helping with plowing Kalman filter
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For a Kalman filter, i am examining how maneuvering parameters affect tuning a filter.
a target can maneuver with as much as 30 m/s2 acceleration and we have a sensor measurement rate of 2 seconds and a measurement variance sigma^2_v of 1,600 m^2 for a nearly constant velocity (NCV) filter with discrete white noise acceleration (DWNA).
I want to plot the min and max values of measuerment variance sigma^2_v for 2 second update rate, a measurement variance of 1,600 m^2, versus the maximum maneuver accelerations. Plot for accelerations of 5,6,…,70 m/s^2.
this is my matlab code and I think the problem with the vectors becuse when I run the plot I have either no curves or vector diminssion problems
clear all
%
% Write a Matlab script that plots the min and max values of σ_v^2 for 2 second update rate,
% a measurement variance of 1,600 m^2, versus the maximum maneuver accelerations. Plot for accelerations
% of 5,6,…,70 m/s2. Label axes. Be sure to give figure a label and reference the label in the report.
% Parameters:
% sigma_v_min= 26.1776 sigma_v_max= 41.2835 sigma_v^2_min= 685.2667 sigma_v^2_max = 1704.3274
A_max= 70; % the maximum acceleration of the target.
A_min= 5; % the min acceleration of the target.
L= A_max-A_min ;
A_plot= A_min:A_max;
T=2; % time in seconds
T_plot=0:2
sigma_w= 40 % measurement variance, noise error standard deviation
sigma_w2= (sigma_w)^2; % measurement variance sqrt, , noise error standard deviation
% sigma_v_max=41.2835; % max system process error standard deviation
% sigma_v2_min= (sigma_v_min)^2; % sqrt min system process error standard deviation
% sigma_v2_max= (sigma_v_max)^2; % sqrt max system process error standard deviation
%
% calculate % system process error standard deviation Gamma_D=(A_max T^2)/sigma_w
% The design and performance of the filter is characterized
% by the maneuver index or random tracking index
Gamma_D=(A_max*T^2)/sigma_w; % Calculate the maneuver index or random tracking index
Gamma_D_plot= ((A_plot)*(T^2))/sigma_w; % estimate the maneuver index or random tracking index
%
% for sigma_v
% κ_1 (Γ_D )=1.67-0.74 log(Γ_D )+0.26[log(Γ_D ) ]^2, 0.01≤Γ≤10
Gamma_D==0.01:10;
k1_GammaD_max= 1.67-0.7*log(Gamma_D)+0.26*(log(Gamma_D))^2; % max
%
%κ_1^min (Γ_D )=0.87-0.09 log(Γ_D )+0.2[log(Γ_D ) ]^2
k1_GammaD_min= 0.87-0.09*log(Gamma_D)+0.02*(log(Gamma_D))^2 % min
%
% Calculate the sigma_v
%
sigma_v_maxCal= (k1_GammaD_max)*(A_max); % calc sigma_v max
sigma_v_minCal= (k1_GammaD_min)*(A_min); % calc sigma_v min
sigma_v2_maxCal= (sigma_v_maxCal)^2;
sigma_v2_minCal= (sigma_v_minCal)^2;
% calc plot A_max and A_min
A_maxPlot= (sigma_v_maxCal)/(k1_GammaD_max);
A_min_Plot= (sigma_v_minCal)/(k1_GammaD_min);
% plots the min and max values of σ_v^2 for 2 second update rate, a measurement variance of 1,600 m2,
% versus the maximum maneuver accelerations. Plot for accelerations of 5,6,…,70 m/s2.
sigma_v2_min
x_val= [A_min_Plot A_maxPlot sigma_w2];
y_val= A_plot;
plot(x_val,y_val);
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