# Kalman Filter - Can someone help me with to find the bug in my program?

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HF on 7 Nov 2020
Commented: Rena Berman on 6 May 2021
Hello everybody, I am trying to implement the Kalman filter. I found a really good paper, which gives me all the equations I need. However I am not quite sure what value should n have (second equation 9.a) ?
Can someone help me with this?
My code is the following:
%% Kalman Filter
% Parameters
x1 = 1;
x2 = 1;
x3 = 1;
w = 0;
X = [x1, x2, x3];
alpha = 1;
n = 1;
k = 1;
lambda = alpha^2 *(n + k) - n;
betha = 1;
Q = 0;
roh = 1;
R = 0;
W_0_m = lambda / (lambda + n);
W_i = 1/(2*(lambda + n));
W_0_c = (lambda / (lambda + n)) + 1 - alpha^2 + betha;
y_t(:,1) = e; % x-acceleration from the sensor
y_t(:,2) = g; % y-acceleration from the sensor
x_dach = zeros;
L = 200000; % length of the simulation
for z = 1:L
%% A priori estimation
[X_est(1,1), X_est(2,1), X_est(3,1)] = stateequation(X(1), X(2), X(3), w);
for i = 0: 2*n
if i == 0
x_t_dach_m = W_0_m * X_est(i+1);
else
x_t_dach_m = W_i * X_est(i+1)+ x_t_dach_m;
end
end
for j = 0: 2*n
if i== 0
P_t_m = W_0_c * (X_est(i+1)-x_t_dach_m) * (X_est(i+1)-x_t_dach_m);
else
P_t_m = W_i * (X_est(i+1)-x_t_dach_m) * (X_est(i+1)-x_t_dach_m) + P_t_m;
end
end
P_t_m = P_t_m + Q;
X_t_t1 = [x_t_dach_m, x_t_dach_m + gamma * sqrt(P_t_m), x_t_dach_m - gamma * sqrt(P_t_m)];
Y_t_t1 = outputtransformation(X_t_t1(1), X_t_t1(2), roh, v);
for i = 0: 2*n
if i == 0
y_t_dach_m = W_0_m * Y_t_t1(i+1);
else
y_t_dach_m = W_i * Y_t_t1(i+1) + y_t_dach_m;
end
end
%% A posteriori estimation
for i = 0:2*n
if i == 0
Py_y = W_0_c * (Y_t_t1(i+1)-y_t_dach_m) * (Y_t_t1(i+1)-y_t_dach_m);
else
Py_y = W_i * (Y_t_t1(i+1)-y_t_dach_m) * (Y_t_t1(i+1)-y_t_dach_m) + Py_y;
end
end
Py_y = Py_y + R;
for i = 0:2*n
if i == 0
Px_y = W_0_c * (X_t_t1(i+1)-x_t_dach_m) * (X_t_t1(i+1)-x_t_dach_m);
else
Px_y = W_i * (X_t_t1(i+1)-x_t_dach_m) * (X_t_t1(i+1)-x_t_dach_m) + Px_y;
end
end
K_t = Px_y * inv(Py_y);
x_dach(z) = x_t_dach_m + K_t * (y_t - y_t_dach_m);
P_t = P_t_m - K_t * Py_y * K_t;
X = X_t_t1;
end
%% Functions
function [x1_new, x2_new, x3_new] = stateequation (x1, x2, x3, w)
x1_new = 2*cos(x3) * x1 -x2;
x2_new = x1;
x3_new = x3 + w;
end
function y_new = outputtransformation (x1, x2, roh, v)
y_new = -(1 + roh^2) * x1 + roh^2 * x2 + v;
end
##### 3 CommentsShow 1 older commentHide 1 older comment
Rik on 8 Mar 2021
@HF You are allowed to ask for removal of your name from a post (I have so often seen Mathworks staff do this, that I have taken the liberty of removing it from Stephen's post).
Rena Berman on 6 May 2021

Image Analyst on 12 Nov 2020
The program never assigns e and g, so it fails at that point. You need to assign them some values.
HF on 12 Nov 2020
Image Analyst on 12 Nov 2020
If you still have problems, then post the missing code where these other variables are mysteriously put into the workspace. Otherwise people can't run your code and reproduce your error(s).