上篇文章我们以卡尔曼跟踪为例介绍了多维卡尔曼滤波的计算原理：

多维卡尔曼滤波

sdff20201029，公众号：萌萌哒程序猴卡尔曼滤波（2）——多维卡尔曼滤波

  本文我们使用matlab实现对单个目标的连续多帧检测框做卡尔曼滤波，并分别画出原始检测框和滤波检测框的曲线。相信读者结合上篇文章来看本文的代码，会觉得卡尔曼滤波并没有那么复杂。

close all;clear;
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dims = size(det_rect);row = dims(1);
q = 0.0001; Q = diag([q q q q q q q q]);  %8*8，过程噪声协方差矩阵R = diag([0.1 0.1 0.1 0.1]);  %4*4，测量噪声协方差矩阵P = diag([1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0]);  %8*8，误差协方差矩阵F = [1, 0, 0, 0, 1, 0, 0, 0;  %8*8，状态转移矩阵	 0, 1, 0, 0, 0, 1, 0, 0;	 0, 0, 1, 0, 0, 0, 1, 0;	 0, 0, 0, 1, 0, 0, 0, 1;	 0, 0, 0, 0, 1, 0, 0, 0;	 0, 0, 0, 0, 0, 1, 0, 0;	 0, 0, 0, 0, 0, 0, 1, 0;	 0, 0, 0, 0, 0, 0, 0, 1];H = [1, 0, 0, 0, 0, 0, 0, 0;  %4*8，观测矩阵	 0, 1, 0, 0, 0, 0, 0, 0;	 0, 0, 1, 0, 0, 0, 0, 0;	 0, 0, 0, 1, 0, 0, 0, 0];
X = zeros(8, 1);   %状态量：cx cy w h vx vy vw vhX(1) = det_rect(1, 1) + det_rect(1, 3) * 0.5;  %cx = x + w / 2X(2) = det_rect(1, 2) + det_rect(1, 4) * 0.5;  %cy = y + h / 2X(3) = det_rect(1, 3);  %wX(4) = det_rect(1, 4);  %hX(5) = 0;    %初始化变化量为0X(6) = 0;    %初始化变化量为0X(7) = 0;    %初始化变化量为0X(8) = 0;    %初始化变化量为0
result = zeros(dims(1), dims(2));Z = zeros(4, 1);  %观测量：cx cy w h
for i = 1:1:row
    Z(1) = det_rect(i, 1) + det_rect(i, 3) * 0.5;  %cx = x + w / 2    Z(2) = det_rect(i, 2) + det_rect(i, 4) * 0.5;  %cy = y + h / 2    Z(3) = det_rect(i, 3);  %w    Z(4) = det_rect(i, 4);  %h
    %预测步骤    X = F * X;    P = F * P * F' + Q;
    %更新步骤    K = P * H' / (H * P * H' + R);    X = X + K * (Z - H * X);    P = P - K * H * P;
    %保存卡尔曼跟踪结果    result(i, 1) = X(1) - X(3) * 0.5;   %x = cx - w / 2    result(i, 2) = X(2) - X(4) * 0.5;   %y = cy - h / 2    result(i, 3) = X(3);  %w    result(i, 4) = X(4);  %h
end
ori_rest_x = det_rect(:, 1);   %原始xori_rest_y = det_rect(:, 2);   %原始yori_rest_w = det_rect(:, 3);   %原始wori_rest_h = det_rect(:, 4);   %原始h
kal_rest_x = result(:, 1);   %滤波xkal_rest_y = result(:, 2);   %滤波ykal_rest_w = result(:, 3);   %滤波wkal_rest_h = result(:, 4);   %滤波h
xx = 1:1:length(ori_rest_x);
figure,plot(xx, ori_rest_x);hold on;plot(xx, kal_rest_x);legend('原始x', '滤波x');figure,plot(xx, ori_rest_y);hold on;plot(xx, kal_rest_y);legend('原始y', '滤波y');figure,plot(xx, ori_rest_w);hold on;plot(xx, kal_rest_w);legend('原始w', '滤波w');figure,plot(xx, ori_rest_h);hold on;plot(xx, kal_rest_h);legend('原始h', '滤波h');

运行结果：