用matlab写ZUPT算法

以下是一个基本的ZUPT算法的Matlab实现，供参考：

function [vel, pos] = zupt(accel, gyro, time, walk)
% ZUPT Algorithm
% 
% Inputs:
%   accel: N x 3 matrix of accelerometer readings (m/s^2)
%   gyro: N x 3 matrix of gyroscope readings (rad/s)
%   time: N x 1 vector of timestamps (s)
%   walk: N x 1 vector of binary indicators of whether or not the user is walking
% 
% Outputs:
%   vel: N x 3 matrix of velocity estimates (m/s)
%   pos: N x 3 matrix of position estimates (m)

% Constants
g = 9.81; % Gravity (m/s^2)
dt = mean(diff(time)); % Time step (s)

% Initializations
N = length(time);
vel = zeros(N, 3);
pos = zeros(N, 3);
R = eye(3);
P = zeros(9);
x = [0;0;0;0;0;0;1;0;0];

% ZUPT Detection
zupt = zeros(N, 1);
for i = 1:N
    if walk(i) == 0
        zupt(i) = 1;
    end
end

% Main Loop
for i = 2:N
    
    % Orientation Update
    w = gyro(i,:)';
    [R, P] = orientation_update(R, P, w, dt);
    
    % Velocity Update
    acc = R*(accel(i,:)' - [0;0;g]);
    [x(1:3), x(4:6), P] = velocity_update(x(1:3), x(4:6), P, acc, zupt(i));
    vel(i,:) = x(1:3)';
    
    % Position Update
    [x(7:9), P] = position_update(x(7:9), P, x(4:6), zupt(i), dt);
    pos(i,:) = x(7:9)';
end

end

function [R, P] = orientation_update(R, P, w, dt)
% Orientation Update

% Constants
q = [1;0;0;0]; % Initial Quaternion
sigma_g = 1e-6; % Gyro Noise Density

% Discrete Time Model
F = eye(4) + 1/2*[0 -w'; w -math_cross(w)]*dt;
G = 1/2*[dt*eye(3); zeros(1,3)]';
Q = sigma_g^2*G*G';

% Predict Step
q = F*q;
P = F*P*F' + Q;

% Normalize Quaternion
q = q/norm(q);

% Correction Step
R = quaternion_to_matrix(q);

end

function [v, dv, P] = velocity_update(v, dv, P, acc, zupt)
% Velocity Update

% Constants
sigma_a = 0.01; % Accelerometer Noise Density
g = 9.81; % Gravity (m/s^2)

% Discrete Time Model
F = eye(3);
G = [eye(3); eye(3)];
H = [zeros(3), eye(3)];
Q = sigma_a^2*eye(6);
R = zeros(3);
if zupt
    R = eye(3)*1e-6;
end

% Predict Step
v = v + dv;
dv = dv + (acc - [0;0;g]);
P = F*P*F' + G*Q*G';

% Correction Step
K = P*H'/(H*P*H' + R);
x = K*(acc - [0;0;g]);
v = v + x(1:3);
dv = dv + x(4:6);
P = (eye(6) - K*H)*P;

end

function [p, P] = position_update(p, P, v, zupt, dt)
% Position Update

% Constants
sigma_v = 0.01; % Velocity Noise Density

% Discrete Time Model
F = eye(3);
G = eye(3)*dt;
H = eye(3);
Q = sigma_v^2*dt*eye(3);
R = zeros(3);
if zupt
    R = eye(3)*1e-6;
end

% Predict Step
p = p + v*dt;
P = F*P*F' + G*Q*G';

% Correction Step
K = P*H'/(H*P*H' + R);
x = K*(p - p);
p = p + x;
P = (eye(3) - K*H)*P;

end

function R = quaternion_to_matrix(q)
% Quaternion to Rotation Matrix Conversion
R = [q(1)^2+q(2)^2-q(3)^2-q(4)^2, 2*(q(2)*q(3)-q(1)*q(4)), 2*(q(2)*q(4)+q(1)*q(3));
     2*(q(2)*q(3)+q(1)*q(4)), q(1)^2-q(2)^2+q(3)^2-q(4)^2, 2*(q(3)*q(4)-q(1)*q(2));
     2*(q(2)*q(4)-q(1)*q(3)), 2*(q(3)*q(4)+q(1)*q(2)), q(1)^2-q(2)^2-q(3)^2+q(4)^2];

end

function c = math_cross(a,b)
% 3D Cross Product
c = [a(2)*b(3) - a(3)*b(2);
     a(3)*b(1) - a(1)*b(3);
     a(1)*b(2) - a(2)*b(1)];

end

使用时，将加速度计、陀螺仪、时间戳和步行标志向量作为输入，即可得到速度和位置估计。请注意，此代码可能需要根据您的特定传感器和应用程序进行调整和改进。