Noise Induced Tracking Error (NITE) refers to the tracking error of the mean of the output in feedback control systems with nonlinear instrumentation subject to zero-mean measurement noise. Most of the previous work rely on the stochastic averaging for NITE analysis, the validity of which requires that the bandwidth of the zero mean measurement noise is much higher than that of the system. This is because the results obtained by stochastic averaging are asymptotic with respect to the noise bandwidth. Due to the asymptotic nature of the analysis tool, it is not straightforward to provide a quantitative argument for high bandwidth. An alternative method in the literature that can analyze NITE is stochastic linearization for random input, which is analogous to the well known describing function approach for sinusoidal input. Unlike stochastic averaging, stochastic linearization is not an asymptotic approximation. Therefore, analysis can be carried out for any given noise bandwidth. We carry out NITE analysis using stochastic linearization for a class of LPNI systems that are prone to NITE; identify the system conditions under which the averaging analysis of NITE may yield inaccurate results for a finite noise bandwidth; and prove that the results from the two methods agree as the noise bandwidth approaches infinity. In addition, an existing NITE mitigation strategy is extended based on the proposed method. Numerical examples are given to illustrate the results.

噪声引起的跟踪误差 (NITE) 是指在具有零均值测量噪声的非线性仪器的反馈控制系统中输出均值的跟踪误差。以前的工作大多依赖于随机平均进行 NITE 分析，其有效性要求零均值测量噪声的带宽远高于系统的带宽。这是因为通过随机平均获得的结果相对于噪声带宽是渐近的。由于分析工具的渐近特性，提供高带宽的定量参数并不简单。文献中可以分析 NITE 的另一种方法是随机输入的随机线性化，这类似于众所周知的正弦输入描述函数方法。与随机平均不同，随机线性化不是渐近近似。因此，可以对任何给定的噪声带宽进行分析。我们使用随机线性化对一类容易出现 NITE 的 LPNI 系统进行 NITE 分析；确定在何种系统条件下，NITE 的平均分析可能会为有限噪声带宽产生不准确的结果；并证明当噪声带宽接近无穷大时，两种方法的结果一致。此外，现有的 NITE 缓解策略基于所提出的方法进行了扩展。给出了数值例子来说明结果。我们使用随机线性化对一类容易出现 NITE 的 LPNI 系统进行 NITE 分析；确定在何种系统条件下，NITE 的平均分析可能会为有限噪声带宽产生不准确的结果；并证明当噪声带宽接近无穷大时，两种方法的结果一致。此外，现有的 NITE 缓解策略基于所提出的方法进行了扩展。给出了数值例子来说明结果。我们使用随机线性化对一类容易出现 NITE 的 LPNI 系统进行 NITE 分析；确定在何种系统条件下，NITE 的平均分析可能会为有限噪声带宽产生不准确的结果；并证明当噪声带宽接近无穷大时，两种方法的结果一致。此外，现有的 NITE 缓解策略基于所提出的方法进行了扩展。给出了数值例子来说明结果。