车载雷达生命体征检测：MCSM与RLSRHS算法详解

车载雷达生命体征检测：MCSM + RLSRHS算法详解（Scientific Reports 2025）

论文信息：

• 标题：A radar vital signs detection method in complex environments
• 期刊：Scientific Reports (Nature)
• 发表时间：2026年1月
• 链接：https://www.nature.com/articles/s41598-025-32042-6

---

核心创新

问题定义： 复杂环境下雷达生命体征检测面临两大挑战：

1. 强反射干扰：静态反射物（墙壁、家具）和动态干扰（风扇）掩盖真实目标
2. 呼吸谐波干扰：呼吸谐波频谱落在心率频段，严重干扰心跳检测

核心方法：

1. MCSM算法：基于Range-Doppler谱的矩阵系数选择方法，提升复杂环境目标定位鲁棒性
2. RLSRHS算法：递归最小二乘自适应陷波滤波，自动消除呼吸谐波干扰

性能提升： 复杂环境下心率检测误差 < 7.4 bpm，呼吸检测误差 < 4.9 bpm

---

1. 技术背景

1.1 FMCW雷达原理

import numpy as np

class FMCWRadar:
    """
    FMCW雷达信号模型
    
    频率调制连续波雷达
    """
    
    def __init__(self, config: dict):
        self.fc = config.get("fc", 60e9)      # 载波频率 60GHz
        self.B = config.get("B", 4e9)          # 扫频带宽 4GHz
        self.Tc = config.get("Tc", 100e-6)     # 扫频周期 100μs
        self.c = 3e8                           # 光速
    
    def transmit_signal(self, t: np.ndarray) -> np.ndarray:
        """
        发射信号
        
        s_tx(t) = exp(j * 2π * (fc*t + B/(2Tc) * t^2))
        """
        phase = 2 * np.pi * (
            self.fc * t + 
            self.B / (2 * self.Tc) * t**2
        )
        return np.exp(1j * phase)
    
    def receive_signal(self, t: np.ndarray, target_distance: float, 
                       breathing_amp: float, breathing_freq: float,
                       heartbeat_amp: float, heartbeat_freq: float) -> np.ndarray:
        """
        接收信号（含生命体征调制）
        
        胸部位移 = 呼吸幅度 * sin(2π * f_br * t) + 心跳幅度 * sin(2π * f_hr * t)
        """
        # 时间延迟
        td = 2 * target_distance / self.c
        
        # 胸部位移
        chest_displacement = (
            breathing_amp * np.sin(2 * np.pi * breathing_freq * t) +
            heartbeat_amp * np.sin(2 * np.pi * heartbeat_freq * t)
        )
        
        # 接收信号
        phase = 2 * np.pi * (
            self.fc * (t - td + chest_displacement) +
            self.B / (2 * self.Tc) * (t - td)**2
        )
        
        return np.exp(1j * phase)
    
    def mix_signal(self, tx: np.ndarray, rx: np.ndarray) -> np.ndarray:
        """
        混频（中频信号）
        
        IF = tx * conj(rx)
        """
        return tx * np.conj(rx)

1.2 生命体征信号特征

class VitalSignsParams:
    """
    生命体征参数
    
    正常成人范围
    """
    
    # 呼吸频率 (Hz)
    BREATHING_FREQ_RANGE = (0.1, 0.5)  # 6-30 次/分钟
    
    # 心率频率 (Hz)
    HEART_RATE_FREQ_RANGE = (0.8, 2.0)  # 48-120 次/分钟
    
    # 胸壁位移幅度 (mm)
    BREATHING_AMPLITUDE = (4, 12)  # 呼吸引起的胸壁位移
    HEARTBEAT_AMPLITUDE = (0.2, 0.5)  # 心跳引起的胸壁位移
    
    @staticmethod
    def get_physiological_params(age_group: str = "adult"):
        """
        根据年龄组获取生理参数
        
        Args:
            age_group: adult, child, infant
        """
        params = {
            "adult": {
                "breathing_freq": (0.2, 0.33),  # 12-20 次/分钟
                "heart_rate_freq": (1.0, 1.67),  # 60-100 次/分钟
            },
            "child": {
                "breathing_freq": (0.33, 0.5),  # 20-30 次/分钟
                "heart_rate_freq": (1.33, 2.0),  # 80-120 次/分钟
            },
            "infant": {
                "breathing_freq": (0.5, 0.83),  # 30-50 次/分钟
                "heart_rate_freq": (2.0, 2.67),  # 120-160 次/分钟
            }
        }
        return params.get(age_group, params["adult"])

---

2. MCSM算法详解

2.1 算法原理

问题： 复杂环境中强反射体（金属家具、墙壁）和动态干扰（风扇、行人）掩盖真实目标。

解决方案： MCSM（Matrix Coefficient Selection Method）基于Range-Doppler谱，结合幅度和相位信息进行目标定位。

class MCSMAlgorithm:
    """
    MCSM算法：复杂环境目标检测
    
    Matrix Coefficient Selection Method
    """
    
    def __init__(self, num_chirps: int = 128, num_samples: int = 256):
        self.num_chirps = num_chirps
        self.num_samples = num_samples
    
    def compute_range_doppler(self, if_signal: np.ndarray) -> np.ndarray:
        """
        计算Range-Doppler谱
        
        Args:
            if_signal: 中频信号 (num_chirps, num_samples)
        
        Returns:
            range_doppler: Range-Doppler谱 (num_chirps, num_samples)
        """
        # 距离FFT
        range_fft = np.fft.fft(if_signal, axis=1)
        
        # 多普勒FFT
        range_doppler = np.fft.fftshift(
            np.fft.fft(range_fft, axis=0),
            axes=0
        )
        
        return np.abs(range_doppler)
    
    def suppress_static_clutter(self, range_doppler: np.ndarray) -> np.ndarray:
        """
        静态杂波抑制
        
        低频零化：消除零多普勒频率分量
        """
        suppressed = range_doppler.copy()
        
        # 零多普勒区域置零
        zero_doppler_range = 2
        center = self.num_chirps // 2
        suppressed[center-zero_doppler_range:center+zero_doppler_range, :] = 0
        
        return suppressed
    
    def compute_matrix_coefficient(self, range_doppler: np.ndarray) -> np.ndarray:
        """
        计算矩阵系数
        
        M = |A|^α * |φ|^β
        
        A: 幅度
        φ: 相位
        α, β: 权重系数
        """
        # 幅度
        amplitude = np.abs(range_doppler)
        
        # 相位
        phase = np.angle(range_doppler)
        
        # 矩阵系数
        alpha = 0.7
        beta = 0.3
        
        matrix_coeff = np.power(amplitude, alpha) * np.power(np.abs(phase), beta)
        
        return matrix_coeff
    
    def detect_target(self, if_signal: np.ndarray) -> dict:
        """
        目标检测
        
        Returns:
            target_info: 目标距离、速度信息
        """
        # 1. Range-Doppler谱
        rd = self.compute_range_doppler(if_signal)
        
        # 2. 杂波抑制
        rd_clean = self.suppress_static_clutter(rd)
        
        # 3. 矩阵系数
        mc = self.compute_matrix_coefficient(rd_clean)
        
        # 4. 目标定位（最大值）
        max_idx = np.unravel_index(np.argmax(mc), mc.shape)
        doppler_idx, range_idx = max_idx
        
        # 5. 计算距离和速度
        distance = self._range_idx_to_distance(range_idx)
        velocity = self._doppler_idx_to_velocity(doppler_idx)
        
        return {
            "distance": distance,
            "velocity": velocity,
            "confidence": mc[max_idx]
        }
    
    def _range_idx_to_distance(self, range_idx: int) -> float:
        """
        Range索引转距离
        """
        # 距离分辨率 = c / (2 * B)
        range_resolution = 3e8 / (2 * 4e9)  # 约37.5mm
        return range_idx * range_resolution
    
    def _doppler_idx_to_velocity(self, doppler_idx: int) -> float:
        """
        Doppler索引转速度
        """
        # 速度分辨率 = λ / (2 * N * Tc)
        wavelength = 3e8 / 60e9  # 5mm
        velocity_resolution = wavelength / (2 * self.num_chirps * 100e-6)
        
        # 频移
        doppler_shift = doppler_idx - self.num_chirps // 2
        
        return doppler_shift * velocity_resolution

---

3. RLSRHS算法详解

3.1 算法原理

问题： 呼吸谐波频谱落在心率频段，严重干扰心跳检测。

解决方案： RLSRHS（Recursive Least Squares Respiratory Harmonic Suppression）自适应消除呼吸谐波。

class RLSRHSAlgorithm:
    """
    RLSRHS算法：呼吸谐波抑制
    
    Recursive Least Squares Respiratory Harmonic Suppression
    """
    
    def __init__(self, filter_order: int = 32, forget_factor: float = 0.99):
        """
        Args:
            filter_order: 滤波器阶数
            forget_factor: 遗忘因子（越接近1，记忆越长）
        """
        self.L = filter_order
        self.lambda_ = forget_factor
        
        # 初始化
        self.w = np.zeros(filter_order, dtype=complex)  # 滤波器系数
        self.P = np.eye(filter_order) * 1000  # 逆相关矩阵
    
    def process(self, signal: np.ndarray, breathing_freq: float, 
                fs: float = 100) -> np.ndarray:
        """
        处理信号，消除呼吸谐波
        
        Args:
            signal: 输入信号
            breathing_freq: 呼吸频率 (Hz)
            fs: 采样率 (Hz)
        
        Returns:
            cleaned_signal: 消除谐波后的信号
        """
        n_samples = len(signal)
        cleaned = np.zeros(n_samples, dtype=complex)
        
        # 生成参考信号（呼吸信号及其谐波）
        t = np.arange(n_samples) / fs
        
        for i in range(self.L, n_samples):
            # 当前采样点
            d = signal[i]
            
            # 参考信号向量
            x = self._generate_reference(t[i], breathing_freq)
            
            # RLS更新
            y = np.dot(self.w.conj(), x)  # 滤波器输出
            e = d - y  # 误差信号
            
            # 增益向量
            Px = np.dot(self.P, x)
            k = Px / (self.lambda_ + np.dot(x.conj(), Px))
            
            # 更新滤波器系数
            self.w = self.w + k * e.conj()
            
            # 更新逆相关矩阵
            self.P = (self.P - np.outer(k, np.dot(x.conj(), self.P))) / self.lambda_
            
            # 输出：误差信号（消除呼吸谐波后的心跳信号）
            cleaned[i] = e
        
        return cleaned
    
    def _generate_reference(self, t: float, breathing_freq: float) -> np.ndarray:
        """
        生成参考信号
        
        包含基频和谐波（2倍、3倍...）
        """
        reference = np.zeros(self.L, dtype=complex)
        
        for harmonic in range(1, 4):  # 1倍、2倍、3倍谐波
            freq = breathing_freq * harmonic
            phase = 2 * np.pi * freq * t
            reference[harmonic-1::3] = np.exp(1j * phase)
        
        return reference

3.2 完整生命体征提取流程

class VitalSignsExtractor:
    """
    完整生命体征提取流程
    
    集成MCSM + RLSRHS
    """
    
    def __init__(self):
        self.mcsm = MCSMAlgorithm()
        self.rlsrhs = RLSRHSAlgorithm()
    
    def extract(self, if_signal: np.ndarray, fs: float = 100) -> dict:
        """
        提取生命体征
        
        Args:
            if_signal: 中频信号
            fs: 采样率
        
        Returns:
            vital_signs: 心率、呼吸频率
        """
        # 1. 目标定位
        target = self.mcsm.detect_target(if_signal)
        print(f"[检测] 目标距离: {target['distance']:.2f}m")
        
        # 2. 提取相位信号（包含生命体征）
        phase_signal = self._extract_phase(if_signal, target)
        
        # 3. 初步估计呼吸频率
        breathing_freq = self._estimate_breathing_freq(phase_signal, fs)
        print(f"[检测] 呼吸频率: {breathing_freq*60:.1f} 次/分钟")
        
        # 4. 消除呼吸谐波
        cleaned_signal = self.rlsrhs.process(phase_signal, breathing_freq, fs)
        
        # 5. 提取心跳频率
        heart_rate_freq = self._estimate_heart_rate(cleaned_signal, fs)
        print(f"[检测] 心率: {heart_rate_freq*60:.1f} 次/分钟")
        
        return {
            "breathing_rate_bpm": breathing_freq * 60,
            "heart_rate_bpm": heart_rate_freq * 60,
            "target_distance_m": target["distance"]
        }
    
    def _extract_phase(self, if_signal: np.ndarray, target: dict) -> np.ndarray:
        """
        提取相位信号
        """
        # 简化：直接使用目标距离处的相位
        phase = np.angle(if_signal[:, int(target["distance"] / 0.0375)])
        return np.unwrap(phase)
    
    def _estimate_breathing_freq(self, phase: np.ndarray, fs: float) -> float:
        """
        估计呼吸频率
        """
        # FFT
        fft_result = np.fft.fft(phase)
        freqs = np.fft.fftfreq(len(phase), 1/fs)
        
        # 呼吸频段搜索
        breathing_band = (freqs >= 0.1) & (freqs <= 0.5)
        fft_breathing = np.abs(fft_result[breathing_band])
        freqs_breathing = freqs[breathing_band]
        
        # 峰值频率
        peak_idx = np.argmax(fft_breathing)
        return np.abs(freqs_breathing[peak_idx])
    
    def _estimate_heart_rate(self, cleaned: np.ndarray, fs: float) -> float:
        """
        估计心率
        """
        # FFT
        fft_result = np.fft.fft(cleaned)
        freqs = np.fft.fftfreq(len(cleaned), 1/fs)
        
        # 心率频段搜索
        hr_band = (freqs >= 0.8) & (freqs <= 2.0)
        fft_hr = np.abs(fft_result[hr_band])
        freqs_hr = freqs[hr_band]
        
        # 峰值频率
        peak_idx = np.argmax(fft_hr)
        return np.abs(freqs_hr[peak_idx])


# 使用示例
if __name__ == "__main__":
    # 模拟数据
    num_chirps = 128
    num_samples = 256
    
    # 生成中频信号
    t = np.linspace(0, 1, num_chirps)
    if_signal = np.random.randn(num_chirps, num_samples) + \
                0.5 * np.sin(2 * np.pi * 0.25 * t[:, np.newaxis]) + \
                0.1 * np.sin(2 * np.pi * 1.2 * t[:, np.newaxis])
    
    # 提取生命体征
    extractor = VitalSignsExtractor()
    vitals = extractor.extract(if_signal)
    
    print(f"\n最终结果:")
    print(f"  呼吸: {vitals['breathing_rate_bpm']:.1f} 次/分钟")
    print(f"  心率: {vitals['heart_rate_bpm']:.1f} 次/分钟")

---

4. 实验结果

4.1 性能对比

方法	HR误差 (bpm)	RR误差 (bpm)
传统FFT	15.2	8.3
EMD分解	12.1	6.5
VMD分解	9.8	5.2
MCSM + RLSRHS	7.4	4.9

4.2 复杂环境测试

环境	目标定位成功率	HR误差	RR误差
空房间	99.5%	5.1	3.2
有风扇	97.2%	6.8	4.1
多人场景	94.8%	8.2	5.5
强反射环境	92.3%	9.1	6.2

---

5. IMS 应用启示

5.1 车载部署架构

graph LR
    A[60GHz FMCW雷达] --> B[Range-Doppler处理]
    B --> C[MCSM目标定位]
    C --> D[相位提取]
    D --> E[RLSRHS谐波抑制]
    E --> F[HR/RR估计]
    F --> G[DMS融合]

5.2 硬件配置建议

参数	推荐值	说明
频段	60GHz	穿透性好，分辨率高
带宽	4GHz	距离分辨率~37mm
扫频周期	100μs	平衡精度和速度
Chirp数/帧	128	多普勒分辨率

5.3 与DMS融合

class IMSVitalSignsFusion:
    """
    IMS生命体征融合
    
    雷达生命体征 + 摄像头疲劳检测
    """
    
    def __init__(self):
        self.radar_extractor = VitalSignsExtractor()
        self.camera_detector = None  # 摄像头疲劳检测
    
    def assess_driver_state(self, radar_signal, camera_image):
        """
        综合评估驾驶员状态
        """
        # 雷达生命体征
        vitals = self.radar_extractor.extract(radar_signal)
        
        # 摄像头疲劳指标
        fatigue = self.camera_detector.detect(camera_image)
        
        # 融合决策
        if vitals["heart_rate_bpm"] > 100 and fatigue["perclos"] > 0.3:
            return "HIGH_RISK"
        elif fatigue["perclos"] > 0.2:
            return "MODERATE_RISK"
        else:
            return "NORMAL"

---

6. 总结

方面	内容
MCSM	Range-Doppler谱目标定位，抗复杂环境干扰
RLSRHS	自适应滤波消除呼吸谐波，提取心跳信号
性能	HR误差<7.4bpm, RR误差<4.9bpm
部署	60GHz FMCW雷达，实时处理

---

参考链接：

1. 论文原文: https://www.nature.com/articles/s41598-025-32042-6
2. TI AWR1642: https://www.ti.com/product/AWR1642
3. FMCW雷达原理: https://www.ti.com/lit/wp/spyy005/spyy005.pdf