怎么用matlab编程实现 改进自适应m-h粒子滤波算法

Question

遇到一个项目：一种改进自适应M-H重采样的粒子滤波算法，希望有人能帮我看看🧐🧐。谢谢了🙏🏻🙏🏻

Answer 1

该回答引用ChatGPT GPT-4

运行结果

代码

% 参数初始化
N = 100; % 粒子数
T = 100; % 时刻数
sigma_sys = 1; % 系统噪声标准差
sigma_obs = 1; % 观测噪声标准差

% 生成真实状态序列
true_state = zeros(T, 1);
for t = 2:T
    true_state(t) = true_state(t-1) + randn() * sigma_sys;
end
% 生成粒子
particles = randn(N, T) * sigma_sys;

% 初始化权重
weights = ones(N, 1) / N;

% 用于保存估计状态的变量
state_estimate = zeros(T, 1);

% 模拟过程
for t = 1:T
    % 生成观测值
    observation = true_state(t) + randn() * sigma_obs;
    
    % M-H算法更新粒子
    for n = 1:N
        % 生成提议粒子
        proposal_particle = particles(n, t) + randn() * sigma_sys;
        
        % 计算接受概率
        likelihood_current = normpdf(observation, particles(n, t), sigma_obs);
        likelihood_proposal = normpdf(observation, proposal_particle, sigma_obs);
        acceptance_ratio = min(1, likelihood_proposal / likelihood_current);
        
        % 以接受概率更新粒子
        if rand() < acceptance_ratio
            particles(n, t) = proposal_particle;
        end
    end
    
    % 计算权重
    for n = 1:N
        weights(n) = normpdf(observation, particles(n, t), sigma_obs);
    end
    weights = weights / sum(weights);
    
    % 重采样
    indices = randsample(1:N, N, true, weights);
    particles(:, t) = particles(indices, t);
    
    % 估计状态
    state_estimate(t) = mean(particles(:, t));
end

% 模拟过程
for t = 1:T
    % 生成观测值
    observation = true_state(t) + randn() * sigma_obs;
    
    % 其他代码不变
end

% 绘制结果图形
figure;
plot(1:T, true_state, 'b', 'LineWidth', 2); % 真实状态用蓝色线表示
hold on;
plot(1:T, state_estimate, 'r', 'LineWidth', 2); % 估计状态用红色线表示
scatter(1:T, observation, 'g', 'filled'); % 观测值用绿色点表示
legend('True State', 'Estimated State', 'Observations');
xlabel('Time');
ylabel('State');
title('Improved Adaptive M-H Particle Filter');
grid on;