WO2022253198A1 - 一种间接测量重力的方法及系统 - Google Patents
一种间接测量重力的方法及系统 Download PDFInfo
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- 230000005484 gravity Effects 0.000 title claims abstract description 90
- 238000000034 method Methods 0.000 title claims abstract description 34
- 230000001133 acceleration Effects 0.000 claims abstract description 89
- 230000008859 change Effects 0.000 claims abstract description 46
- 239000013598 vector Substances 0.000 claims abstract description 29
- 238000005259 measurement Methods 0.000 claims abstract description 16
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- 230000006870 function Effects 0.000 claims description 10
- 238000012544 monitoring process Methods 0.000 claims description 9
- 238000004590 computer program Methods 0.000 claims description 8
- 230000005358 geomagnetic field Effects 0.000 claims description 3
- 238000004364 calculation method Methods 0.000 description 6
- 238000005516 engineering process Methods 0.000 description 5
- 230000008569 process Effects 0.000 description 4
- QSHDDOUJBYECFT-UHFFFAOYSA-N mercury Chemical compound [Hg] QSHDDOUJBYECFT-UHFFFAOYSA-N 0.000 description 2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
- G01V7/02—Details
- G01V7/06—Analysis or interpretation of gravimetric records
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/12—Simultaneous equations, e.g. systems of linear equations
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
Definitions
- the invention relates to the technical field of measurement, in particular to a technical solution for indirectly measuring gravity.
- Gravity measurement plays an important role in geodesy, geophysics, resource exploration, marine research and military affairs.
- the current gravity measurement methods mainly include laser interference, atomic interference, springs, superconductivity and other technologies.
- laser interference atomic interference
- springs superconductivity
- superconductivity mainly include laser interference, atomic interference, springs, superconductivity and other technologies.
- its structure is complex and the conditions of use are harsh.
- the present invention proposes a technical solution for indirectly measuring gravity.
- the present invention proposes a method for indirectly measuring gravity, which is based on the synthesis of the gravitational force produced by celestial bodies, the gravitational force produced by the earth, and other inertial forces, resulting in changes in the gravitational acceleration of the position to be measured.
- f() is the difference in direction with respect to The function
- the way to obtain the gravity measurement result of the position to be measured is by inversion, according to its own coordinates Find the approximate value of the acceleration vector caused by the earth at the current position As the initial solution, calculate the estimated data of the change in the direction of the acceleration of gravity, combined with the observation data of the change in the direction of the acceleration of gravity, through the corresponding equations of the change in the direction of the acceleration of gravity, iteratively linearize the solution until the error is less than the error limit, and the gravity measurement result is obtained.
- an inclinometer is used to measure the direction of gravity.
- high-precision clocks such as atomic clocks or GNSS timing equipment are used to obtain the current time.
- the self-coordinates adopt a current approximate position obtained from GNSS positioning or inertial positioning equipment or geomagnetic field positioning equipment.
- the celestial bodies include the sun and the moon.
- acceleration vector obtained above and Perform vector synthesis to form acceleration vectors at four or more moments i 1...k, k+1, k is an integer not less than 3;
- the present invention also provides a system for indirectly measuring gravity, which is used to implement the above-mentioned method for indirectly measuring gravity.
- the memory is used to store program instructions
- the processor is used to call the stored instructions in the memory to execute the method for indirectly measuring gravity as described above.
- a readable storage medium is included, and a computer program is stored on the readable storage medium.
- the computer program is executed, the above-mentioned method for indirect gravity measurement is realized.
- the present invention utilizes the relationship between the gravitational force produced by celestial bodies and the gravitational force produced by the earth and other inertial forces are constantly changing, resulting in extremely weak changes in the direction of gravity at this place, the direction of force is the direction of acceleration, the magnitude of acceleration and the magnitude of force Proportional. Measuring acceleration is therefore equivalent to measuring force.
- the change over time at each position is different, and by regularly monitoring the change in the direction of the acceleration of gravity at this position, the gravity can be reversed.
- the change in the direction of gravity can be measured only by an inclinometer.
- the scheme of the invention is simple and convenient to implement, has strong practicability, solves the problems of low practicability and inconvenient practical application in related technologies, can improve user experience, and has important market value.
- the gravity of the earth is actually the resultant force of gravitation and inertial force.
- the present invention utilizes the gravitational force produced by celestial bodies, the gravitational force produced by the earth, and the relationship between other inertial forces are constantly changing, resulting in extremely weak changes in the direction of gravity at this place.
- the direction of force is the direction of acceleration.
- the magnitude of acceleration and force proportional to the size of . Measuring acceleration is therefore equivalent to measuring force.
- the change over time at each position is different, and by regularly monitoring the change in the direction of the acceleration of gravity at this position, the gravity can be reversed. Changes in the direction of gravity can be measured with an inclinometer.
- the gravitational acceleration it receives is formed by the vector synthesis of several forces: the gravitational force of the earth, the moon, the sun and other planets, the centrifugal force formed by the rotation of the earth, the centrifugal force in the earth-moon system, The centrifugal force in the sun-earth system, and the gravitational force on it from other objects that cannot be ignored (such as nearby heavy objects).
- These forces are divided into two categories according to whether they are constant in the short run or changing all the time:
- the first category short-term constant: the gravitational force formed by the earth, the centrifugal force formed by the earth's rotation, generally speaking, the nearby heavy objects will not change much in the short term;
- the second category always changing with time: the universal gravitational force formed by the moon, the sun and other planets; the centrifugal force in the earth-moon system and the sun-earth system.
- the direction and magnitude of gravity can be accurately calculated only by knowing the time and its own position.
- the gravitational force of the earth cannot be directly calculated by the formula, because the earth is an uneven object with internal The structure is very complicated, and the influence of these factors on the gravity of the earth is huge, and the gravitational force cannot be directly calculated by using the universal gravitational formula.
- the change in the direction of gravity caused by the moon on ground objects is on the order of 10 -6 arc seconds, and if the change is to be accurately extracted, the accuracy of the inclinometer needs to reach at least 10 -10 arc seconds .
- the change in the direction of gravity caused by the moon on ground objects is on the order of 10 -5 arcseconds, and if the change is to be accurately extracted, the accuracy of the inclinometer needs to reach at least 10 -7 arcseconds.
- the change in the direction of gravity caused by the moon on ground objects is on the order of 10 -4 arc seconds, and if the change is to be accurately extracted, the accuracy of the required inclinometer must reach at least 10 -5 arc seconds.
- the change in the direction of gravity caused by the moon on ground objects is on the order of 10 -3 arc seconds, and if the change is to be accurately extracted, the accuracy of the inclinometer needs to reach at least 10 -4 arc seconds.
- the change in direction of gravity caused by the sun is about 1/3 that of the moon.
- the above considers that the sun-earth and earth-moon systems are non-inertial systems.
- the influence of other planets is smaller, and the influence of planets such as Venus, Mars, Jupiter, Mercury and Saturn can be considered with higher precision.
- the existing technology already has the ability to accurately calculate the trajectories of these celestial bodies, and only needs to know the exact time.
- the precision clock technology is also very advanced.
- the accuracy of the current cesium clock can easily reach the level of 10 -14 /5Day, which can guarantee that the error within one year will not exceed 100ps.
- Observations of tilt can achieve an accuracy of 10 -5 arcseconds.
- Precise positioning can also be carried out by means such as GNSS.
- the conditions for calculating gravity according to the direction change of universal gravitation have been met. Obviously, the higher the accuracy of the inclinometer, the shorter the interval observation time can be, the shorter the calculation period is, and the higher the accuracy of the result is.
- a capacitive inclinometer only needs a plate area of about 100 square millimeters, a pendulum length of 50 millimeters, and a spacing of 0.25 millimeters. Its size is like a thermos cup, and the accuracy of 10 -5 arc seconds can be achieved.
- Optical inclinometers are also at similar levels. It's just that before this, there was no need for a more accurate inclinometer.
- the technical solution of the present invention can be realized by using a corresponding customized inclinometer. Therefore, it can be predicted that the positioning method described in the present invention may promote the further improvement of the accuracy of the inclinometer market products.
- the measuring method that the present invention proposes is:
- Calculate the angle between two adjacent gravitational accelerations that is, more than three calculated direction differences ⁇ V 1 , ⁇ V 2 , ⁇ V 3 ...
- ⁇ 1 , ⁇ 2 , ⁇ 3 ... should be equal to ⁇ V 1 , ⁇ V 2 , ⁇ V 3 ... and in fact, is the required unknown. Since ⁇ V 1 , ⁇ V 2 , ⁇ V 3 ... are and a function of time, so the above formula for calculating the angle difference can be expressed as:
- t 1 , t 2 , t 3 , t 4 ... are known accurate observation values
- ⁇ V 1 , ⁇ V 2 , ⁇ V 3 ... are known observation values ⁇ 1 , ⁇ 2 , ⁇ 3 ...
- f ( ) is the difference in direction about The function. Therefore, the above formula becomes a system of equations with three unknowns, including at least three formulas, so if nothing else, it has a unique solution.
- This equation is a nonlinear equation, which can be solved by Taylor expansion and iteration. Get the acceleration caused by the earth's gravity After that, it is vector-combined with the acceleration formed by other forces, which is the acceleration of gravity at this place.
- the number of observations can be increased to obtain an overdetermined equation system, and then solved using methods such as least squares.
- a method for indirectly measuring gravity is provided, and its specific examples are as follows: (for simplification, this example only considers the gravitational influence caused by the moon and the sun, and assumes that the current precise position can be obtained. If you want Considering other factors, you only need to add the corresponding conditions according to this example. If you can’t get the current position, you need to repeat steps 2, 3, and 4 at least 7 times (that is, observe the data more than 7 times), and at the same time compare your own position and The current gravity vector has a total of 6 unknowns to solve)
- Required equipment high-precision clock (generally use atomic clock or GNSS timing equipment), computing equipment (computer or other equipment with processor and memory can be used), precision inclinometer, own coordinate acquisition equipment, that is, positioning equipment (such as GNSS or inertial navigation positioning equipment, geomagnetic field positioning equipment);
- Tilt angle ⁇ 1 , ⁇ 2 , ⁇ 3 , ⁇ 4 ... and current position (If there is a positioning device such as GNSS, the position can be observed)
- step f the two steps b and c are to calculate the function with time as the independent variable
- step d is to calculate the function with time as the independent variable and time are functions of independent variables, where is an unknown quantity, and time is a known quantity.
- step e is based on the four steps b, c, and d, so ⁇ V i is actually function, so we have the following equations:
- f() is the difference in direction with respect to The function.
- Equation 1 Equation 1
- Equation 2 Gv is the Jacobian matrix corresponding to f(), is the variation between the current solution and the previous solution (the first iteration is the initial solution), ⁇ ( ⁇ V) is the variation of the acceleration direction value between the current solution and the previous solution (the first iteration is the initial solution), Substituting ⁇ i into Equation 2, we get while the current solution At this time, the solution of the gravitational force of the earth has been updated, Compare Closer to the actual Earth's gravity at the observation point. Iterates like this until If it is less than the predetermined limit, the iteration ends, the current solution is taken as the final solution, and the measurement is completed.
- the k value will be greater than 3, so as to obtain overdetermined equations, improve the reliability of the results, and further use
- it is solved by methods such as least squares, so as to obtain the acceleration vector formed by the gravity of the earth at the current position And then combined with the acceleration formed by other forces in steps a, b, and c, the acceleration of gravity at this place can be obtained.
- the method proposed by the technical solution of the present invention can be implemented by those skilled in the art using computer software technology to realize the automatic operation process.
- the system device for realizing the method is, for example, a computer-readable storage medium that stores the corresponding computer program of the technical solution of the present invention and includes a computer that runs the corresponding computer program.
- the computer equipment of the program should also be within the protection scope of the present invention.
- a system for indirect measurement of gravity including a processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the above-mentioned indirect measurement of gravity system. method.
- a system for indirectly measuring gravity including a readable storage medium, on which a computer program is stored, and when the computer program is executed, the above-mentioned indirect gravity measurement system is realized.
- a method of measuring gravity is provided, including a readable storage medium, on which a computer program is stored, and when the computer program is executed, the above-mentioned indirect gravity measurement system is realized.
- multiple inclinometers can be used to make a difference to eliminate certain errors and obtain more accurate and reliable results.
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Abstract
一种间接测量重力的方法及系统，基于天体产生的万有引力、地球产生的万有引力以及其他惯性力影响的合成，导致待测位置的重力加速度发生变化，通过定期监测待测位置的重力加速度方向变化，反推得到该待测位置的重力测量结果；监测重力加速度的方向变化时，测量各个时刻重力的方向，得到重力加速度的方向变化观测数据；根据自身坐标求得当前位置的地球引起的加速度矢量的概略值作为初始解，计算重力加速度方向变化估测数据，结合重力加速度方向变化观测数据，进行迭代线性化求解得到重力测量结果。
Description
本发明涉及测量技术领域，具体涉及一种间接测量重力的技术方案。
重力测量在大地测量、地球物理、资源勘查、海洋研究以及军事方面有着重要地位。目前的重力测量方法主要有激光干涉、原子干涉、弹簧、超导等技术，其精度不断在提高，技术也由最早的自由落体法向着量子、超导等方向拓展。但其结构复杂，使用条件苛刻。
发明内容
为了解决上述现有技术中存在的不足，本发明提出了一种间接测量重力的技术方案。
为了实现上述目的，本发明提出一种间接测量重力的方法，基于天体产生的万有引力、地球产生的万有引力以及其他惯性力影响的合成，导致待测位置的重力加速度发生变化，通过定期监测待测位置的重力加速度方向变化，反推得到该待测位置的重力测量结果；监测重力加速度的方向变化时，测量各个时刻t
1,t
2,…,t
k+1重力的方向θ
1,θ
2,…,θ
k+1，得到重力加速度的方向变化观测数据Δθ
i＝θ
i+1–θ
i，i＝1…k；设根据坐标
时刻、相关天体位置，能够求出在
处各个时刻t
1,t
2,…,t
k+1各个力的合成形成的加速度矢量为V
1,V
2,…,V
k+1，则加速度的方向变化估测数据ΔV
i＝V
i+1-V
i，i＝1…k，k为不小于3的整数，设当前的地球引起的万有引力造成的加速度为三维矢量
建立如下的重力加速度的方向变化相应方程组，
其中，f()是方向的差值关于
的函数；
反推得到待测位置的重力测量结果实现方式为，根据自身坐标
求得 当前位置的地球引起的加速度矢量的概略值
作为初始解，计算重力加速度方向变化估测数据，结合重力加速度方向变化观测数据，通过重力加速度的方向变化相应方程组，进行迭代线性化求解直至收敛到误差小于误差限，得到重力测量结果。
而且，监测重力加速度的方向变化时，采用倾斜仪实现测量重力的方向。
而且，定期监测待测位置的重力加速度变化时，采用原子钟或者GNSS授时设备等高精度时钟获取当前时刻。
而且，所述自身坐标采用根据GNSS定位或者惯性定位设备或者地磁场定位设备得到的当前的概略位置。
而且，所述自身坐标未知时，通过观测7次以上的数据，将自身位置和当前重力矢量一共6个未知数求解。
而且，所述天体包括太阳和月亮。
而且，计算重力加速度方向变化估测数据，实现方式如下，
根据自身位置、地球自转速度计算地球自转造成的加速度矢量
根据时刻、月球质量、月球坐标、万有引力常数、地心坐标、自身位置计算在地月系统中的加速度a
em及其方向v
em；
根据时刻、太阳质量、太阳坐标、万有引力常数、地心坐标、自身位置计算在日地系统中的加速度a
se及其方向v
se；
设将以上得到的加速度矢量与
进行矢量合成，形成四个或以上时刻的加速度矢量
i＝1…k,k+1，k为不小于3的整数；
根据
计算加速度方向的夹角ΔV
i,ΔV
i＝V
i+1-V
i，得到加速度的方向变化估测数据。
另一方面，本发明还提供一种间接测量重力的系统，用于实现如上所述的一种间接测量重力的方法。
而且，包括处理器和存储器，存储器用于存储程序指令，处理器用于调用存储器中的存储指令执行如上所述的一种间接测量重力的方法。
或者，包括可读存储介质，所述可读存储介质上存储有计算机程序，所述计算机程序执行时，实现如上所述的一种间接测量重力的方法。
本发明利用了天体产生的万有引力与地球产生的万有引力以及其他惯性力的关系不断在变化，导致该处的重力方向发生极其微弱的变化，力的方向就是加速度的方向，加速度的大小和力的大小成正比。因此测量加速度与测量力是等价的。而每一个位置上随着时间的变化都是不同的，通过定期监测该位置的重力加速度方向变化，即可反推出重力。实施时只需通过倾斜仪即可测量出重力方向的变化。
本发明方案实施简单方便，实用性强，解决了相关技术存在的实用性低及实际应用不便的问题，能够提高用户体验，具有重要的市场价值。
以下结合实施例具体说明本发明的技术方案。
地球重力其实是万有引力和惯性力的合力。本发明即是利用了天体产生的万有引力与地球产生的万有引力以及其他惯性力的关系不断在变化，导致该处的重力方向发生极其微弱的变化，力的方向就是加速度的方向，加速度的大小和力的大小成正比。因此测量加速度与测量力是等价的。而每一个位置上随着时间的变化都是不同的，通过定期监测该位置的重力加速度方向变化，即可反推出重力。通过倾斜仪即可测量出重力方向的变化。
设在地球某处，其在地心地固坐标系下的坐标为
那么在任意时刻，其所受到的重力加速度是由这么几种力的矢量合成而形成的：地球、月球、太阳以及其他星球对其的万有引力，地球自转形成的离心力，地月系统中的离心力，日地系统中的离心力，以及其他不能忽略的物体(例如附近的重物)对其的万有引力。按照短期恒定不变与始终在变化对这些力分为两大类：
第一类，短期恒定不变的：地球形成的万有引力，地球自转形成的离心力，通常来说，附近的重物短期内也不会有很大的变化；
第二类：始终在随着时间变化的：月球、太阳以及其他星球形成的万有引力；地月系统以及日地系统中的离心力。
对于第二类力，虽然随着时间在变化，但是其运行规律早已经被人们熟知，只需要知道时间，就可以准确计算其大小和方向。
理论上来说，只需要精确知道时间，又知道自身位置，就可以精确计算重力的方向和大小，然而由于地球的引力实际上并不能直接由公式准确算得，因为地球是一个不均匀的物体，内部结构十分复杂，而这些因素对地球引力的影响是巨大的，不能使用万有引力公式直接计算其引力。但是，通过重力方向的变化来反推重力却是可行的。这样既可以不被水平方向所干扰，又能通过差的方法减弱甚至消除掉大多数其他因素的误差，例如重力异常等。
从目前掌握的知识，地球周围有很多天体，但是因为这些天体的质量以及和地球之间的距离不同，他们对重力的影响是不同的。影响最大的是月球，其次是太阳，再其次是金星、火星、木星、水星和土星。由于目前的仪器水平尚不能测量出金星等星体对地球的万有引力的影响，因此在此暂不予考虑。待以后仪器的精度水平提高后，再进行考虑，从而进一步提高观测精度。
通过计算，有如下结果：
每间隔1秒钟，月球对地面物体造成的重力方向的影响变化量为10
-6角秒量级，而如果要准确提取其变化量，需要的倾斜仪的精度至少需要达到10
-10角秒。
每间隔1分钟，月球对地面物体造成的重力方向的影响变化量为10
-5角秒量级，而如果要准确提取其变化量，需要的倾斜仪的精度至少需要达到10
-7角秒。
每间隔10分钟，月球对地面物体造成的重力方向的影响变化量为10
-4角秒量级，而如果要准确提取其变化量，需要的倾斜仪的精度至少需要达到10
-5角秒。
每间隔60分钟，月球对地面物体造成的重力方向的影响变化量为10
-3角秒量级，而如果要准确提取其变化量，需要的倾斜仪的精度至少需要达到10
-4角秒。
太阳造成的重力方向变化大约为月球的1/3。以上考虑了日地、地月系统为非惯性系。其他星球造成的影响更小，其中金星、火星、木星、水星和土星等行星的影响如果考虑则精度更高。
目前，现有技术已经能够已经有能力对这些天体的运行轨迹进行精确计算，只需要知道准确的时刻即可。而目前精密时钟技术也非常先进，现在的铯钟，精度可以轻易达到10
-14/5Day的水平，可以保证1年的误差不超过100ps。对于倾斜的观测可以达到10
-5角秒的精度。通过GNSS等手段，也可以进行精确定位。基于以上设备，已经具备了根据万有引力方向变化计算重力的条件。显然，倾斜仪的精度越高，则间隔观测时间可以越短，计算的周期也就越短，结果的精度也越高。从目前的技术来说，倾斜仪精度的提高要远比提高重力仪精度容易，且成本也低得多。例如电容式倾斜仪，只需要极板面积100平方毫米左右，摆长50毫米，间距0.25毫米，其大小如同保温杯，即可达到10
-5角秒的精度。光学法倾斜仪的也在相似水平。只是在此以前，没有更高精度的倾斜仪这种需求。具体实施时，可以采用相应的定制倾斜仪实现本发明技术方案。因此可以预见，本发明所述的定位方法可能会促进倾斜仪市场产品的精度进一步提高。
本发明提出的测量方法为：
1)设定当前的地球引起的万有引力造成的加速度为三维矢量
短时间内，地球引起的 万有引力的方向和大小变化很小，可以认为是恒定的。在一定的时间间隔，在至少4个时刻t
1,t
2,t
3,t
4观测倾斜仪的角度θ
1,θ
2,θ
3,θ
4…，然后将相邻的两个观测值作差，可以得到三个以上观测值差Δθ
1,Δθ
2,Δθ
3…Δθ
1＝θ
2-θ
1,
Δθ
2＝θ
3-θ
2,
Δθ
3＝θ
4-θ
3
…
2)再根据
时刻、星体位置，可以准确求出各个时刻前面提到的除了地球引力造成的加速度之外的各个加速度的三维矢量
(i＝1…k,k+1，k为不小于3的整数)，将其与而在这些时刻地球引起的万有引力造成的加速度做矢量合成，即得到该处的重力加速度矢量
(i＝1…k,k+1，k为不小于3的整数)。计算相邻两个重力加速度的夹角，即可以求得3个以上计算方向差ΔV
1,ΔV
2,ΔV
3…
ΔV
1＝V
2-V
1,
ΔV
2＝V
3-V
2,
ΔV
3＝V
4-V
3,
…
3)如果
就是倾斜仪所在位置的准确的加速度，那么Δθ
1，Δθ
2，Δθ
3…应该分别等于ΔV
1，ΔV
2，ΔV
3…而事实上，
是需要求的未知数。由于ΔV
1，ΔV
2，ΔV
3…是
以及时间的函数，因此以上的计算角度差的算式可以表达为：
其中，t
1，t
2，t
3，t
4…均为已知的精确观测值，而ΔV
1，ΔV
2，ΔV
3…是已知的观测值Δθ
1，Δθ
2，Δθ
3…，f()是方向的差值关于
的函数。因此上式成为了一个有三个未知数的方程组，包含了至少三个公式，因此不出意外的话，其有唯一解。该方程是非线性方程，可 以通过泰勒展开、迭代求解。得到地球引力形成的加速度
后，将其与其他的力形成的加速度进行矢量合成，即为该处的重力加速度。
为了能够缩短收敛时间，并提高定位的成功率，可以用
计算该处地球万有引力形成的加速度作为初始解。
为了达到更精确的解，可以增加观测次数，以得到超定方程组，然后使用最小二乘等方法求解。
即使不知道自身位置，也可以通过增加观测次数到至少7次，从而得到6个以上的方程，将自身位置也当成未知数一并计算得到。但这样无疑增加了观测时间以及计算量。
以上涉及的计算方法均为成熟的方法，具体过程不再赘述。
为便于实施参考起见，提供一种间接测量重力的方法，其具体实施例如下：(为简化表述，该实施例仅考虑月球、太阳造成的引力影响，并假设可以得到当前的精确位置。如果要考虑其它因素，只需要仿照该例加入相应的条件即可。如果无法得到当前位置，则需要至少重复2，3，4步骤7次(即观测7次以上的数据)，并且同时将自身位置和当前重力矢量一共6个未知数求解)
1，所需的设备：高精密时钟(一般用原子钟或者GNSS授时设备)，计算设备(可采用计算机或者其他带处理器和存储器的设备)，精密倾斜仪，自身坐标获取设备，即定位设备(如GNSS或者惯性导航定位设备、地磁场定位设备)；
2，从高精密时钟获取当前时刻(年月日时分秒)，根据当前时刻计算月球、太阳等天体的位置；由于最终要计算自身在地球上的位置，因此一般使用地心地固坐标系；该计算方法是既有方法，不再详述；
3，测量当前重力的方向(倾斜仪的倾斜角度)；
4，间隔一段时间；
5，从定位设备获取当前位置
6，重复步骤2，3，4一共执行至少4个循环，从而得到至少4组数据：
观测时刻：t
1，t
2，t
3，t
4…
月球坐标：
太阳坐标：
倾斜角度：θ
1，θ
2，θ
3，θ
4…以及当前位置
(如果有定位设备如GNSS，就可以观测得到位置)
7，由于经过了航行、晃动等过程，不能保证倾斜仪观测到的角度是绝对倾斜角度，因此需要根据倾斜角度θ
1，θ
2，θ
3，θ
4…计算倾斜角度的变化量Δθ
i＝θ
i+1–θ
i,(i＝1…k，k为不小于3的整数)，从而得到至少3个倾斜角度变化量Δθ
1，Δθ
2，Δθ
3…，即重力加速度的方向变化观测数据；
8，由
以及观测时刻t
i，月球坐标
太阳坐标
(i＝1…k，k为不小于3的整数)，可以求得在
处，每个观测时刻的地球引力大小Ae和方向Ve，月球引力大小Am和方向Vm，太阳引力大小As和方向Vs，以及地球自转、地月系统中、日地系统中的离心力的大小和方向。由这些可以进一步计算合力的大小和方向。这个合力的大小和方向应该与观测值一致；
9，根据
求得当前位置的地球引起的加速度矢量的概略值
此即为初始解；
10，设所处位置由地球引力形成的加速度矢量为
根据初始解
以及步骤6中得到的天体坐标数据(月球坐标和太阳坐标)，计算4个或以上时刻的万有引力(同时也是加速度)的大小和方向分别求差值(即重力加速度的方向变化估测数据)，然后基于步骤7得到的重力加速度的方向变化观测数据，根据设定的误差限，进行迭代，直至收敛到误差小于误差限，即可求得
从而可以进一步求得该处的重力加速度。具体实现过程如下：
a)根据自身位置、地球自转速度计算地球自转造成的加速度矢量
b)根据时刻、月球质量、月球坐标、万有引力常数、地心坐标、自身位置计算在地月系统中的加速度a
em及其方向v
em；
c)根据时刻、太阳质量、太阳坐标、万有引力常数、地心坐标、自身位置计算在日地系统中的加速度a
se及其方向v
se；
d)设将以上a,b,c三个步骤得到的三个加速度矢量与
进行矢量合成，形成四个或以上时刻的加速度矢量
(i＝1…k,k+1，k为不小于3的整数)；
e)根据
计算加速度方向的夹角ΔV
i,ΔV
i＝V
i+1-V
i，(i＝1…k，k为不小于3的整数)，即加速度的方向变化估测数据：
ΔV
1＝V
2-V
1,
ΔV
2＝V
3-V
2,
ΔV
3＝V
4-V
3…
f)其中b,c两个步骤均是计算以时间为自变量的函数，而d步骤是计算以
和时间为自变量的函数，其中
是未知量，时间是已知量。而步骤e的结果是基于b,c,d四个步骤的，因此ΔV
i实为
的函数，因此有如下的方程组：
其中，f()是方向的差值关于
的函数。
残差ωi＝ΔV
i-Δθ
i(i＝1…k，k为不小于3的整数)，只有
是观测点处地球引力的准确值的时候，残差才为0，Δθ
i均为已知的观测量。因此f()也是残差ωi关于
的函数。
在
处，将方程1进行泰勒展开实施线性化，可以得到：
其中，Gv是对应于f()的雅各比矩阵，
是当前解与上一次解(第一次迭代则为初始解)的变化量，Δ(ΔV)为当前解与上一次的解(第一次迭代则为初始解)加速度方向值的变化量，将ωi代入方程2，即可得到
而当前解
此时已经将地球引力值得解进行了更新，
比
更接近观测点实际的地球引力。如此迭代，直到
小于预定限值则结束迭代，将当前解作为最终解，完成测量。
通常，k值会大于3，从而得到超定方程组，提高结果的可靠性，进一步以
作为初始解，通过最小二乘等方法求解，从而得到当前位置地球引力形成的加速度矢量
进而与步骤a,b,c中的其他力形成的加速度合成，即可得到该处的重力加速度。
具体实施时，本发明技术方案提出的方法可由本领域技术人员采用计算机软件技术实现自动运行流程，实现方法的系统装置例如存储本发明技术方案相应计算机程序的计算机可读存储介质以及包括运行相应计算机程序的计算机设备，也应当在本发明的保护范围内。
在一些可能的实施例中，提供一种间接测量重力的系统，包括处理器和存储器，存储器用于存储程序指令，处理器用于调用存储器中的存储指令执行如上所述的一种间接测量重力的方法。
在一些可能的实施例中，提供一种间接测量重力的系统，包括可读存储介质，所述可读存储介质上存储有计算机程序，所述计算机程序执行时，实现如上所述的一种间接测量重力的方法。
在一些可能的实施例中,可以使用多台倾斜仪做差分以消除某些误差，得到更精确和可靠的结果。
本文中所描述的具体实施例仅仅是对本发明精神作举例说明。本发明所属技术领域的技术人员可以对所描述的具体实施例做各种各样的修改或补充或采用类似的方式替代，但并不 会偏离本发明的精神或者超越所附权利要求书所定义的范围。
Claims (10)
- 一种间接测量重力的方法，其特征在于：基于天体产生的万有引力、地球产生的万有引力以及其他惯性力影响的合成，导致待测位置的重力加速度发生变化，通过定期监测待测位置的重力加速度方向变化，反推得到该待测位置的重力测量结果；监测重力加速度的方向变化时，测量各个时刻t 1,t 2,…,t k+1重力的方向θ 1,θ 2,…,θ k+1，得到重力加速度的方向变化观测数据Δθ i＝θ i+1–θ i，i＝1…k；设根据坐标时刻、相关天体位置，能够求出在
处各个时刻t 1,t 2,…,t k+1各个力的合成形成的加速度矢量为V 1,V 2,…,V k+1，则加速度的方向变化估测数据ΔV i＝V i+1-V i，i＝1…k，k为不小于3的整数，设当前的地球引起的万有引力造成的加速度为三维矢量
建立如下的重力加速度的方向变化相应方程组，
其中，f()是方向的差值关于的函数；
反推得到待测位置的重力测量结果实现方式为，根据自身坐标求得当前位置的地球引起的加速度矢量的概略值
作为初始解，计算重力加速度方向变化估测数据，结合重力加速度方向变化观测数据，通过重力加速度的方向变化相应方程组，进行迭代线性化求解直至收敛到误差小于误差限，得到重力测量结果。
- 根据权利要求1所述间接测量重力的方法，其特征在于：监测重力加速度的方向变化时，采用倾斜仪实现测量重力的方向。
- 根据权利要求1所述间接测量重力的方法，其特征在于：定期监测待测位置的重力加速度变化时，采用原子钟或者GNSS授时-高精度时钟获取当前时刻。
- 根据权利要求1所述间接测量重力的方法，其特征在于：所述自身坐标采用根据GNSS定位、惯性定位设备或者地磁场定位设备得到的当前的概略位置。
- 根据权利要求1所述间接测量重力的方法，其特征在于：所述自身坐标未知时，通过观测7次以上的数据，将自身位置和当前重力矢量一共6个未知数求解。
- 根据权利要求1或2或3或4或5所述间接测量重力的方法，其特征在于：所述天体包括太阳和月亮。
- 根据权利要求6所述间接测量重力的方法，其特征在于：计算重力加速度方向变化估测数据，实现方式如下，根据自身位置、地球自转速度计算地球自转造成的加速度矢量
根据时刻、月球质量、月球坐标、万有引力常数、地心坐标、自身位置计算在地月系统中的加速度a em及其方向v em；根据时刻、太阳质量、太阳坐标、万有引力常数、地心坐标、自身位置计算在日地系统中的加速度a se及其方向v se；设将以上得到的加速度矢量与进行矢量合成，形成四个或以上时刻的加速度矢量
k为不小于3的整数；
根据计算加速度方向的夹角ΔV i,ΔV i＝V i+1-V i，得到加速度的方向变化估测数据。
- 一种间接测量重力的系统，其特征在于：用于实现如权利要求1-7任一项所述的一种间接测量重力的方法。
- 根据权利要求8所述间接测量重力的系统，其特征在于：包括处理器和存储器，存储器用于存储程序指令，处理器用于调用存储器中的存储指令执行如权利要求1-7任一项所述的一种间接测量重力的方法。
- 根据权利要求8所述间接测量重力的系统，其特征在于：包括可读存储介质，所述可读存储介质上存储有计算机程序，所述计算机程序执行时，实现如权利要求1-7任一项所述的一种间接测量重力的方法。
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| CN108267792A (zh) * | 2018-04-13 | 2018-07-10 | 武汉大学 | 全球重力场模型反演方法 |
| CN111366984A (zh) * | 2020-03-23 | 2020-07-03 | 东华理工大学 | 一种基于重力卫星星间激光测距系统确定引力场模型的方法 |
| CN113311495A (zh) * | 2021-05-31 | 2021-08-27 | 武汉大学 | 一种间接测量重力的方法及系统 |
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| CN113311495A (zh) | 2021-08-27 |
| US20240142660A1 (en) | 2024-05-02 |
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