Main Content


Sensor states

Since R2022a



s = sensorStates(filter,options) returns a structure that describes the states used by the sensor model and tracked by the insEKF filter object.


Implement this method only if you want to estimate sensor-specific states, such as biases, using the filter.


collapse all

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.

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.    

        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);
        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;
        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;
        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);
        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);

Input Arguments

collapse all

INS filter, specified as an insEKF object.

Options for the INS filter, specified as an insOptions object.

Output Arguments

collapse all

State structure, returned as a structure. The field names of the structure are the names of the states that you want estimate. The filter uses the value of each field as the default value of the corresponding state component, and uses the size of the value as the size of the corresponding state component.


You can use the stateparts object function of the insEKF filter object to access the states saved in the filter.

Version History

Introduced in R2022a