% 交叉定位 - 最小二乘法定位算法模擬

% 參數(shù)設(shè)置
numIterations = 1000; % 模擬迭代次數(shù)
maxDistance = 1000; % 最遠(yuǎn)定位距離（設(shè)定范圍）
speedOfSound = 343; % 聲速（單位：m/s）

% 預(yù)警機(jī)坐標(biāo)
source = [0, 0];

% 初始化結(jié)果
crbResults = zeros(numIterations, 1);
rmseResults = zeros(numIterations, 1);

% 模擬迭代
for i = 1:numIterations
% 隨機(jī)生成無人機(jī)坐標(biāo)
drone = generateRandomPosition(maxDistance);

% 計(jì)算距離
distance1 = calculateDistance(source, drone);
distance2 = calculateDistance(source, drone);% 添加測量誤差
measurement1 = distance1 + normrnd(0, 1);
measurement2 = distance2 + normrnd(0, 1);% 定位算法 - 最小二乘法
estimatedPosition = leastSquaresLocalization(source, measurement1, measurement2, speedOfSound);% 計(jì)算CRB
crb = calculateCRB(source, drone, speedOfSound);
crbResults(i) = crb;% 計(jì)算RMSE
rmse = norm(estimatedPosition - drone);
rmseResults(i) = rmse;

end

% 尋找最遠(yuǎn)定位距離
maxDistanceIdx = find(rmseResults == max(rmseResults));
maxDistanceValue = sqrt(crbResults(maxDistanceIdx));

% 顯示結(jié)果
fprintf(‘最遠(yuǎn)定位距離：%.2f m\n’, maxDistanceValue);

% 生成隨機(jī)位置
function position = generateRandomPosition(maxDistance)
angle = rand * 2 * pi;
distance = rand * maxDistance;
position = distance * [cos(angle), sin(angle)];
end

% 計(jì)算距離
function distance = calculateDistance(source, target)
distance = norm(target - source);
end

% 最小二乘法定位算法
function estimatedPosition = leastSquaresLocalization(source, measurement1, measurement2, speedOfSound)
A = 2 * [source(1) - measurement1(1), source(2) - measurement1(2); …
source(1) - measurement2(1), source(2) - measurement2(2)];
b = [measurement1(1)^2 - source(1)^2 + measurement1(2)^2 - source(2)^2 - speedOfSound^2 * measurement1(3)^2; …
measurement2(1)^2 - source(1)^2 + measurement2(2)^2 - source(2)^2 - speedOfSound^2 * measurement2(3)^2];
estimatedPosition = (A’ * A) \ (A’ * b);
end

% 計(jì)算CRB（Cramér-Rao下界）
function crb = calculateCRB(source, target, speedOfSound)
distance = norm(target - source);
crb = (speedOfSound^2 / (4 * pi^2)) * (1 / distance)^2;
end