is modeled as:
where Temperature is a property of imuSensor
, and TemperatureScaleFactor is a property of accelparams
. The constant 25 corresponds to a standard temperature.
The quantization is modeled by first saturating the continuous signal model:
and then setting the resolution:
where MeasurementRange is a property of accelparams
.
Gyroscope
The following algorithm description assumes an NED navigation frame. The gyroscope model uses
the ground-truth orientation, acceleration, and angular velocity inputs, and the
imuSensor
and gyroparams
properties to model accelerometer readings.
The ground-truth angular velocity is converted from the local frame to the sensor frame using the ground-truth orientation:
If the orientation is input in quaternion form, it is converted to a rotation matrix before processing.
The ground-truth angular velocity in the sensor frame, a, passes through the bulk model, which adds axes misalignment and bias:
where ConstantBias is a property of gyroparams
, and α1, α2, and α3 are given by the first, second, and third elements of the AxesMisalignment property of gyroparams
.
The bias instability drift β1 is modeled as white noise biased and then filtered:
where k is the discrete time step index, BiasInstability is
a property of gyroparams
,
w is white noise that follows a normal distribution of mean 0 and
variance of 1. The discrete time step size is the reciprocal of the SampleRate
property. [g1,
g2, …,
gn+1] are the
denominator coefficients specified in the
BiasInstabilityCoefficients
property of the gyroparams
object.
[f1,
f2, …,
fm+1] are the
numerator coefficients of the BiasInstabilityCoefficients
property.
n and m are the orders of the denominator and
numerator coefficients, respectively.
White noise drift is modeled by multiplying elements of the white noise random stream by the standard deviation:
where w is white noise that follows a normal
distribution of mean 0 and variance of 1, SampleRate is an
imuSensor
property, and NoiseDensity is an
gyroparams
property.
The scale variable s = 2 if the NoiseType
property of the gyroparams
object is
double-sided and s = 1 if the NoiseType
property is single-sided.
The random walk drift is modeled by biasing elements of the white noise random stream and then filtering:
where k is the discrete time step index, RandomWalk is a
property of gyroparams
, SampleRate is a
property of imuSensor
, and w is white noise that
follows a normal distribution of mean 0 and variance of 1. The discrete time step size
is the reciprocal of the SampleRate
property. The scale variable s = 2 if the
NoiseType
property of the gyroparams
object is
double-sided and s = 1 if the NoiseType
property is single-sided.
The environmental drift noise is modeled by multiplying the temperature difference from a standard with the temperature bias:
where Temperature is a property of imuSensor
, and TemperatureBias is a property of gyroparams
. The constant 25 corresponds to a standard temperature.
The acceleration bias drift is modeled by multiplying the acceleration input and acceleration bias:
where AccelerationBias is
a property of gyroparams
.
The temperature scale factor error is modeled as:
where Temperature is a property of imuSensor
, and TemperatureScaleFactor is a property of gyroparams
. The constant 25 corresponds to a standard temperature.
The quantization is modeled by first saturating the continuous signal model:
and then setting the resolution:
where MeasurementRange is a property of gyroparams
.
Magnetometer
The following algorithm description assumes an NED navigation frame. The magnetometer model
uses the ground-truth orientation and acceleration inputs, and the
imuSensor
and magparams
magparams
(Sensor Fusion and Tracking Toolbox)
properties to model magnetometer readings.
The ground-truth acceleration is converted from the local frame to the sensor frame using the ground-truth orientation:
If the orientation is input in quaternion form, it is converted to a rotation matrix before processing.
The ground-truth acceleration in the sensor frame, a, passes through the bulk model, which adds axes misalignment and bias:
where ConstantBias is a property of magparams
, and α1, α2, and α3 are given by the first, second, and third elements of the AxesMisalignment property of magparams
.
The bias instability drift β1 modeled as white noise biased and then filtered:
where k is the discrete time step index, BiasInstability is
a property of magparams
,
w is white noise that follows a normal distribution of mean 0 and
variance of 1. The discrete time step size is the reciprocal of the SampleRate
property. [g1,
g2, …,
gn+1] are the
denominator coefficients specified in the
BiasInstabilityCoefficients
property of the magparams
object.
[f1,
f2, …,
fm+1] are the
numerator coefficients of the BiasInstabilityCoefficients
property.
n and m are the orders of the denominator and
numerator coefficients, respectively.
White noise drift is modeled by multiplying elements of the white noise random stream by the standard deviation:
where w is white noise that follows a normal
distribution of mean 0 and variance of 1, SampleRate is an
imuSensor
property, and NoiseDensity is an
magparams
property.
The scale variable s = 2 if the NoiseType
property of the magparams
object is
double-sided and s = 1 if the NoiseType
property is single-sided.
The random walk drift is modeled by biasing elements of the white noise random stream and then filtering:
where k is the discrete time step index, RandomWalk is a
property of magparams
, SampleRate is a
property of imuSensor
, w is white noise that follows
a normal distribution of mean 0 and variance of 1. The discrete time step size is the
reciprocal of the SampleRate
property. The scale variable s = 2 if the
NoiseType
property of the magparams
object is
double-sided and s = 1 if the NoiseType
property is single-sided.
The environmental drift noise is modeled by multiplying the temperature difference from a standard with the temperature bias:
where Temperature is a property of imuSensor
, and TemperatureBias is a property of magparams
. The constant 25 corresponds to a standard temperature.
The temperature scale factor error is modeled as:
where Temperature is a property of imuSensor
, and TemperatureScaleFactor is a property of magparams
. The constant 25 corresponds to a standard temperature.
The quantization is modeled by first saturating the continuous signal model:
and then setting the resolution:
where MeasurementRange is a property of magparams
.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
The object functions, perturbations
and
perturb
, do not support code generation.
Usage notes and limitations:
See System Objects in MATLAB Code Generation (MATLAB Coder).
Version History
Introduced in R2019bR2023b: Specify bias instability noise coefficients and noise type for accelerometer, gyroscope, and magnetometer
You can use the new BiasInstabilityCoefficients
property of the
accelparams
, gyroparams
, and magparams
objects to
specify the coefficients of the transfer function used to generate the bias instability
noise. Additionally, you can use the new NoiseType
property of these
objects to set the scale factor of the noise coefficients as 1
or
2
.
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