MATLAB实现TDOA麦克风阵列声源定位

一、系统设计

1. 硬件配置参数

% 麦克风阵列参数
c = 343;        % 声速(m/s)
fs = 48000;     % 采样率(Hz)
mic_pos = [0,0; 0.1,0; 0.1,0.05; 0,0.1]; % 四麦克风正方形阵列坐标

2. 信号流图

声源 → 麦克风1 → 预处理 → GCC-PHAT → TDOA1
↓               ↓               ↓
麦克风2 → 预处理 → GCC-PHAT → TDOA2
↓               ↓               ↓
麦克风3 → 预处理 → GCC-PHAT → TDOA3
↓               ↓               ↓
麦克风4 → 预处理 → GCC-PHAT → TDOA4

---

二、核心算法

1. 数据采集模块

function [data, t] = acquire_data()
    % 使用声卡采集四通道音频
    d = daq.createSession('ni');
    d.addAnalogInputChannel('Dev1', 0:3, 'Voltage');
    d.Rate = fs;
    duration = 2; % 采集时长(s)
    [data, t] = d.startForeground(duration);
end

2. 预处理模块

function processed = preprocess(raw)
    % 带通滤波(50Hz-4kHz)
    [b,a] = butter(4, [50,4000]/(fs/2));
    filtered = filter(b,a,raw);
    % 去均值和去趋势
    processed = detrend(filtered - mean(filtered));
end

3. GCC-PHAT算法实现

function tau = gcc_phat(x, y)
    N = length(x);
    X = fft(x, N*2);
    Y = fft(y, N*2);
    
    % PHAT加权
    Gxy = (X .* conj(Y)) ./ (abs(X .* conj(Y)) + 1e-10);
    gcc = ifft(Gxy);
    
    % 峰值检测
    [~, idx] = max(abs(gcc));
    tau = (idx - 1) / fs; % 时间延迟(s)
end

4. TDOA计算

% 读取预处理后的信号
[mic1, mic2, mic3, mic4] = deal(preprocessed(:,1), preprocessed(:,2), ...
                               preprocessed(:,3), preprocessed(:,4));

% 计算时延
tau12 = gcc_phat(mic1, mic2);
tau13 = gcc_phat(mic1, mic3);
tau14 = gcc_phat(mic1, mic4);

5. 近场定位解算

% 近场球面波模型
A = [mic_pos(2,:) - mic_pos(1,:); 
     mic_pos(3,:) - mic_pos(1,:);
     (mic_pos(2,:) - mic_pos(1,:)).^2 - (tau12*c).^2, 
     (mic_pos(3,:) - mic_pos(1,:)).^2 - (tau13*c).^2];
b = 0.5*[norm(mic_pos(2,:)-mic_pos(1,:))^2 - (tau12*c)^2 + c^2*tau12^2;
         norm(mic_pos(3,:)-mic_pos(1,:))^2 - (tau13*c)^2 + c^2*tau13^2];

% 最小二乘解
pos = (A' * A) \ (A' * b);

---

三、可视化模块

1. 定位结果展示

figure;
plot3(mic_pos(:,1), mic_pos(:,2), 'ko', 'MarkerSize', 10);
hold on;
plot3(pos(1), pos(2), 'rx', 'MarkerSize', 12, 'LineWidth', 2);
xlabel('X(m)');
ylabel('Y(m)');
grid on;
legend('麦克风阵列', '声源位置');

2. 相关函数分析

figure;
subplot(2,1,1);
plot(abs(gcc_result));
title('GCC相关函数');
xlabel('延迟样本');
ylabel('幅度');

subplot(2,1,2);
plot(tau_est, 'r-o');
title('TDOA估计结果');
xlabel('帧序号');
ylabel('时间延迟(s)');

---

四、常见问题解决方案

1. 时延估计抖动

% 滑动窗口平均
window_size = 10;
tau_avg = movmean(tau_est, window_size);

2. 非刚性阵列形变

% 温度补偿算法
delta_d = 0.001*(temperature-25); % 温度补偿系数
d12 = tau12*c + delta_d;

3. 多声源干扰

% 波束形成技术
W = steering_vector(theta_target); % 目标方向波束
enhanced_signal = W' * mic_signals;

参考代码 基于TDOA 麦克风阵列 算法 声源定位 www.youwenfan.com/contentcnk/70592.html

五、扩展应用

1. 三维定位扩展

   增加Z轴麦克风坐标，使用Chan算法扩展至三维空间：

   A = [mic_pos(2,:) - mic_pos(1,:);
        mic_pos(3,:) - mic_pos(1,:);
        mic_pos(4,:) - mic_pos(1,:)];
   b = 0.5*[norm(mic_pos(2,:)-mic_pos(1,:))^2 - (tau12*c)^2 + c^2*tau12^2;
           norm(mic_pos(3,:)-mic_pos(1,:))^2 - (tau13*c)^2 + c^2*tau13^2;
           norm(mic_pos(4,:)-mic_pos(1,:))^2 - (tau14*c)^2 + c^2*tau14^2];
   pos = (A' * A) \ (A' * b);
   

2. 实时处理优化

   使用MATLAB Parallel Computing Toolbox加速计算：

   parfor i = 1:num_channels
       processed(:,i) = preprocess(raw(:,i));
   end