Root tracking is a powerful technique that provides insight into the mechanisms of various time-varying processes. The poles and the zeros of a signal-generating system determine the spectral characteristics of the signal under consideration. In this work, time-frequency analysis is achieved by tracking the roots of time-varying processes using autoregressive moving average (ARMA) models in cascade form. A cascade ARMA model is essentially a high-order infinite impulse response (IIR) filter decomposed into a series of first- and second-order sections. Each section is characterized by real or conjugate pole/zero pairs. This filter topology allows individual root tracking as well as immediate stability monitoring and correction. Also, it does not suffer from high round-off error sensitivity, as is the case with the filter coefficients of the direct-form ARMA structure. Instead of using conventional gradient-based recursive methods, we investigate the performance of derivative-free sigma-point Kalman filters for root trajectory tracking over time. Based on simulations, the sigma-point estimators provide more accurate estimates, especially in the case of tightly clustered poles and zeros. The proposed framework is applied to real data, and more specifically, it is used to examine the time-frequency characteristics of raw ultrasonic signals from medical ultrasound images.

根跟踪是一项功能强大的技术，可洞察各种时变过程的机制。信号发生系统的极点和零点决定了所考虑信号的频谱特性。在这项工作中，通过使用级联形式的自回归移动平均（ARMA）模型跟踪时变过程的根源来实现时频分析。级联ARMA模型本质上是分解为一系列一阶和二阶部分的高阶无限冲激响应（IIR）滤波器。每个部分的特征是实数或共轭极点/零对。这种过滤器拓扑结构允许进行单独的根跟踪以及即时的稳定性监视和纠正。而且，它不会遭受较高的舍入误差敏感性，就像直接形式的ARMA结构的滤波器系数一样。代替使用传统的基于梯度的递归方法，我们研究了无导数的sigma-point Kalman滤波器随时间推移跟踪根轨迹的性能。基于模拟，西格玛点估计器可提供更准确的估计，尤其是在极点和零点紧密聚集的情况下。提出的框架应用于实际数据，更具体地说，它用于检查来自医学超声图像的原始超声信号的时频特性。σ点估计器可提供更准确的估计，尤其是在极点和零点紧密聚集的情况下。提出的框架应用于实际数据，更具体地说，它用于检查来自医学超声图像的原始超声信号的时频特性。σ点估计器可提供更准确的估计，尤其是在极点和零点紧密聚集的情况下。提出的框架应用于实际数据，更具体地说，它用于检查来自医学超声图像的原始超声信号的时频特性。