外文文献翻译译稿和原文(2)

自适应滤波器是能够根据输入信号自动调整性能进行数字信号处理的数字滤波器。作为对比，非自适应滤波器有静态的滤波器系数，这些静态系数一起组成传

递函数。

对于一些应用来说，由于事先并不知道所需要进行操作的参数，例如一些噪声信号的特性，所以要求使用自适应的系数进行处理。在这种情况下，通常使用自适应滤波器，自适应滤波器使用反馈来调整滤波器系数以及频率响应。

总的来说，自适应的过程涉及到将代价函数用于确定如何更改滤波器系数从而减小下一次迭代过程成本的算法。价值函数是滤波器最佳性能的判断准则，比如减小输入信号中的噪声成分的能力。

随着数字信号处理器性能的增强，自适应滤波器的应用越来越常见，时至今日它们已经广泛地用于手机以及其它通信设备、数码录像机和数码照相机以及医疗监测设备中

假设医院正在监测一个患者的心脏跳动，即心电图，这个信号受到 50 Hz （许多国家供电所用频率）噪声的干扰

剔除这个噪声的方法之一就是使用 50Hz 的陷波滤波器（en:notch filter）对信号进行滤波。但是，由于医院的电力供应会有少许波动，所以我们假设真正的电力供应可能会在 47Hz 到 53Hz 之间波动。为了剔除 47 到 53Hz 之间的频率的静态滤波器将会大幅度地降低心电图的质量，这是因为在这个阻带之内很有可能就有心脏跳动的频率分量。

为了避免这种可能的信息丢失，可以使用自适应滤波器。自适应滤波器将患者的信号与电力供应信号直接作为输入信号，动态地跟踪噪声波动的频率。这样的自适应滤波器通常阻带宽度更小，这就意味着这种情况下用于医疗诊断的输出信号就更加准确。

扩展卡尔曼滤波器

在扩展卡尔曼滤波器（Extended Kalman Filter，简称EKF）中状态转换和观测模型不需要是状态的线性函数，可替换为（可微的）函数。

函数f可以用来从过去的估计值中计算预测的状态，相似的，函数h可以用来以

预测的状态计算预测的测量值。然而f和h不能直接的应用在协方差中，取而代之的是计算偏导矩阵（Jacobian）。

在每一步中使用当前的估计状态计算Jacobian矩阵，这几个矩阵可以用在卡尔曼滤波器的方程中。这个过程，实质上将非线性的函数在当前估计值处线性化了。 这样一来，卡尔曼滤波器的等式为：

预测

使用Jacobians矩阵更新模型

更新

预测

如同扩展卡尔曼滤波器（EKF）一样, UKF的预测过程可以独立于UKF的更新过程之外，与一个线性的（或者确实是扩展卡尔曼滤波器的）更新过程合并来使用；或者，UKF的预测过程与更新过程在上述中地位互换亦可。

外文文献翻译原文1 Kalman filtering, also known as linear quadratic estimation (LQE), is

an algorithm that uses a series of measurements observed over time,

containing noise (random variations) and other inaccuracies, and produces estimates

of unknown variables that tend to be more precise than those based on a single measurement alone. More formally, the Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimate of the

underlying system state. The filter is named after Rudolf (Rudy) E. Kálmán, one of the primary developers of its theory.

The Kalman filter has numerous applications in technology. A common application is for guidance, navigation and control of vehicles, particularly aircraft and spacecraft. Furthermore, the Kalman filter is a widely applied concept in time series analysis used in fields such as signal processing and econometrics. Kalman filters also are one of the main topics in the field of Robotic motion planning and control, and sometimes included in Trajectory optimization.

The algorithm works in a two-step process. In the prediction step, the Kalman filter

produces estimates of the current state variables, along with their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some amount of error, including random noise) is observed, these estimates are updated using a weighted average, with more weight being given to estimates with higher certainty. Because of the algorithm's recursive nature, it can run in real time using only the present input

measurements and the previously calculated state and its uncertainty matrix; no additional past information is required.

It is a common misconception that the Kalman filter assumes that all error terms and measurements are Gaussian distributed. Kalman's original paper derived the filter using orthogonal projection theory to show that the covariance is minimized, and this result does not require any assumption, e.g., that the errors are Gaussian.[1] He then showed that the filter yields the exact conditional probability estimate in the special case that all errors are Gaussian-distributed.

Extensions and generalizations to the method have also been developed, such as

the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The underlying model is a Bayesian model similar to a hidden Markov model but where the state space of the latent variables is continuous and where all latent and observed variables have Gaussian distributions.

The Kalman filters are based on linear dynamic systems discretized in the time domain. They are modelled on a Markov chain built on linear operators perturbed by errors that may include Gaussian noise. The state of the system is represented as a vector of real numbers. At each discrete time increment, a linear operator is applied to the state to generate the new state, with some noise mixed in, and optionally some information from the controls on the system if they are known. Then, another linear operator mixed with more noise generates the observed outputs from the true ("hidden") state. The Kalman

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