AP_Airspeed: fixup line endings
This commit is contained in:
Kevin Hester
Randy Mackay
parent
c34c4d79f6
commit
d09e871319
@ -1,122 +1,122 @@
|
||||
% Implementation of a simple 3-state EKF that can identify the scale
|
||||
% factor that needs to be applied to a true airspeed measurement
|
||||
% Paul Riseborough 27 June 2013
|
||||
|
||||
% Inputs:
|
||||
% Measured true airsped (m/s)
|
||||
|
||||
clear all;
|
||||
|
||||
% Define wind speed used for truth model
|
||||
vwn_truth = 4.0;
|
||||
vwe_truth = 3.0;
|
||||
vwd_truth = -0.5; % convection can produce values of up to 1.5 m/s, however
|
||||
% average will zero over longer periods at lower altitudes
|
||||
% Slope lift will be persistent
|
||||
|
||||
% Define airspeed scale factor used for truth model
|
||||
K_truth = 1.2;
|
||||
|
||||
% Use a 1 second time step
|
||||
DT = 1.0;
|
||||
|
||||
% Define the initial state error covariance matrix
|
||||
% Assume initial wind uncertainty of 10 m/s and scale factor uncertainty of
|
||||
% 0.2
|
||||
P = diag([10^2 10^2 0.001^2]);
|
||||
|
||||
% Define state error growth matrix assuming wind changes at a rate of 0.1
|
||||
% m/s/s and scale factor drifts at a rate of 0.001 per second
|
||||
Q = diag([0.1^2 0.1^2 0.001^2])*DT^2;
|
||||
|
||||
% Define the initial state matrix assuming zero wind and a scale factor of
|
||||
% 1.0
|
||||
x = [0;0;1.0];
|
||||
|
||||
for i = 1:1000
|
||||
|
||||
%% Calculate truth values
|
||||
% calculate ground velocity by simulating a wind relative
|
||||
% circular path of of 60m radius and 16 m/s airspeed
|
||||
time = i*DT;
|
||||
radius = 60;
|
||||
TAS_truth = 16;
|
||||
vwnrel_truth = TAS_truth*cos(TAS_truth*time/radius);
|
||||
vwerel_truth = TAS_truth*sin(TAS_truth*time/radius);
|
||||
vwdrel_truth = 0.0;
|
||||
vgn_truth = vwnrel_truth + vwn_truth;
|
||||
vge_truth = vwerel_truth + vwe_truth;
|
||||
vgd_truth = vwdrel_truth + vwd_truth;
|
||||
|
||||
% calculate measured ground velocity and airspeed, adding some noise and
|
||||
% adding a scale factor to the airspeed measurement.
|
||||
vgn_mea = vgn_truth + 0.1*rand;
|
||||
vge_mea = vge_truth + 0.1*rand;
|
||||
vgd_mea = vgd_truth + 0.1*rand;
|
||||
TAS_mea = K_truth * TAS_truth + 0.5*rand;
|
||||
|
||||
%% Perform filter processing
|
||||
% This benefits from a matrix library that can handle up to 3x3
|
||||
% matrices
|
||||
|
||||
% Perform the covariance prediction
|
||||
% Q is a diagonal matrix so only need to add three terms in
|
||||
% C code implementation
|
||||
P = P + Q;
|
||||
|
||||
% Perform the predicted measurement using the current state estimates
|
||||
% No state prediction required because states are assumed to be time
|
||||
% invariant plus process noise
|
||||
% Ignore vertical wind component
|
||||
TAS_pred = x(3) * sqrt((vgn_mea - x(1))^2 + (vge_mea - x(2))^2 + vgd_mea^2);
|
||||
|
||||
% Calculate the observation Jacobian H_TAS
|
||||
SH1 = (vge_mea - x(2))^2 + (vgn_mea - x(1))^2;
|
||||
SH2 = 1/sqrt(SH1);
|
||||
H_TAS = zeros(1,3);
|
||||
H_TAS(1,1) = -(x(3)*SH2*(2*vgn_mea - 2*x(1)))/2;
|
||||
H_TAS(1,2) = -(x(3)*SH2*(2*vge_mea - 2*x(2)))/2;
|
||||
H_TAS(1,3) = 1/SH2;
|
||||
|
||||
% Calculate the fusion innovaton covariance assuming a TAS measurement
|
||||
% noise of 1.0 m/s
|
||||
S = H_TAS*P*H_TAS' + 1.0; % [1 x 3] * [3 x 3] * [3 x 1] + [1 x 1]
|
||||
|
||||
% Calculate the Kalman gain
|
||||
KG = P*H_TAS'/S; % [3 x 3] * [3 x 1] / [1 x 1]
|
||||
|
||||
% Update the states
|
||||
x = x + KG*(TAS_mea - TAS_pred); % [3 x 1] + [3 x 1] * [1 x 1]
|
||||
|
||||
% Update the covariance matrix
|
||||
P = P - KG*H_TAS*P; % [3 x 3] *
|
||||
|
||||
% force symmetry on the covariance matrix - necessary due to rounding
|
||||
% errors
|
||||
% Implementation will also need a further check to prevent diagonal
|
||||
% terms becoming negative due to rounding errors
|
||||
% This step can be made more efficient by excluding diagonal terms
|
||||
% (would reduce processing by 1/3)
|
||||
P = 0.5*(P + P'); % [1 x 1] * ( [3 x 3] + [3 x 3])
|
||||
|
||||
%% Store results
|
||||
output(i,:) = [time,x(1),x(2),x(3),vwn_truth,vwe_truth,K_truth];
|
||||
|
||||
end
|
||||
|
||||
%% Plot output
|
||||
figure;
|
||||
subplot(3,1,1);plot(output(:,1),[output(:,2),output(:,5)]);
|
||||
ylabel('Wind Vel North (m/s)');
|
||||
xlabel('time (sec)');
|
||||
grid on;
|
||||
subplot(3,1,2);plot(output(:,1),[output(:,3),output(:,6)]);
|
||||
ylabel('Wind Vel East (m/s)');
|
||||
xlabel('time (sec)');
|
||||
grid on;
|
||||
subplot(3,1,3);plot(output(:,1),[output(:,4),output(:,7)]);
|
||||
ylim([0 1.5]);
|
||||
ylabel('Airspeed scale factor correction');
|
||||
xlabel('time (sec)');
|
||||
grid on;
|
||||
|
||||
% Implementation of a simple 3-state EKF that can identify the scale
|
||||
% factor that needs to be applied to a true airspeed measurement
|
||||
% Paul Riseborough 27 June 2013
|
||||
|
||||
% Inputs:
|
||||
% Measured true airsped (m/s)
|
||||
|
||||
clear all;
|
||||
|
||||
% Define wind speed used for truth model
|
||||
vwn_truth = 4.0;
|
||||
vwe_truth = 3.0;
|
||||
vwd_truth = -0.5; % convection can produce values of up to 1.5 m/s, however
|
||||
% average will zero over longer periods at lower altitudes
|
||||
% Slope lift will be persistent
|
||||
|
||||
% Define airspeed scale factor used for truth model
|
||||
K_truth = 1.2;
|
||||
|
||||
% Use a 1 second time step
|
||||
DT = 1.0;
|
||||
|
||||
% Define the initial state error covariance matrix
|
||||
% Assume initial wind uncertainty of 10 m/s and scale factor uncertainty of
|
||||
% 0.2
|
||||
P = diag([10^2 10^2 0.001^2]);
|
||||
|
||||
% Define state error growth matrix assuming wind changes at a rate of 0.1
|
||||
% m/s/s and scale factor drifts at a rate of 0.001 per second
|
||||
Q = diag([0.1^2 0.1^2 0.001^2])*DT^2;
|
||||
|
||||
% Define the initial state matrix assuming zero wind and a scale factor of
|
||||
% 1.0
|
||||
x = [0;0;1.0];
|
||||
|
||||
for i = 1:1000
|
||||
|
||||
%% Calculate truth values
|
||||
% calculate ground velocity by simulating a wind relative
|
||||
% circular path of of 60m radius and 16 m/s airspeed
|
||||
time = i*DT;
|
||||
radius = 60;
|
||||
TAS_truth = 16;
|
||||
vwnrel_truth = TAS_truth*cos(TAS_truth*time/radius);
|
||||
vwerel_truth = TAS_truth*sin(TAS_truth*time/radius);
|
||||
vwdrel_truth = 0.0;
|
||||
vgn_truth = vwnrel_truth + vwn_truth;
|
||||
vge_truth = vwerel_truth + vwe_truth;
|
||||
vgd_truth = vwdrel_truth + vwd_truth;
|
||||
|
||||
% calculate measured ground velocity and airspeed, adding some noise and
|
||||
% adding a scale factor to the airspeed measurement.
|
||||
vgn_mea = vgn_truth + 0.1*rand;
|
||||
vge_mea = vge_truth + 0.1*rand;
|
||||
vgd_mea = vgd_truth + 0.1*rand;
|
||||
TAS_mea = K_truth * TAS_truth + 0.5*rand;
|
||||
|
||||
%% Perform filter processing
|
||||
% This benefits from a matrix library that can handle up to 3x3
|
||||
% matrices
|
||||
|
||||
% Perform the covariance prediction
|
||||
% Q is a diagonal matrix so only need to add three terms in
|
||||
% C code implementation
|
||||
P = P + Q;
|
||||
|
||||
% Perform the predicted measurement using the current state estimates
|
||||
% No state prediction required because states are assumed to be time
|
||||
% invariant plus process noise
|
||||
% Ignore vertical wind component
|
||||
TAS_pred = x(3) * sqrt((vgn_mea - x(1))^2 + (vge_mea - x(2))^2 + vgd_mea^2);
|
||||
|
||||
% Calculate the observation Jacobian H_TAS
|
||||
SH1 = (vge_mea - x(2))^2 + (vgn_mea - x(1))^2;
|
||||
SH2 = 1/sqrt(SH1);
|
||||
H_TAS = zeros(1,3);
|
||||
H_TAS(1,1) = -(x(3)*SH2*(2*vgn_mea - 2*x(1)))/2;
|
||||
H_TAS(1,2) = -(x(3)*SH2*(2*vge_mea - 2*x(2)))/2;
|
||||
H_TAS(1,3) = 1/SH2;
|
||||
|
||||
% Calculate the fusion innovaton covariance assuming a TAS measurement
|
||||
% noise of 1.0 m/s
|
||||
S = H_TAS*P*H_TAS' + 1.0; % [1 x 3] * [3 x 3] * [3 x 1] + [1 x 1]
|
||||
|
||||
% Calculate the Kalman gain
|
||||
KG = P*H_TAS'/S; % [3 x 3] * [3 x 1] / [1 x 1]
|
||||
|
||||
% Update the states
|
||||
x = x + KG*(TAS_mea - TAS_pred); % [3 x 1] + [3 x 1] * [1 x 1]
|
||||
|
||||
% Update the covariance matrix
|
||||
P = P - KG*H_TAS*P; % [3 x 3] *
|
||||
|
||||
% force symmetry on the covariance matrix - necessary due to rounding
|
||||
% errors
|
||||
% Implementation will also need a further check to prevent diagonal
|
||||
% terms becoming negative due to rounding errors
|
||||
% This step can be made more efficient by excluding diagonal terms
|
||||
% (would reduce processing by 1/3)
|
||||
P = 0.5*(P + P'); % [1 x 1] * ( [3 x 3] + [3 x 3])
|
||||
|
||||
%% Store results
|
||||
output(i,:) = [time,x(1),x(2),x(3),vwn_truth,vwe_truth,K_truth];
|
||||
|
||||
end
|
||||
|
||||
%% Plot output
|
||||
figure;
|
||||
subplot(3,1,1);plot(output(:,1),[output(:,2),output(:,5)]);
|
||||
ylabel('Wind Vel North (m/s)');
|
||||
xlabel('time (sec)');
|
||||
grid on;
|
||||
subplot(3,1,2);plot(output(:,1),[output(:,3),output(:,6)]);
|
||||
ylabel('Wind Vel East (m/s)');
|
||||
xlabel('time (sec)');
|
||||
grid on;
|
||||
subplot(3,1,3);plot(output(:,1),[output(:,4),output(:,7)]);
|
||||
ylim([0 1.5]);
|
||||
ylabel('Airspeed scale factor correction');
|
||||
xlabel('time (sec)');
|
||||
grid on;
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user