measurementJacobian

Jacobian of measurement function

Since R2022a

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Syntax

jac = measurementJacobian(sensor,filter)

Description

jac = measurementJacobian(sensor,filter) returns the Jacobian matrix for the measurement function of the 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.

example

Examples

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Open Live Script

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 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. Note that this example 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: [17×1 double]
         StateCovariance: [17×17 double]
    AdditiveProcessNoise: [17×17 double]
             MotionModel: [1×1 insMotionPose]
                 Sensors: {[1×1 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 ds = stateTransition(~,~,~,~)
            % Return the derivative of the sensor state with respect to
            % time as a structure. 
            ds = struct('Bias',0);
        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

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Sensor model used with an INS filter, specified as an object inherited from the positioning.INSSensorModel abstract class.

INS filter, specified as an insEKF object.

Output Arguments

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Jacobian matrix for the measurement equation, returned as an M-by-N real-valued matrix. M is the dimension of the sensor measurement, and N is the dimension of the state maintained in the State property of the filter.

Version History

Introduced in R2022a

See Also

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