CN104501810A - Symmetric diagonal configuration method based on pentahedron - Google Patents

Abstract

The invention relates to the technical field of inertial navigation, in particular to a symmetric diagonal configuration method based on a pentahedron. The symmetric diagonal configuration method based on the pentahedron is characterized in that directions of measuring axes of four inertial components are diagonal relatively to an orthogonal coordinate system, the directions of the measuring axes of the four inertial components are vertical to four side faces of the pentahedron, each inertial component comprises a spinning top and an accelerometer, the directions of each spinning top and each accelerometer keep consistent, intersection angles of the four side faces and the bottom face of the pentahedron are all 54.74 degrees, each side face of the pentahedron is an equilateral triangle, the bottom face of the pentahedron is a square, and an original point of the orthogonal coordinate system is the center of the bottom face of the pentahedron. According to the symmetric diagonal configuration method based on the pentahedron, the four inertial components in the configuration scheme are distributed in symmetric mode, and are all diagonally placed relatively to the orthogonal coordinate system, and when a single fault is caused on an arbitrarily one of the four inertial components, measuring accuracy of the orthogonal coordinate system can not change along with change of the inertial component which breaks down.

Description

Symmetric inclined configuration method based on pentahedron

Technical Field

The invention relates to the technical field of inertial navigation, in particular to a pentahedron-based symmetrical oblique configuration method.

Background

In order to realize accurate striking of a navigation system and guarantee navigation tasks of carriers such as a submersible vehicle, a ship, a satellite and the like, the requirements on the precision and the reliability of inertial navigation are higher and higher. The redundancy configuration is carried out by increasing the number of inertia devices, which is the most mainstream method for improving the precision and the reliability of the system at present. Because the inertia devices are installed according to a certain combination mode, the axial redundancy of the inertia measurement unit can be improved, and the navigation precision can be improved by using repeated measurement data. For the small carrier, because the self volume of the inertia device is larger, the reliability of the system can be improved by simply increasing the number of the inertia devices, but the volume, the weight and the cost of the inertial navigation system are also greatly increased. Therefore, the research on the inertial navigation system with the number of the inertial devices of 4 has practical significance.

The patent (a high-reliability redundant four-axis fiber optic gyroscope inertial measurement device, 201310741033.7) of Wang Wei, et al, of Beijing aerospace time opto-electronic technology Co., Ltd. in the patent, four gyroscopes are respectively mounted on three orthogonal axes and one inclined axis, so that the system reliability is improved relative to a non-redundant inertial device. When the inertial device is free of faults, the corresponding configuration matrix is as follows:

$H_1=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\\ 0.5774& 05774& 0.5774\end{array}\right]$

then the process of the first step is carried out, $H_1^T{H}_1=\left[\begin{array}{ccc}1.333& 0.333& 0.333\\ 0.333& 1.333& 0.333\\ 0.333& 0.333& 1.333\end{array}\right]$

the configuration matrix does not meet the optimization criteria.

Disclosure of Invention

The invention aims to provide a symmetric inclined configuration method based on a pentahedron, which ensures the precision of a system and improves the reliability of the system under the condition that the redundancy number is 4.

The purpose of the invention is realized as follows:

the directions of the measuring axes of the four inertia assemblies are inclined relative to the orthogonal coordinate system, and the directions of the four inertia assemblies are vertical to the four side surfaces of the pentahedron; the included angles between the four side surfaces and the bottom surface of the pentahedron are 54.74 degrees, the side surfaces are equilateral triangles, the bottom surface is square, the origin of an orthogonal coordinate system is the center of the bottom surface of the pentahedron, the x axis and the y axis are diagonal lines of the bottom surface respectively, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system; the included angles of the first measuring shaft and the x negative half shaft, the y negative half shaft and the z positive half shaft are all 54.74 degrees; the included angles of the second measuring shaft and the x positive half shaft, the y negative half shaft and the z positive half shaft are all 54.74 degrees; the included angles of the third measuring shaft and the x positive half shaft, the y positive half shaft and the z positive half shaft are all 54.74 degrees; the fourth measuring axis forms an angle of 54.74 degrees with the x negative half axis, the y positive half axis and the z positive half axis.

The invention has the beneficial effects that:

the invention discloses a symmetrical oblique configuration method based on a pentahedron.

When the inertial device has no fault, the corresponding configuration matrix is as follows:

$H=\left[\begin{array}{ccc}-0.5774& -0.5774& 0.5774\\ 0.5774& -0.5774& 0.5774\\ 0.5774& 0.5774& 0.5774\\ -0.5774& 0.5774& 0.5774\end{array}\right]$

then the process of the first step is carried out, $H_2^T{H}_2=\left[\begin{array}{ccc}1.333& 0& 0\\ 0& 1.333& 0\\ 0& 0& 1.333\end{array}\right]$

therefore, the configuration matrix corresponding to the patent can be obtained to meet the optimal navigation criterionThe method has good reference value for practical application.

In the inertial measurement unit, a symmetrical inclined configuration scheme is adopted, so that not only is the reliability of the system improved, but also the volume and the weight of the inertial measurement unit can be reduced and the cost of the system is reduced compared with a system-level redundancy scheme.

Drawings

FIG. 1 is a schematic diagram of the symmetric inclined configuration scheme based on pentahedron in the invention.

FIG. 2 is a schematic structural diagram of a pentahedron of the present invention.

Fig. 3 is a schematic structural diagram of the inertia assembly of the present invention.

FIG. 4 is a schematic diagram of the solution of the present invention.

FIG. 5 is a schematic diagram of a data processing flow according to the present invention.

Detailed Description

The invention is further described below with reference to the accompanying drawings.

A symmetrical oblique configuration method based on pentahedron is disclosed, the configuration scheme comprises four inertia components, each inertia component comprises a gyroscope and an accelerometer, and the gyroscope and the accelerometer in each inertia component are installed together to enable the directions of the measuring axes of two inertia devices to be consistent; the included angles between the direction of the measuring axis of the inertia component 1 and the x negative half axis, the y negative half axis and the z positive half axis are all 54.74 degrees, and the inertia component is arranged in the center of the side surface ABE of the pentahedron; the included angles between the measuring axis direction of the inertia assembly 2 and the x positive half axis, the y negative half axis and the z positive half axis are all 54.74 degrees, and the inertia assembly is arranged in the center of the side face ABC of the pentahedron; the included angles between the direction of the measuring axis of the inertia component 3 and the positive x half axis, the positive y half axis and the positive z half axis are all 54.74 degrees, and the inertia component is arranged in the center of the side surface ACD of the pentahedron; the angle between the direction of the measuring axis of the inertia assembly 4 and the x negative half axis, the y positive half axis and the z positive half axis is 54.74 degrees, and the inertia assembly is arranged in the center of the side surface ADE of the pentahedron.

The pentahedron is characterized in that the included angles between the four side surfaces and the bottom surface of the pentahedron are 54.74 degrees, the side surfaces are equilateral triangles, and the bottom surface is square.

And in the orthogonal coordinate system, the origin of the orthogonal coordinate system is the center of the bottom surface of the pentahedron, the x axis and the y axis are diagonal lines of the bottom surface respectively, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system.

The symmetric oblique configuration matrix based on the pentahedron meets the optimal configuration criterion;

and carrying out fault detection on an inertia measurement unit of the system by using a generalized likelihood ratio test method.

1. As shown in fig. 1 and 3, the configuration of the present invention includes 4 gyros and 4 accelerometers; wherein the gyroscope is preferably a single-degree-of-freedom fiber optic gyroscope, and the accelerometer is preferably a single-degree-of-freedom quartz accelerometer. The calculation of the included angle between the side surface and the bottom surface of the constructed pentahedron is as follows:

reference numerals: 1 is No. 1 inertia subassembly, 2 is No. 2 inertia subassemblies, 3 is No. 3 inertia subassemblies, 4 is No. 4 inertia subassemblies, 5 is inertia subassemblies, 6 is the top, 7 is the accelerometer, 8 inertia subassembly measuring axes.

Setting: the included angle between the bottom surface and the side surface is beta, the side length of the bottom surface is a, and the side lengths of the pentahedron are a as the side surfaces of the pentahedron are regular triangles, as shown in fig. 2.

From the triangle algorithm, it can be known that:

$\mathrm{AF}=\frac{\sqrt{3}}{2}a---\left(1\right)$

then:

<math> <mrow> <mi>cos</mi> <mi>&beta;</mi> <mo>=</mo> <mfrac> <mi>OF</mi> <mi>AF</mi> </mfrac> <mo>=</mo> <mfrac> <msqrt> <mn>3</mn> </msqrt> <mn>3</mn> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

i.e., β 54.74 °.

For a carrier coordinate system, the center of the bottom surface is selected as the origin of coordinates, the diagonal lines of the bottom surface are respectively taken as an x axis and a y axis, and a right-hand rectangular coordinate system is formed by the z axis, the x axis and the y axis.

2. Deriving a relation which should be satisfied by an optimal configuration matrix H of the redundant strapdown inertial navigation system from two different mathematical angles:

2.1 for a strapdown inertial navigation system using n single degree of freedom gyroscopes, the measurement equation for the gyroscope can be expressed as:

m＝HX+η (3)

in the formula, m isn x 1 dimensional inertial measurement vector; h is an n multiplied by 3 dimensional configuration matrix; x is a 3X 1-dimensional vector to be solved; η is the n × 1 dimensional measurement noise vector. Setting the measurement noise eta as zero mean value and variance as sigma²The statistical characteristics of the white gaussian noise are as follows:

E(η)＝0；E(ηη^T)＝σ²I_n (4)

according to the linear minimum variance theory, the estimated value of the strapdown inertial navigation resolving input X can be obtained:

$\hat{X}={\left(H^{T}H\right)}^{-1}{H}^{T}m---\left(5\right)$

meanwhile, the corresponding estimation error covariance matrix can be obtained as follows:

<math> <mrow> <mi>C</mi> <mo>=</mo> <mi>E</mi> <mo>{</mo> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <mover> <mi>X</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <mover> <mi>X</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mo>}</mo> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>H</mi> <mi>T</mi> </msup> <mi>H</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow> </math>

the optimal criteria for defining the navigation characteristics are:

J＝min{trace(C)} (7)

where trace (C) represents the trace of matrix C, i.e., the sum of the diagonal elements.

The following demonstrates that the navigation performance optimization criterion defined by the above formula is equivalent to

1) First, it provesAnd (3) decomposing the configuration matrix H by using singular values:

<math> <mrow> <mi>H</mi> <mo>=</mo> <msup> <mi>UAV</mi> <mi>T</mi> </msup> <mo>=</mo> <mo>[</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>,</mo> <msub> <mi>u</mi> <mi>n</mi> </msub> <mo>]</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mi>&Sigma;</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>[</mo> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>v</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>v</mi> <mn>3</mn> </msub> <mo>]</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, <math> <mrow> <mi>&Sigma;</mi> <mo>=</mo> <mi>diag</mi> <mrow> <mo>(</mo> <msqrt> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> </msqrt> <mo>,</mo> <msqrt> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> </msqrt> <mo>,</mo> <msqrt> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> </msqrt> <mo>)</mo> </mrow> <mo>=</mo> <mi>diag</mi> <mrow> <mo>(</mo> <msqrt> <mi>n</mi> <mo>/</mo> <mn>3</mn> </msqrt> <mo>,</mo> <msqrt> <mi>n</mi> <mo>/</mo> <mn>3</mn> </msqrt> <mo>,</mo> <msqrt> <mi>n</mi> <mo>/</mo> <mn>3</mn> </msqrt> <mo>)</mo> </mrow> </mrow> </math> diag () represents a diagonal matrix, and the elements in (are) the elements on the diagonal.

Then:

<math> <mrow> <msup> <mi>H</mi> <mi>T</mi> </msup> <mi>H</mi> <mo>=</mo> <msup> <mi>VA</mi> <mi>T</mi> </msup> <msup> <mi>U</mi> <mi>T</mi> </msup> <msup> <mi>UAV</mi> <mi>T</mi> </msup> <mo>=</mo> <msup> <mi>&Sigma;</mi> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mi>n</mi> <mn>3</mn> </mfrac> <msub> <mi>I</mi> <mn>3</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

2) re-certificationThe formula (7) is equivalent to the formula (9) and is defined as₁、λ₂、λ₃Are respectively H^TCharacteristic value of H.

The sufficiency: suppose that $H^{T}H=\frac{n}{3}{I}_3,$ Then:

<math> <mrow> <mi>J</mi> <mo>=</mo> <mi>trace</mi> <mrow> <mo>(</mo> <mi>C</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mi>trace</mi> <mo>{</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>H</mi> <mi>T</mi> </msup> <mi>H</mi> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>}</mo> <mo>=</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> </mfrac> <mo>)</mo> </mrow> <mo>&GreaterEqual;</mo> <mfrac> <msup> <mrow> <mn>3</mn> <mi>&sigma;</mi> </mrow> <mn>2</mn> </msup> <mroot> <mrow> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> </mrow> <mn>3</mn> </mroot> </mfrac> <mo>.</mo> </mrow> </math> when in use ₃I.e. byWhen the above inequality equal sign is true, that is, the trace of C takes the minimum value, the corresponding configuration matrix H is the optimal matrix, and thus the navigation characteristic is optimal.

The necessity: assuming that the configuration matrix H is an optimal matrix, i.e. the trace of C takes the minimum value, as can be known from the proof of sufficiency, <math> <mrow> <mi>J</mi> <mo>&GreaterEqual;</mo> <mfrac> <msup> <mrow> <mn>3</mn> <mi>&sigma;</mi> </mrow> <mn>2</mn> </msup> <mroot> <mrow> <msub> <mi>&lambda;</mi> <mn>1</mn> </msub> <msub> <mi>&lambda;</mi> <mn>2</mn> </msub> <msub> <mi>&lambda;</mi> <mn>3</mn> </msub> </mrow> <mn>3</mn> </mroot> </mfrac> </mrow> </math> get the equal sign true, and <math> <mrow> <mi>trace</mi> <mrow> <mo>(</mo> <msup> <mi>H</mi> <mi>T</mi> </msup> <mi>H</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>trace</mi> <mrow> <mo>(</mo> <msup> <mi>HH</mi> <mi>T</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mi>n</mi> <mo>,</mo> </mrow> </math> and isI.e. when the equal sign is established, lambda₁＝λ₂＝λ₃＝n/3。

2.2 analyze the optimal configuration matrix from the noise angle, and set the noise η as zero mean gaussian white noise, and the corresponding probability density function is:

<math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>&eta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>&pi;</mi> <mo>)</mo> </mrow> <mrow> <mi>n</mi> <mo>/</mo> <mn>2</mn> </mrow> </msup> <msup> <mrow> <mo>|</mo> <mi>G</mi> <mo>|</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mi>exp</mi> <mo>{</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>&eta;</mi> <mi>T</mi> </msup> <msup> <mi>G</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mi>&eta;</mi> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein G ═ H^TH)^-1And the locus of η satisfies:

η^TG^-1η＝K (11)

k is the amplification factor.

Equation (11) represents a family of ellipsoids, given a value of K, a fixed ellipsoid is obtained, and the corresponding ellipsoid volume can be expressed as:

<math> <mrow> <mi>V</mi> <mo>=</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> <msup> <mi>K</mi> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mi>&pi;</mi> <msqrt> <mo>|</mo> <mi>G</mi> <mo>|</mo> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow> </math>

thus, it can be seen that: the smaller the volume V, the smaller the error generated by the noise η, and thus the better the navigation characteristics of the system, the optimal criterion is defined as:

$F=\sqrt{\left|G\right|}=\sqrt{\left|{\left(H^{T}H\right)}^{-1}\right|}---\left(13\right)$

the smaller the value of F is, the smaller the ellipsoid volume of the error generated by the noise eta is, so that the selected configuration matrix is judged to be optimal.

According to the optimal essential conditions of the navigation characteristics, the following conditions are known:

$H^{T}H=-\frac{4}{3}{I}_3---\left(14\right)$

as can be seen from fig. 1:

<math> <mrow> <mi>H</mi> <mo>=</mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <mo>-</mo> <mi>cos</mi> <mi>&alpha;</mi> </mtd> <mtd> <mo>-</mo> <mi>cos</mi> <mi>&alpha;</mi> </mtd> <mtd> <mi>cos</mi> <mi>&alpha;</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mi>&alpha;</mi> </mtd> <mtd> <mo>-</mo> <mi>cos</mi> <mi>&alpha;</mi> </mtd> <mtd> <mi>cos</mi> <mi>&alpha;</mi> </mtd> </mtr> <mtr> <mtd> <mi>cos</mi> <mi>&alpha;</mi> </mtd> <mtd> <mi>cos</mi> <mi>&alpha;</mi> </mtd> <mtd> <mi>cos</mi> <mi>&alpha;</mi> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>cos</mi> <mi>&alpha;</mi> </mtd> <mtd> <mi>cos</mi> <mi>&alpha;</mi> </mtd> <mtd> <mi>cos</mi> <mi>&alpha;</mi> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow> </math>

from formulae (14) and (15): α is 54.74 °.

The optimal configuration matrix based on the symmetric skew of the pentahedron is:

$H^T=\left[\begin{array}{cccc}-0.5774& 0.5774& 0.5774& -0.5774\\ -0.5774& -0.5774& 0.5774& 0.5774\\ 0.5774& 0.5774& 0.5774& 0.5774\end{array}\right]---\left(16\right)$

3. and installing a gyroscope and an accelerometer according to the optimal configuration matrix, and resolving the measured angular velocity and acceleration through a navigation computer to obtain the motion information of the carrier, such as velocity, position and attitude.

4. FIG. 5 is a data processing diagram of the present invention, in which the angular velocity and acceleration output by the sensing element are firstly diagnosed and isolated, and the present invention utilizes the generalized likelihood ratio algorithm to detect and isolate the fault.

The measurement equation shown in equation (3) is the parity equation under no fault and fault:

wherein V is an (n-3) x n-dimensional matrix satisfying VH 0 and VV^T＝I_(n-3)×(n-3)V can be obtained by a Potter algorithm.

V＝[-0.5 0.5 -0.5 0.5]

Equation (18) is used to calculate the fault decision function of the system, and it can be determined whether the system has a fault:

FD_GLT＝P^TP/σ² (18)

equation (19) is used for calculating the fault isolation function of the system, and the gyroscope generating the fault can be judged:

<math> <mrow> <msub> <mi>FI</mi> <mi>GLT</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>P</mi> <mi>T</mi> </msup> <msub> <mi>v</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mrow> <mo>(</mo> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <msubsup> <mi>v</mi> <mi>i</mi> <mi>T</mi> </msubsup> <msub> <mi>v</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow> </math>

in the formula, v_iIs column i of V. If:

<math> <mrow> <msub> <mi>FI</mi> <mi>CLT</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mi>max</mi> <mrow> <mn>1</mn> <mo>&le;</mo> <mi>i</mi> <mo>&le;</mo> <mi>n</mi> </mrow> </munder> <mo>{</mo> <msub> <mi>FI</mi> <mi>GLT</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow> </math>

it indicates that the kth gyro is faulty.

After judging out the trouble top, need utilize the algorithm to rearrange the configuration matrix, isolate the trouble top to avoid reducing the precision of system, if top 1 breaks down, then the configuration matrix turns into:

$H=\left[\begin{array}{ccc}0.5774& -0.5774& 0.5774\\ 0.5774& 0.5774& 0.5774\\ -0.5774& 0.5774& 0.5774\end{array}\right]---\left(21\right)$

if the gyroscope in the system has no fault, the precision of the system can be improved by using the repeatedly measured data, and the estimated value of the input X is solved by strapdown inertial navigation according to the least square algorithm:

$\hat{X}={\left(H^{T}H\right)}^{-1}{H}^{T}m---\left(22\right)$

in the formula, H is a configuration matrix, and m is an inertia measurement vector.

Claims (2)

1. A symmetrical oblique configuration method based on pentahedrons is characterized in that: the directions of the measuring axes of the four inertia assemblies are inclined relative to the orthogonal coordinate system, and the directions of the four inertia assemblies are vertical to the four side surfaces of the pentahedron; the included angles between the four side surfaces and the bottom surface of the pentahedron are 54.74 degrees, the side surfaces are equilateral triangles, the bottom surface is square, the origin of an orthogonal coordinate system is the center of the bottom surface of the pentahedron, the x axis and the y axis are diagonal lines of the bottom surface respectively, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system; the included angles of the first measuring shaft (1) and the x negative half shaft, the y negative half shaft and the z positive half shaft are all 54.74 degrees; the included angles of the second measuring shaft (2) and the x positive half shaft, the y negative half shaft and the z positive half shaft are all 54.74 degrees; the included angles of the third measuring shaft (3) and the x positive half shaft, the y positive half shaft and the z positive half shaft are all 54.74 degrees; the included angles of the fourth measuring shaft (4) and the x negative half shaft, the y positive half shaft and the z positive half shaft are all 54.74 degrees.

2. The symmetric slant configuration method based on pentahedrons according to claim 1, characterized in that: when the inertial device has no fault, the corresponding configuration matrix is as follows:

$H=\left[\begin{array}{ccc}-0.5774& -0.5774& 0.5774\\ 0.5774& -0.5774& 0.5774\\ 0.5774& 0.5774& 0.5774\\ -0.5774& 0.5774& 0.5774\end{array}\right]$

$H_2^T{H}_2=\left[\begin{array}{ccc}1.333& 0& 0\\ 0& 1.333& 0\\ 0& 0& 1.333\end{array}\right].$