两类惯导误差模型（PHI or PSI）（译文）
作者：互联网
PHI or PSI: 2 flavours of error propagation models
In order to be able to write a Kalman filter for your INS, you have to derive a linear error propagation model for your navigation system. In the existing literature, such error propagation models are broadly categorized into 2 groups.
为了使用卡尔曼估计惯导误差，我们需要惯导系统线性误差传播模型的推导。当前各种文献中使用的误差传播模型大致可以分为两类。
The first group is called as PHI-model. This is nothing but the simple perturbation of the equations of kinematics (which are wrongfully called as INS equations among navigation engineers). Because the difference between the true attitude and the INS derived attitude is represented as the letter PHI, this model is called as PHI.
第一种就是PHI角模型，它是在惯导的动力学模型基础上进行扰动分析得到的。因为INS的姿态和真实姿态角之间（P系平台系和真地理系N之间）的误差角使用PHI角表示，因此这个模型叫做PHI角误差模型。
The second group is the PSI-model. In fact, this model is also obtained as a result of a certain perturbation. However, in the PSI-model we perturb the equation of kinematics around a fictitious navigation frame which is called as the “computer frame”. The difference between the INS derived attitude and computer frame is represented as the letter PSI. That is where this name comes from.
第二类误差模型成为PSI模型，也是使用扰动法推导而来。
There are sufficient number of papers in the existing literature describing the derivation of psi-models. Especially the Benson’s short papers on the psi model (both his 1975 and 1978 dated papers) describe everything related with it in plain English. There are some other papers further unifying several concepts and deriving a bunch of other models also. However, Benson’s papers (especially the one titled “A Comparison of Two Approaches to Pure-Inertial and Doppler-Inertial Error Analysis”) is all you need to learn everything regarding PSI models.
已经有许多文献进行了PSI角误差模型的研究，尤其是Benson的文章。在其文章中有详细的PSI角误差模型的推导（ “A Comparison of Two Approaches to Pure-Inertial and Doppler-Inertial Error Analysis”，DOI：10.1109/TAES.1975.308106）
Having learned both the PHI and PSI models, then you will face the real question: which model should you use? This is the main topic of this blog note.
那么应该选择那种模型？
The short answer is that you should prefer the PHI model in all your Kalman filter implementations.
回答如下：
This answer may at first be surprising for you as all the canonical sources about navigation systems usually favours the psi model. So, let me elaborate my answer a little bit more.
所有关于导航系统的规范来源通常都支持psi模型
It is indeed true that PSI-model is more clean than the PHI model as the transport rate is not perturbed in it. Being clean means that less number of floating point calculations are required in the Kalman filter cycles. However, in today’s computing capabilities such a tinny reduction in the model computation is not important at all.
事实上PSI模型比PHI模型更为简洁，因为其 transport rate不受到扰动方程推导的影响，这意味着能够减小浮点计算的负载...虽然现在这一点小小的计算量微不足道了。
Even though psi-model does not have any clear advantage over phi-model, every navigation engineer must definitely learn how to derive PSI model even if he does not use it at all. (I personally had been able to learn the real meaning of navigation frame only after studying the PSI model.) Mostly because of its conceptual importance, navigation engineers learn it in the early stages of their careers and then continue to use it out of habitual tendency. This is in fact the main reason why psi-model is more commonly used in the navigation systems with high-grade sensors.
虽然PSI模型并没有更多明显的优势，但是每一个导航工程师都需要知道PSI模型如何推导，虽然不一定会使用（我自己在学习了PSI角模型之后才真正理解了导航解算的框架）。主要是因为它在概念上的重要性，导航工程师在职业生涯的早期阶段就学习了它，然后出于习惯性的倾向继续使用它。这实际上是为什么psi模型更常用于带有高级传感器的导航系统的主要原因。
On the other hand, psi model has one big disadvantage that makes it not so suitable for low-grade units. One of the significant problems that we face in the design of low-cost systems is the azimuth initialization. High grade system can perform gyro-compasing to reduce the initial attitude uncertainty to the levels suitable for small-angle assumption. However, in low cost system, we almost always have to perform in-motion alignment starting with a large heading uncertainty. Because of the definition of the “computer frame”, the effect of large heading uncertainty manifest itself on the velocity errors in the PSI-models. Therefore both the position and the velocity errors are affected by the non-linearity of the large attitude errors in the PSI-models. On the other hand, the large heading uncertainty only affects the position errors in the PHI-models. Therefore, PHI-models behaves better than PSI-models under large azimuth errors.
另一方面，psi模型有一个很大的缺点，使其不太适合低等级的IMU。在设计低成本系统时，我们面临的一个重要问题是方位角初始化。高精度系统可以进行陀螺自对准，使得初始失准角满足小角度假设。然而，在低成本系统中，我们几乎总是要从大航向误差开始进行动基座初始对准。由于“计算坐标系”的定义，大航向失准角对PSI模型中的速度误差的影响表现出来。因此，位置和速度误差都受到PSI模型中大姿态误差非线性的影响。另一方面，大航向不确定性仅影响PHI模型中的位置误差。因此，在大方位角误差下，PHI模型比PSI模型表现得更好。
As far as I know, in the entire literature it is only Scherzinger who uses a PSI-model based large heading filter. However, in his paper titled “Inertial Navigator Error Models For Large Heading Uncertainty”, he also recognizes the aforementioned difficulty of standard psi-models and therefore proposes a modifed version of it. I find his modified psi-model unnecessarily complex. I cannot see any advantage of his method over much easier (and almost standard) method described in “T. M. Pham, Kalman filter Mechanization for INS airstart, IEEE, 1992″.
据我所知，在整个文献中，只有Scherzinger使用了基于PSI模型的大航向误差角滤波。然而，在其题为“Inertial Navigator Error Models For Large Heading Uncertainty”的论文中，他也认识到标准psi模型的上述困难，因此提出了一种改进版本。我觉得他修改的psi模型不必要地复杂。我看不出他的方法比“T. M. Pham, Kalman filter Mechanization for INS airstart, IEEE, 1992”中描述的更简单（几乎是标准）的方法有任何优势。
As a result, if you are going to desing an INS with low-cost sensors, you should only consider using PHI-models as long as you do not have a robust mean of attitude initialization. You should always remember that under small angle assumption phi and psi models are equivalent. Therefore, there is absolutely no theoretical advantage of choosing one over the other. However, this does not mean that PSI-model is not important. On the contrary, if you are a navigation engineer you have to learn it by heart in order to understand the basic navigation frame concepts.
因此，如果你打算设计一个低成本传感器的惯导系统，只要你没有一个稳健的姿态初始化平均值，你就应该考虑使用PHI模型。您应该始终记住，在小角度假设下，PHI和PSI模型是等效的。因此，从理论上来说，选择其中一个绝对没有优势。然而，这并不意味着PSI模型不重要。相反，如果你是一名导航工程师，你必须背诵它才能理解基本的导航框架概念。
http://instk.org/blog/index.html%3Fp=183.html标签：PHI,PSI,models,模型,psi,惯导,model 来源： https://blog.csdn.net/red_awn/article/details/121394481