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🔥 内容介绍
一、引言
在对自行车运动进行监测时，由于传感器噪声以及实际环境干扰，获取的自行车在 X、Y 方向上的位置测量值往往存在误差。扩展卡尔曼滤波器（EKF）作为一种处理非线性系统状态估计的有效工具，能够在这种嘈杂测量情况下，较为准确地估计自行车的真实位置。本文将详细阐述如何设计并应用扩展卡尔曼滤波器来实现这一目标。
二、自行车运动模型构建
（一）状态空间模型
⛳️ 运行结果
📣 部分代码
% Written by Professor Mark Mueller, UC Berkeley
%%
% Evaluate a provided solution against many tests.
%%
% Provide the index of the experimental run you would like to use. Note
% that using "0" means that you will load the measurement calibration data.
%%
%==========================================================================
% Here, we run your estimator's initialization
%==========================================================================
clear all;
clc;
% provide the index of the experimental runs
experimentalRun0 = 100;
experimentalRunf = 120;
totalError = 0;
for experimentalRun = experimentalRun0:(experimentalRunf-1),
fprintf(['Run = ', num2str(experimentalRun)])
filename = ['evaluationData/run_' num2str(experimentalRun,'%03d') '.csv'];
experimentalData = csvread(filename);
internalState = estInitialize();
%%
% Here we will store the estimated position and orientation, for later
% plotting:
numDataPoints = size(experimentalData,1);
estimatedPosition_x = zeros(numDataPoints,1);
estimatedPosition_y = zeros(numDataPoints,1);
estimatedAngle = zeros(numDataPoints,1);
dt = experimentalData(2,1) - experimentalData(1,1);
for k = 1:numDataPoints
t = experimentalData(k,1);
gamma = experimentalData(k,2);
omega = experimentalData(k,3);
measx = experimentalData(k,4);
measy = experimentalData(k,5);
%run the estimator:
[x, y, theta, internalState] = estRun(t, dt, internalState, gamma, omega, [measx, measy]);
%keep track:
estimatedPosition_x(k) = x;
estimatedPosition_y(k) = y;
estimatedAngle(k) = theta;
end
% make sure the angle is in [-pi,pi]
estimatedAngle = mod(estimatedAngle+pi,2*pi)- pi;
posErr_x = estimatedPosition_x - experimentalData(:,6);
posErr_y = estimatedPosition_y - experimentalData(:,7);
angErr = mod(estimatedAngle - experimentalData(:,8) + pi, 2*pi) - pi;
ax = sum(abs(posErr_x))/numDataPoints;
ay = sum(abs(posErr_y))/numDataPoints;
ath = sum(abs(angErr))/numDataPoints;
score = ax + ay + ath;
fprintf([' pos x = ' num2str(ax) ' m ']);
fprintf([' pos y = ' num2str(ay) ' m ']);
fprintf([' angle = ' num2str(ath) ' rad ']);
% our scalar score
fprintf(['Average score: ' num2str(score) ' ']);
fprintf('\n');
totalError = totalError + score;
end
fprintf('===========================================\n');
fprintf(['Total score = ',num2str(totalError),'\n'])
)
