stateTransitionJacobian
Description
returns the Jacobian matrix for the state transition function of the
jac
= stateTransitionJacobian(sensor
,filter
,dt
,varargin
)sensor
object inherited from the positioning.INSSensorModel
abstract class.
Note
Implementing this method is optional for a subclass of the positioning.INSSensorModel
abstract class. If you do not implement this
method, the subclass uses a Jacobian matrix calculated by numerical
differentiation.
Examples
Customize Sensor Model Used with insEKF
Customize a sensor model used with the insEKF
object. The sensor measures the velocity state, including a bias affected by random noise.
Customize the sensor model by inheriting from the positioning.INSSensorModel
interface class and implementing its methods. Note that only the measurement
method is required for implementation in the positioning.INSSensorModel
interface class. These sections provide an overview of how the BiasSensor
class implements the positioning.INSSensorModel
methods, but for details on their implementation, see the details of the implementation are in the attached BiasSensor.m
file.
Implement sensorStates
method
To model bias, the sensorStates
method needs to return a state, Bias
, as a structure. When you add a BiasSensor
object to an insEKF
filter object, the filter adds the bias component to the state vector of the filter.
Implement measurement
method
The measurement is the velocity component of the filter state, including the bias. Therefore, return the summation of the velocity component from the filter and the bias.
Implement measurementJacobian
method
The measurementJacobian
method returns the partial derivative of the measurement
method with respect to the state vector of the filter as a structure. All the partial derivatives are 0
, except the partial derivatives of the measurement with respect to the velocity and bias state components.
Implement stateTransition
method
The stateTransiton
method returns the derivative of the sensor state defined in the sensorStates
method. Assume the derivative of the bias is affected by a white noise with a standard deviation of 0.01
. Return the derivative as a structure. Note that this only showcases how to set up the method, and does not correspond to any practical application.
Implement stateTransitionJacobian
method
Since the stateTransiton
function does not depend on the state of the filter, the Jacobian matrix is 0.
Create and add inherited object
Create a BiasSensor
object.
biSensor = BiasSensor
biSensor = BiasSensor with no properties.
Create an insEKF
object with the biSensor
object.
filter = insEKF(biSensor,insMotionPose)
filter = insEKF with properties: State: [17x1 double] StateCovariance: [17x17 double] AdditiveProcessNoise: [17x17 double] MotionModel: [1x1 insMotionPose] Sensors: {[1x1 BiasSensor]} SensorNames: {'BiasSensor'} ReferenceFrame: 'NED'
The filter state contains the bias component.
stateinfo(filter)
ans = struct with fields:
Orientation: [1 2 3 4]
AngularVelocity: [5 6 7]
Position: [8 9 10]
Velocity: [11 12 13]
Acceleration: [14 15 16]
BiasSensor_Bias: 17
Show customized BiasSensor
class
type BiasSensor.m
classdef BiasSensor < positioning.INSSensorModel %BIASSENSOR Sensor measuring velocity with bias % Copyright 2021 The MathWorks, Inc. methods function s = sensorstates(~,~) % Assume the sensor has a bias. Define a Bias state to enable % the filter to estimate the bias. s = struct('Bias',0); end function z = measurement(sensor,filter) % Measurement is the summation of the velocity measurement and % the bias. velocity = stateparts(filter,'Velocity'); bias = stateparts(filter,sensor,'Bias'); z = velocity + bias; end function dzdx = measurementJacobian(sensor,filter) % Compute the Jacobian, which is the partial derivative of the % measurement (velocity plus bias) with respect to the filter % state vector. % Obtain the dimension of the filter state. N = numel(filter.State); % The partial derviative of the Bias with respect to all the % states is zero, except the Bias state itself. dzdx = zeros(1,N); % Obtain the index for the Bias state component in the filter. bidx = stateinfo(filter,sensor,'Bias'); dzdx(:,bidx) = 1; % The partial derivative of the Velocity with respect to all the % states is zero, except the Velocity state itself. vidx = stateinfo(filter,'Velocity'); dzdx(:,vidx) = 1; end function dBias = stateTransition(~,~,dt,~) % Assume the derivative of the bias is affected by a zero-mean % white noise with a standard deviation of 0.01. noise = 0.01*randn*dt; dBias = struct('Bias',noise); end function dBiasdx = stateTransitonJacobian(~,filter,~,~) % Since the stateTransiton function does not depend on the % state of the filter, the Jacobian is all zero. N = numel(filter.State); dBiasdx = zeros(1,N); end end end
Input Arguments
sensor
— Sensor model used with INS filter
object inherited from positioning.INSSensorModel
class
Sensor model used with an INS filter, specified as an object inherited from the positioning.INSSensorModel
abstract class.
filter
— INS filter
insEKF
object
INS filter, specified as an insEKF
object.
dt
— Filter time step
positive scalar
Filter time step, specified as a positive scalar.
Data Types: single
| double
Output Arguments
jac
— Jacobian matrix for state transition equation
S-by-N real-valued matrix
Jacobian matrix for the state transition equation, returned as an
NS-by-N real-valued matrix. S
is the number of fields in the returned structure of the sensorState
method of sensor, and N is the dimension of the state maintained in
the State
property of the filter
.
Version History
Introduced in R2022a
See Also
measurement
| measurementJacobian
| sensorStates
| stateTransition
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