本研究提出了一种利用GPS和IMU数据融合的卡尔曼滤波算法，有效提升移动设备在信号弱或无GPS情况下的定位精度与稳定性。
clear all;
N = 100;
T = 4 * pi / N;
t = 0 : (4 * pi - T) : 4 * pi - T;
w = 2 * pi / (24 * 3600);
X1 = zeros(15, N);
X2 = zeros(15, N);
L = zeros(6, N);
% 初始化
X2(:, 1)=[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ,0 ,0 ,0];
X1(:,1)= X2(:,1);
E = eye(15);
% W矩阵定义
W=[zeros(3),-w*eye(3); w*eye(3), zeros(3)];
A=zeros(15, 15);
A(1:3,4:6) = eye(3);
A(4:6,4:6)= -2 * W;
for i=10 : 12
A(i,i)=-1/7200;
end
for i=13 : 15
A(i,i)=-1/1800;
end
A = eye(15)+A*T + A*A*(T.^2)/2;
Z1=zeros(15, 15);
Z2=eye(15);
R=eye(6);
Q=zeros(15, 15);
Q(15, 15)= 1;
K = zeros(15, 6);
H=zeros(6, 15);
for i = 1 : 6
H(i,i) = 1;
end
% 噪声L的生成
for i=1:N
L(:,i)=zeros(6,1);
L(1,i)=randn(1);
end
% 状态更新和预测循环
for i=2 : N
X1(:,i) = A * X2(:,i-1);
Z1=A*Z2*A+Q;
K=Z1*H/(R + H*Z1*H);
X2(:,i)=X1(:,i)+K*(L(:,i)-H*X1(:,i));
Z2=(eye(15) - K * H)*Z1;
end
% 绘图
plot(t, L(1,:), g.);
hold on;
plot(t, X1(1,:), r.);
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