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Millimeter-Wave Radar Heart Rate Estimation Method Based on Parameter-Adaptive Multivariate Variational Mode Decomposition
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摘要: 心率作为反映人体健康的核心生理指标，其精准监测在心律失常筛查、冠心病预警、慢性心衰管理等场景中具有重要临床意义。然而，心跳回波信号易受呼吸运动伪影、环境电磁干扰等耦合影响，导致信号信噪比降低，进而影响心率估计的准确性。针对上述问题，该文充分挖掘不同通道间的共有心跳信息，提出一种基于多变量变分模态分解(MVMD)的多通道联合心率估计方法。该方法首先构建以模态总带宽最小化为目标、以重构残差为约束的多通道联合优化模型；其次，利用多通道频谱峰值的累积效应自适应初始化中心频率，从而在多通道数据中稳健分离出具有频率一致性的心跳模态；最后，依据能量最大准则从分解模态中筛选出心率模态，完成心率估计。基于6名受试者的实测数据验证显示，该文所提出的基于多通道联合估计方法的心率中位误差为1.53 bpm，性能优于传统单通道及现有多通道融合心率估计方法。Abstract: Heart rate (HR), a core physiological indicator of human health, is of substantial clinical importance when accurately monitored in applications such as arrhythmia screening, early warning of coronary heart disease, and chronic heart failure management. However, cardiac echo signals are susceptible to coupled disturbances, including respiratory motion artifacts and environmental electromagnetic interference, which degrade the signal-to-noise ratio and compromise HR estimation accuracy. To address these challenges, we propose a multi-channel joint HR estimation method based on multivariate variational mode decomposition that exploits shared cardiac information across different channels. Specifically, the proposed method first constructs a multi-channel joint optimization model that minimizes the total modal bandwidth under reconstruction residual constraints. It then adaptively initialize the center frequency by leveraging the cumulative effect of multi-channel spectral peaks, enabling robust separation of heartbeat modes with consistent frequencies across channels. Finally, the HR mode is selected from the decomposed modes using a maximum energy criterion to complete HR estimation. Validation on real-world data from six subjects demonstrated that the proposed method achieves a median HR error of 1.53 bpm, outperforming conventional single-channel approaches and existing multi-channel fusion-based HR estimation methods.
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图 7 固定初始频率与自适应初始频率心率绝对误差结果对比
Figure 7. Comparison of absolute heart rate errors between fixed and adaptive initial frequencies
图 9 各通道MVMD分解模态波形及其能量分布
Figure 9. Waveforms and energy distribution of MVMD modes for each channel
图 13 多通道预处理后心率频带内的频谱特性对比
Figure 13. Comparison of spectral characteristics within the heart rate band following multi-channel preprocessing
图 15 不同输入信噪比下的心率估计性能对比
Figure 15. Comparison of heart rate estimation performance under different input Signal-to-Noise ratios
1 MVMD算法流程
1. Algorithm of MVMD
Algorithm of MVMD 1: Initialization $\hat{u}_{k,b}^1$, $\omega_k^1 $, $\lambda_b^1 $ 2: repeat 3: for $k\to 1$: K do 4: for $b\to 1$: B do Update mode $\hat{u}_{k,b}$ 5: $u_{k,b}^{n+1}(\omega)=\dfrac{y_b(\omega)-\displaystyle\sum\limits_{i\neq K}u_{i,b}(\omega)+\frac{\lambda_b^n(\omega)}{2}}{1+2\alpha(\omega-\omega_k^n)^2} $ 6: 7: end for 8: end for 9: for $k\to 1$: K do Update center frequency $\omega_k$ 10: $\omega_k^{n+1}=\frac{\displaystyle\sum\limits_{b=1}^B \displaystyle\int\limits_0^\infty \omega|u_{k,b}^{n+1}(\omega)|^2 d\omega}{\displaystyle\sum\limits_{b=1}^B\displaystyle\int\limits_0^\infty |u_{k,b}^{n+1}(\omega)|^2 d\omega}$ 11: end for 12: for $b\to 1$: B do Update $\lambda_b$ for all $\omega\geq 0$ 13: $\lambda_b^{n+1}(\omega)=\lambda_b^n(\omega)+\tau(y_b(\omega)-\displaystyle\sum\limits_{k=1}^K\hat{u}_{k,b}^{n+1}(\omega))$ 14: end for 15: until Convergence 16: $\left\|\omega_k^{(n)}-\omega_k^{(n-1)}\right\|_\infty< \epsilon_1$ & $ \max_{k,b}\left(1-\rho_k^{(n)}(b)\right)<\epsilon_2$ 
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表 1 实测参数Tab. 1Measured Parameters
参数类型 实测数值 中心频率 60.75 GHz 调频斜率 54.7 MHz/us 频带宽度 3.23 GHz 发射功率 12 dBm 采样频率 2.95 MHz 脉冲数 96 帧周期 111 ms 帧数目 2700
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表 2 不同心率估计算法的计算复杂度与耗时对比
Table 2. Comparison of computational complexity and time consumption
算法 时间复杂度 浮点运算次数估算 实际单窗平均耗时(s) VMD O (IKNlog2N) 7.35×107 0.041 EMD O(N2) 1.62×105 0.035 MCA O(BN) 3.24×103 0.028 MRC O(BN) 4.32×103 0.029 PCA O(B2N+ B3) 8.70×103 0.030 所提MVMD方法 O(BIKNlog2N) 2.94×108 0.099
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