用matlab语言，考虑正弦信号频率估计问题，在高斯白噪声和高斯色噪声情况下，绘制频率估计的方差随信噪比的变化曲线。其中高斯色噪声由AR1模型产生，模型参数为0.8，运用蒙特卡洛方法，频率真值为0.25，运用网格搜索法进行频率估计

首先，我们需要定义信号和噪声的生成函数：

function [x, n] = generate_signal_noise(fs, f, SNR, N, ar_coeff)
% fs: 采样频率
% f: 正弦信号频率
% SNR: 信噪比
% N: 采样点数
% ar_coeff: AR1模型参数
    t = (0:N-1)/fs;
    x = sin(2*pi*f*t);
    P_signal = var(x);  % 信号功率
    noise_power = P_signal / SNR;  % 噪声功率
    n = sqrt(noise_power) * randn(1, N);
    if nargin == 5
        % 生成高斯色噪声
        n = filter(1, [1, -ar_coeff], n);
    end
end

然后，我们可以定义频率估计函数，这里使用网格搜索法：

function freq_est = freq_estimation(x, fs)
    N = length(x);
    freqs = 0:0.001:0.5;  % 频率搜索范围
    variances = zeros(size(freqs));
    for i = 1:length(freqs)
        f = freqs(i);
        t = (0:N-1)/fs;
        s = sin(2*pi*f*t);
        c = cos(2*pi*f*t);
        X = [s(:), c(:)];
        coeffs = X \ x(:);
        est = atan2(coeffs(1), coeffs(2)) / (2*pi);
        residuals = x(:) - X * coeffs;
        variances(i) = var(residuals);
    end
    [~, idx] = min(variances);
    freq_est = freqs(idx);
end

最后，我们可以运用蒙特卡洛方法，绘制频率估计方差随信噪比的变化曲线：

fs = 1000;
f_true = 0.25;
ar_coeff = 0.8;
SNRs = -10:2:30;  % 信噪比范围
n_trials = 100;  % 实验次数

variances_white = zeros(size(SNRs));
variances_color = zeros(size(SNRs));

for i = 1:length(SNRs)
    SNR = 10^(SNRs(i)/10);
    for j = 1:n_trials
        [x_white, n_white] = generate_signal_noise(fs, f_true, SNR, 1000);
        [x_color, n_color] = generate_signal_noise(fs, f_true, SNR, 1000, ar_coeff);
        freq_est_white = freq_estimation(x_white + n_white, fs);
        freq_est_color = freq_estimation(x_color + n_color, fs);
        variances_white(i) = variances_white(i) + (freq_est_white - f_true)^2/n_trials;
        variances_color(i) = variances_color(i) + (freq_est_color - f_true)^2/n_trials;
    end
end

figure;
plot(SNRs, variances_white, 'b-o', 'linewidth', 2);
hold on;
plot(SNRs, variances_color, 'r-o', 'linewidth', 2);
grid on;
xlabel('信噪比 (dB)');
ylabel('频率估计方差');
legend('高斯白噪声', '高斯色噪声 (AR1, \alpha=0.8)');

运行结果如下所示：