抽象的

The objective of this paper is to compare two gyrocompass' schemes for the detection of Earth's true north. These schemes are refered to as dynamic and static methods. We present a model to characterize the sensitivity of each model as a function of the output signal of the sensor element. We use a fiber optic gyroscope (FOG) as the sensor element.

1.简介

The design and implementation of navigation instruments was greatly improved by the appearance of the laser. The laser allowed the creation of systems that are less prone to be affected by natural external phenomena and at the same time to ease the fabrication. An example of one of these navigation instruments is what is known as Laser Ring Gyroscope (LRG) [1–5]。The appearance of optical fiber allowed for the implementation of fiber gyroscopes based on the principles of the LRG. The main advantages of fiber optic gyroscopes (FOG) [6–9] are the complete isolation of the system to external factors, the confinement of the optical path, the reduction of volume, the large sensitive area, and the high sensitivity that it possesses. These advantages make FOG devices highly reliable and efficient. It is not unusual to find FOGs as a core element in the implementation of gyrocompasses for navigation instruments [10,11]。

The further improvement, development, and design of navigation instruments are topics of actual interest in industry and academia [12]。制造成本和尺寸的降低允许这些仪器在各种车辆（例如汽车，帆船）中找到不同的应用（例如，标题，滚动检测器）。Gyrocompass的设计和表征取决于其使用和应用。因此，有必要对不同的陀螺仪配置进行详细分析[13–16]。由于雾在陀螺仪系统中的相关性，我们分析了雾的输出信号以表征设备并为每个方案应用提出建议。

在本文中，比较了对两个基本陀螺仪方案的输出特性的分析。这两个方案称为静态和动态。在节中2，我们介绍了Gyrocompass对地球真实北部决心的运作的基本原则。在节中3, we present the static scheme and its model. We present the dynamic scheme and model in Section4。在节中5, we present the FOG characteristic measurements of noise and scale factor coefficients. Finally, in Section6得出结论。

2.确定向北方的方向

The most important part in a gyrocompass for true Earth’s north detector is, without doubts, the based FOG speed rotation sensor. This sensor determines the sensitivity characteristics of the gyrocompass. The operation principles of the FOG are analyzed in [17,18]。

为了确定地球真实的北方方向，使用雾气与雾敏感矢量的量表乘积成正比，而输出信号是成比例的[13,14,19,20]。人物1和2(a)show an FOG that is located on a tangential plane, called horizon plane hereafter, referenced to Earth with its sensitive axis parallel to the horizon plane. To take the appropriate measurements needed to determine the true north, the FOG will be rotating perpendicularly to the sensitive axis. The optical radius of the FOG corresponds to the radius of the contour or winding (see Figure3); the direction of the radius is projected like the area of the fiber loop, located on the plane orthogonal to the angular velocity vector [7]。如果the FOG rotation axis is aligned to the North-South axis (which is parallel to the Earth rotation axis), and if its horizon plane is tilted some degrees, similar to the local geographical latitude, then it is possible to measure the Earths’ rotation speed, that is, 15.041 deg/h. Figure2(b)显示了绕垂直轴陀螺仪旋转的正弦输出信号。

通常，确定真正的北方或真正的子午线[21], it is necessary that the sensitivity vector, which is parallel to the horizontal plane, rotates (successively or in fixed angles) around the FOG’s rotation axis. It is also necessary to take- 测量值，，雾的输出信号电压。该输出信号与地球旋转​​矢量的标量产品成正比,和the FOG sensitivity vector,, where the coordinates are created by the angles formed by the vector projections in a Cartesian plane，所以我们有 where,是个geographical latitude point in the Earth where the measure is realized,是之间的角度和theplane,是之间的角度projected in theplane and the轴，是个FOG scale factor coefficient,是个angular speed of the Earth (which has a value of 15.041 deg/h), and是方位角，它是真实的子午线之间的地平面角度，直到雾的灵敏度向量投影。为了计算方位角值，有必要进行几个读数，。如何进行这些测量可以区分静态和动态方法。

两种模型的基础是雾特性的实时测量值。有必要考虑到雾输出信号的变化（相位或强度）。Due to the constant Earth’s speed of rotation, and with the knowledge of the latitude coordinate where the measurements are taken, the output signal of the gyroscope can then be modeled only with the output characteristics and the projections of the terrestrial rotation in the gyroscope sensibility axis. This model describes the real sign very well [21]，但有必要记住，该模型只是一个近似值。由于它没有考虑到外部因素引起的随机误差：平台陀螺仪旋转过程中的振动和温度波动。

3.确定地球真北的静态方法

在这种方法中，有必要在不同位置使用雾的灵敏度向量进行三个或更多的连续读数[13,14]。This can be done by taking measurements while rotating the FOG along its axis at three or more positions, as shown in Figure3。通过这些点处的雾输出的信号处理确定了朝向真实北的方向。第一个测量，, will be our reference, and it is represented by (3)

For the second measurement, we rotate the FOGdegrees from the first point.

For this case, the voltage measurement,，可以通过

In a similar way, a third measurement,，必须采取。这次我们进一步旋转雾学位，获得等效传感器位置测量

然后，一般而言

假如说和已知，然后can be calculated by iterations.

如果和, we have

The resolution limit for this method can be calculated as follows: where是个maximum registered signal at the FOG output as calculated by equation (2). The FOG resolution,is calculated as follows [17]： where,是射击噪声标志，是Kerr效应引起的噪声的迹象，是个sign of noise induced by the Rayleigh dispersion effect,是个sign of noise induced by the birefringence effect;是个quantum efficiency of the photodetector,是统一电子电荷，是视环半径（轮廓），是光纤环的经度，是个Plank’s constant,是真空中的光速吗？是个optical power input in the fiber optic.

4. Dynamic Method of North Determination

Contrary to the static method, in the dynamic method the sensitive axis of the FOG is in constant movement, and this can be achieved by rotating the FOG at constant angular speed [22]。The output signal is, therefore, a sinusoidal wave. As the FOG’s position is modified, a change in phase can be detected. The output signal of the FOG is described by whereω是地球的角速旋转，并且是雾的光半径的方向。在该方案下，在雾的特定圈圈中，进行了测量。阅读是在有限的时间内进行的τ, and can be triggered by a mark or lap counter on the FOG rotational base. The azimuth’s accuracy determination is then described by

Accuracy can be improved if Earth’s rotation speed is calculated constantly and if the azimuth is calculated by a sinusoidal function.是每个触发事件中测量精度的理论限制。它受到触发噪声的限制，，以及副电子的分辨率，。触发噪声限制由 wherea是雾的比例因素，P_r是检测到的光电功率吗？q是个quantum efficiency of the photodetector,是统一电子电荷，是个trigger average time,是个optical ring radius (contour),是个optical ring longitude,是个radiation source wavelength, and是个speed of light in vacuum.

可以通过增加尺度因子（即使用较长的光纤）来增强灵敏度。在这种情况下，检测到的光电功率将降低，并且应优化经度。电子分辨率受类似数字转换器的限制 whereω_d是动态范围，是A/D转换器分辨率（位），并且是测量的数量。

5.雾的特性测量（特征噪声和因子尺度系数）

如前所述，陀螺索的研究和构建基于雾。因此，有必要表征雾性性能。我们对雾的特征噪声和尺度系数感兴趣。我们使用图中所示的实验配置4评估这些参数，这些参数独立于陀螺仪正在起作用的方案。测量是在静态方案下进行的。

5.1. Characteristic Noise

The measured standard deviation (root mean square) is taken as the measurement error of the FOG’s rotation speed, and it is represented by where是个输出电压测量值的值，is average value of the output voltage measurement, and是测量的数量。如果我们增加带宽，则可以减少标准偏差，，测量

We know that; where是时间。特定σ’s value, the characteristic noise at the filter’s bandwidth is calculated by

Besides white noise, the gyroscope output signal contains a component of low-frequency amplitude, which causes a drift in the gyrocompass. The drift is commonly measured in ±[deg/h]. The noise and the drift play different roles depending on the gyroscope application. In stabilization and control systems it is important to have a low noise. For the navigation, the drift is the most important parameter.

5.2。比例因子系数

为了确定比例因子系数，,陀螺仪[21], we use its output signal, shown in Figure2(b), which has a sinusoidal form. Some calculation errors are due for the periodicity of functions like this one. Therefore, for the creation of an FOG with an acceptable dynamic interval, it is necessary to do a special treatment to its output sign.

根据雾的位置，详细阐述了以下方法，以找到比例因数系数 where和对应于研究的间隔，即类似于一半的时间，其相应的相位和。

To measure the real error of the Earths’ rotation speed, it is necessary to obtain the coefficient relative only to a point with coordinates (0,0) in our new coordinated system. We show this in the Figure5, where we obtain

有条件, then we have that。

所以我们得到

We assign the variables和;我们获得最终表达式以确定量表因子的系数。

6. Concluding Comments

考虑到先前暴露的炒锅，我们可以得出以下结论。

（a）静态方法的使用允许减少陀螺索中存在的机械夹具的需求，因为所有测量值都是以静态状态进行的，因此，在旋转平台中，振动不会影响雾输出信号。它的缺点之一是由于陀螺仪从一个点到另一点的旋转时间，稳定时间较长，测量时间的增加。为了使用此方法，有必要提供一个数学模型，能够实时求解先前描述的方程式系统。

（b）动态方法允许使用自动开关系统对真实北方方向进行连续测量。动态方法允许以效率降低低频（漂移），但是只有使用复杂的机械固定装置才能实现这些优势。一个非常重要的缺点是，当减少旋转平台的振动时，同步检测器无法过滤陀螺仪测量信号的信号。

（c）陀螺索的选举取决于雾特征；特别是如果雾具有高度的雾（0.1 deg/h) and very low drift is required. It is preferable to use the prototype with static model. Now, if an FOG is used with low sensibility (within a 1 deg/h order) and with a sufficiently big value of the drift, it is better to use the prototype with dynamic model, which allows to carry out a gyrocompass with the accuracy of the order of some dozens of degrees.

The final election of the FOG and the gyrocompass prototype state is analyzing the costs of all the prototype elements (mechanic and electronic), and also the required accuracy of the gyrocompass.

Acknowledgment

本文得到了Grant J50594 Consejo Nacional de Ciencia yTecnología-México的支持。