CN117433517A - Four-way shuttle high-precision positioning algorithm based on multi-sensor fusion - Google Patents
Four-way shuttle high-precision positioning algorithm based on multi-sensor fusion Download PDFInfo
- Publication number
- CN117433517A CN117433517A CN202311402686.2A CN202311402686A CN117433517A CN 117433517 A CN117433517 A CN 117433517A CN 202311402686 A CN202311402686 A CN 202311402686A CN 117433517 A CN117433517 A CN 117433517A
- Authority
- CN
- China
- Prior art keywords
- error
- representing
- equation
- uwb
- vector
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000004422 calculation algorithm Methods 0.000 title claims abstract description 20
- 230000004927 fusion Effects 0.000 title claims abstract description 20
- 239000013598 vector Substances 0.000 claims abstract description 75
- 125000004122 cyclic group Chemical group 0.000 claims abstract description 6
- 238000000034 method Methods 0.000 claims description 41
- 238000005259 measurement Methods 0.000 claims description 27
- 239000011159 matrix material Substances 0.000 claims description 22
- 238000013213 extrapolation Methods 0.000 claims description 16
- 230000008569 process Effects 0.000 claims description 9
- 238000004364 calculation method Methods 0.000 claims description 8
- 230000005484 gravity Effects 0.000 claims description 8
- 238000004458 analytical method Methods 0.000 claims description 7
- 238000009826 distribution Methods 0.000 claims description 4
- 238000001914 filtration Methods 0.000 claims description 4
- 230000009466 transformation Effects 0.000 claims description 4
- 230000005540 biological transmission Effects 0.000 claims description 3
- 230000007704 transition Effects 0.000 claims description 3
- 230000007547 defect Effects 0.000 description 4
- 230000000007 visual effect Effects 0.000 description 4
- 230000009471 action Effects 0.000 description 3
- 230000008859 change Effects 0.000 description 3
- 238000009795 derivation Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 3
- 238000005299 abrasion Methods 0.000 description 2
- 230000001133 acceleration Effects 0.000 description 2
- 230000010354 integration Effects 0.000 description 2
- 206010034719 Personality change Diseases 0.000 description 1
- 238000009825 accumulation Methods 0.000 description 1
- 230000004075 alteration Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005286 illumination Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000005096 rolling process Methods 0.000 description 1
- 238000001228 spectrum Methods 0.000 description 1
- 238000003860 storage Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
- G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
- G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
- G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
- G01C21/1652—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments with ranging devices, e.g. LIDAR or RADAR
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/20—Instruments for performing navigational calculations
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
- G01C21/34—Route searching; Route guidance
- G01C21/3407—Route searching; Route guidance specially adapted for specific applications
- G01C21/343—Calculating itineraries, i.e. routes leading from a starting point to a series of categorical destinations using a global route restraint, round trips, touristic trips
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
- G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
- G01C21/34—Route searching; Route guidance
- G01C21/3446—Details of route searching algorithms, e.g. Dijkstra, A*, arc-flags, using precalculated routes
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Automation & Control Theory (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Navigation (AREA)
Abstract
The invention discloses a multi-sensor fusion-based four-way shuttle high-precision positioning algorithm, which comprises state vector determination, attitude error differential equation modeling, speed error differential equation modeling, position error differential equation modeling, sensor error modeling, inertial navigation system state error differential equation modeling, UWB position error observation equation modeling and Kalman cyclic positioning; the invention belongs to the technical field of surveying, navigation and gyroscopes, in particular to a four-way shuttle vehicle high-precision positioning algorithm based on multi-sensor fusion, which has the advantages that: the invention combines the high-frequency inertial navigation data of the IMU, comprehensively utilizes the observation data of UWB, and uses Kalman circulation positioning to predict the carrier position, so that the whole algorithm is more robust and accurate, and the sensor used by the invention has low price, thus being a positioning scheme with low cost.
Description
Technical Field
The invention belongs to the technical field of surveying, navigation and gyroscopes, and particularly relates to a four-way shuttle vehicle high-precision positioning algorithm based on multi-sensor fusion.
Background
The four-way shuttle is an automatic storage device capable of moving in the horizontal and vertical directions, has the advantages of high efficiency, flexibility, space saving and the like, and is widely applied to industries such as logistics, manufacturing, electronic commerce and the like. In order to achieve autonomous operation of the four-way shuttle, it is necessary to address its positioning problem in an unknown environment.
Currently, the positioning methods commonly used include a Global Positioning System (GPS) based method, an IMU based method, a wheel speed meter based method, a vision based method, a laser radar based method, and the like, which have advantages and disadvantages, for example, in the open field where the GPS signal is strong and no shielding exists, such as a farmland, an open road surface, and the like, which can provide higher accuracy, and generally ranges from several meters to tens of meters; when GPS signals are influenced by factors such as shielding, multipath effect, signal interference and the like, navigation accuracy is reduced, and even positioning cannot be performed in shielding environments such as urban canyons, indoor environments and the like; an Inertial Measurement Unit (IMU) is used as a common sensor for measuring the acceleration and angular velocity of an object, and can provide information such as attitude, motion and attitude change, however, the IMU also has the problem of accumulated errors, and the measurement of the IMU is based on integration, so that there is the problem of error accumulation in time, even if the measurement at the initial moment is accurate, as small errors in the integration process gradually accumulate along with the time, so that the inaccuracy of attitude and position estimation increases; wheel speed meters are used for measuring the wheel speed and the driving distance of a vehicle or a mobile device, however, the wheel speed meter is usually used for measuring depending on the rolling between a tire and the ground, so that the mobile device is indirectly positioned, and if the vehicle slides or slips, errors can occur in the measurement result of the wheel speed meter; in addition, the abrasion and the change of the tire also influence the measurement accuracy of the wheel speed meter, and the diameter and the circumference of the wheel speed meter change along with the abrasion of the tire, so that the measurement result of the wheel speed meter is deviated; in addition, factors such as tire pressure and elasticity may also have an effect on the measurement results; vision is affected by illumination and texture; the laser radar has the defects of high cost, large data volume and the like; therefore, a single sensor is difficult to meet the requirements of autonomous positioning and mapping of the four-way shuttle.
In order to improve the positioning accuracy and robustness, a multi-sensor fusion technology is introduced into the positioning problem of the four-way shuttle, wherein the multi-sensor fusion technology is to collect different types of data by utilizing a plurality of sensors, and more accurate, more reliable and more complete information is obtained by data processing and information fusion compared with a single sensor, so that the multi-sensor fusion technology can effectively utilize the complementarity of various sensors and improve the stability and reliability of a system.
Disclosure of Invention
First, the technical problem to be solved
The invention discloses a multi-sensor fusion-based four-way shuttle high-precision positioning algorithm, which aims to solve the following problems:
(1) The traditional positioning modes based on visual positioning, laser positioning, ultrasonic positioning and magnetic navigation have low positioning precision and high cost;
(2) The traditional positioning method based on vision and laser requires a large amount of computing resources, and has longer positioning time and poorer instantaneity;
(3) The four-way shuttle is larger in size due to the scheme based on laser positioning, so that the positioning scheme occupies smaller layout space.
Technical scheme (one)
In order to solve the problems, the invention adopts the following technical scheme: a four-way shuttle high-precision positioning algorithm based on multi-sensor fusion comprises state vector determination, attitude error differential equation modeling, speed error differential equation modeling, inertial navigation position error differential equation modeling, sensor error modeling, inertial navigation system state error differential equation modeling, UWB position error observation equation modeling and Kalman cyclic positioning; the determination of the state vector is to determine the state vector in a Kalman filtering equation, and the state vector comprises a navigation state error vector and a sensor:
δx＝[δr n δv n φ b g b a s g s a ]
in the above formula, δx represents a state error, δr n Representing the projection of the inertial navigation position error vector in the n-system (local horizontal coordinate system), δv n Representing the projection of the inertial navigation speed error vector under the n system, the third term on the right of the equal sign represents the inertial navigation attitude error vector, b g Representing three-axis gyroscope zeroOffset vector, b a Representing the zero deflection of the triaxial accelerometer, s g Representing the scale factor error vector of the triaxial gyroscope, s a Representing the triaxial accelerometer scale factor error vector, each term on the right of the equal sign is a three-dimensional column vector, so δx has 21 dimensions in total.
Further, the posing error differential equation is modeled as:
in the above-mentioned method, the step of,derivative, phi, representing the attitude error of inertial navigation np The attitude error of inertial navigation is represented, and the superscript n represents the projection of each physical quantity under an n system (local horizontal coordinate system); the superscript b denotes the projection of each physical quantity under the b system (carrier coordinate system); omega in Representing the angular velocity of the n-system (local horizontal coordinate system) relative to the i-system (practical inertial system); δω in Representing the angular velocity error of the n-system (local horizontal coordinate system) relative to the i-system (practical inertial system); δω ib An angular velocity error of the b-system (carrier coordinate system) with respect to the i-system (practical inertial system); />The direction cosine matrix of the b-series relative to the n-series where inertial navigation is located is shown.
Preferably, the speed error differential equation is modeled as:
in the above formula, the left side of the equal sign represents the first derivative of the velocity vector in the local horizontal coordinate system, δf b Representing the projection of the specific force error measured by the accelerometer in the b system; f (f) n Representing a projection of the specific force measured by the accelerometer in the n-series; omega ie Representing the angular velocity of the e-system (geocentric-earth-fixed-coordinate system) relative to the i-system；δω ie Representing the angular velocity error of the e-system (geocentric-earth fixed coordinate system) relative to the i-system; omega en An angular velocity of n series relative to e series; δω en An angular velocity error of n series relative to e series is represented; upsilon (v) n Representing a velocity vector in a local horizontal coordinate system; delta v n Representing a velocity error vector in a local horizontal coordinate system; δg p Is representative of local gravity error; the expansion of local gravity is:
in the above formula, g represents a gravity vector; omega ie An angular velocity vector representing the e-system relative to the i-system; r represents the position vector of the carrier; thus, there are:
in the above formula, the superscript n denotes a projection in the n system.
Further, the inertial navigation position error differential equation is modeled as a position error differential equation form under n series:
in the above-mentioned method, the step of,is the latitude of the carrier; h is the elevation of the carrier; r is R M Representing the radius of curvature, R, of the meridian N Indicating mortiseRadius of curvature, v of unitary ring N 、υ E And v D Respectively representing the north speed, the east speed and the vertical speed under the n series; the disturbance analysis of the derivative of latitude is as follows: delta v N Is north velocity error, delta v E For east speed error δv D Represents the vertical speed error, and the left side of the equal sign represents the corresponding delta v respectively N 、δυ E And δv D And (5) derivative is obtained.
Preferably, the sensor error modeling is as follows:
first, modeling accelerometer errors:
in the formula 1 above, the left side of the equal sign represents the actual specific force measurement output of the accelerometer; f (f) b Representing the theoretical output of the accelerometer; i is a unit vector; s is S a Is the scale factor error of the accelerometer, b g Zero offset for the accelerometer; omega a White noise representing accelerometer measurements; in formula 2, δf b Representing accelerometer measurement errors;
secondly, modeling gyroscope errors:
in the formula 3, the left side of the equal sign represents the actual angular velocity measurement output omega of the gyro ib b The theoretical angular velocity in the b system; s is S g Is the scale factor error of the gyroscope, b g Zero offset of the gyroscope; w (w) g Representing gyroscope measurementsWhite noise of (a); δω ib b Representing gyroscope measurement errors; the accelerometer zero bias, the gyroscope zero bias, the scale factor error of the accelerometer and the scale factor error of the gyroscope are modeled as a first order Gaussian Markov process, which has:
in the above, T gb 、T ab 、T gs And T as Respectively representing the related time of the gyro zero bias, the accelerometer zero bias, the gyro scale factor and the accelerometer scale factor; omega gb 、ω ab 、ω gs And omega as The method respectively represents gyro zero bias driving white noise, accelerometer zero bias driving white noise, gyro scale factor driving white noise and accelerometer scale factor driving white noise.
Further, modeling of the inertial navigation system state error differential equation comprises the following specific steps:
firstly, combining the results of state vector determination, attitude error differential equation modeling, velocity error differential equation modeling, inertial navigation position error differential equation modeling and sensor error modeling, a system state error differential equation of inertial navigation can be constructed, wherein the system state error differential equation comprises:
wherein F (t) represents a system matrix; g (t) represents an input equation; ω (t) represents continuous-time system gaussian white noise; δx (t) represents a state error at time t;
and then, further deducing an error state extrapolation equation according to the differential equation, wherein the error state extrapolation equation comprises the following steps:
δx k ＝Φ k,k-1 δx k-1 +ω k-1
wherein:
in the above, phi k,k-1 Representing a state transition matrix, ω k-1 δx is a linear transformation of system gaussian white noise ω (t) k A state error at time k; δx k-1 A state error at time k-1; note the discretization time interval Δt=t k -t k-1 F (t) is at time interval [ t ] when Δt is relatively small k-1 ，t k ]The internal changes are not great, and at this time, there are:
Φ k,k-1 ≈I+F(t k-1 )Δt
omega can be demonstrated k-1 Is a zero-mean white noise sequence, and meets the following conditions:
ω k ～N(0，Q k )
in the above formula, the symbol "N" represents a Gaussian distribution, and the symbols "to" represent compliance, i.e., ω k-1 Obeys Gaussian distribution, Q k The method for calculating the system state noise covariance matrix comprises the following steps:
in the above, Q k The calculation of (1) uses the Le trapezoidal integral formula.
Further, the step of modeling the UWB position error observation equation is as follows: fixing UWB labels at the central position of a carrier, fixing UWB base stations on the ground with known positions (longitude, latitude and elevation), wherein the number of the base stations is set to be 4, and the base stations are marked as a No. 1 base station, a No. 2 base station, a No. 3 base station and a No. 4 base station; the distance from the UWB tag to the UWB base station is determined by utilizing the time-of-flight principle, so that the absolute position of the carrier is determined, and the specific ranging mode is as follows:
in the above, T 14 Representing the time interval from the transmission of the request to the receipt of the feedback signal by the tag; t (T) 23 Representing a time interval from receiving the request to transmitting the feedback signal by the base station; t represents a time-of-flight interval; the superscript indicates the corresponding base station number; then, the distance between the tag and each base station is calculated, and the calculation formula is as follows:
D 1 ＝cT 1
D 2 ＝cT 2
D 3 ＝cT 3
D 4 ＝cT 4
in the above formula, c is the light velocity, D 1 、D 2 、D 3 And D 4 The distances from the labels on the carrier to the 4 base stations respectively; calculating the coordinates of the label on the carrier relative to the base station, and setting the coordinates of the No. 1 base station as (x 1, y1 and z 1) and the coordinates of the No. 2 base station as(x 2, y2, z 2), base station 3 coordinates (x 3, y3, z 3), base station 4 coordinates (x 4, y4, z 4), and tag seat label r UWB = (x, y, z), then there is the following relation:
the coordinates of the tag relative to the base station can be obtained by using a least square method; based on the above steps, the UWB error observation equation is modeled as:
in the above, δr UWB For UWB position observation errors, the superscript "≡" indicates the position of the UWB tag calculated by inertial navigation, and the superscript "-" indicates the position of the UWB tag with errors calculated by the UWB tag itself.
The Kalman cyclic positioning consists of an error state extrapolation equation, an error state covariance extrapolation equation, a Kalman gain equation, a UWB error state updating equation and an error state covariance updating equation; the above equations are derived from an error state extrapolation equation and a UWB position error observation equation; the invention fuses the IMU and UWB multi-source data, takes the IMU as a main sensor for deducing an error state equation, and takes UWB observation data as a sensor for deducing an observation equation.
(II) advantageous effects
The invention provides a four-way shuttle high-precision positioning algorithm based on multi-sensor fusion, which overcomes the defect that a VINS system can only provide higher precision under good visual conditions; the invention can utilize the UWB observation data and the IMU to carry out fusion positioning, thereby making the whole algorithm more robust and accurate, and being a positioning scheme with low cost;
the defects of low positioning precision and high cost of the traditional positioning modes based on visual positioning, laser positioning, ultrasonic positioning and magnetic navigation are effectively overcome;
the invention avoids the defects of long positioning time and poor instantaneity of visual positioning and laser positioning, and the scheme is easy to be deployed on other embedded equipment;
inertial navigation and UWB tags used in the present invention have very small volumes, so the positioning scheme of the present invention occupies less layout space.
Drawings
FIG. 1 is a schematic diagram of Kalman cycle positioning according to the present invention;
fig. 2 is a flow chart of modeling of the differential equation of the state error of the inertial navigation system.
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
Detailed Description
The technical solutions in the embodiments of the present solution will be clearly and completely described below with reference to the drawings in the embodiments of the present solution, and it is apparent that the described embodiments are only some embodiments of the present solution, but not all embodiments; all other embodiments, based on the embodiments in this solution, which a person of ordinary skill in the art would obtain without inventive faculty, are within the scope of protection of this solution.
The invention relates to a multi-sensor fusion-based four-way shuttle high-precision positioning algorithm, which comprises state vector determination, attitude error differential equation modeling, speed error differential equation modeling, inertial navigation position error differential equation modeling, sensor error modeling, inertial navigation system state error differential equation modeling, UWB position error observation equation modeling and Kalman cyclic positioning; the detailed deduction process of each step is as follows: first, determination of a state vector: the state vector includes a navigation state error vector and a sensor
δx＝[δr n δv n φ b g b a s g s a ]
In the above, the first term on the right of the equal sign represents the inertial navigation position error vector, the second term on the right of the equal sign represents the inertial navigation velocity error vector, the third term on the right of the equal sign represents the inertial navigation attitude error vector, the fourth term on the right of the equal sign represents the three-axis gyroscope zero offset vector, the fifth term on the right of the equal sign represents the three-axis accelerometer zero offset vector, the sixth term on the right of the equal sign represents the three-axis gyroscope scale factor error vector, the last term on the right of the equal sign represents the three-axis accelerometer scale factor error vector, and each term of the above is three-dimensional, thus 21 dimensions are taken in total.
Modeling an attitude error equation of inertial navigation:
s1, defining an attitude error, wherein the attitude indicates the relative angle relation between two coordinate systems, and when the attitude has deviation, the attitude can be completely calculated to a certain coordinate system, and the method comprises the following steps:
the above formula represents a definition formula, the left term represents the attitude estimation value of the carrier coordinate system (b system) relative to the true local horizontal coordinate system (n system), the middle term represents the directional cosine matrix of the carrier coordinate system (b system) relative to the local horizontal coordinate system (n 'system) with deviation, the right equal sign represents the directional cosine matrix of the carrier coordinate system (b system) relative to the p system, and therefore the n' system is the p system; three euler angles corresponding to the alignment of the real local horizontal coordinate system (n-system) and the calculated local horizontal coordinate system (p-system) are defined as attitude errors, and are defined as follows:
in the above formula, the first term on the right of the equal sign is a 3×3 identity matrix, the second term on the right of the equal sign is an antisymmetric matrix formed by vectors corresponding to three euler angles of a p system relative to an n system, and because the update frequency of the IMU is relatively high, the time between adjacent epochs is very short, and the sequence of a rotating shaft can be ignored; vectors corresponding to three Euler angles of the p-series relative to the n-series are called attitude errors; the attitude error is small.
The target form of the inertial navigation attitude error differential equation is:
the above expression is to express the attitude error as a form of a first-order linear differential equation, the first term on the right of the equation is the projection of the position error in the n-system, the second term on the right of the equation is the projection of the velocity error in the n-system, and the third term on the right of the equation is the attitude error; the fourth term on the right of the equation is the projection of the accelerometer specific force error in the b system, and the last term on the right of the equation is the projection of the gyroscope acceleration error in the b system;
the conditions are known:
in the above formula, formula 1 represents a transformation relationship between a direction cosine matrix of b system relative to n' system and a direction cosine matrix of b system relative to n system; formula 2 represents the relationship between the derivative of the direction cosine matrix of the b-system relative to the n-system and the direction cosine matrix itself and the projection vector of the b-system relative to the angular velocity of the n-system; formula 3 shows the relationship between the projection vector of the angular velocity of the b-system with respect to the n-system and the projection vector of the b-system with respect to the angular velocity of the i-system and the projection vector of the b-system with respect to the angular velocity of the n-system; 4 represents the result of bringing formula 3 to formula 2; 5 represents the relationship between the projection vector of n series with respect to the angular velocity of i series and the projection vector of b series with respect to the angular velocity of n series; formula 6 represents the results of the derivation of formulas 4 and 5; the method comprises the steps of deriving the formula 1 containing the attitude error, carrying out error disturbance on the formula 6, and obtaining an inertial navigation attitude error differential equation by equalizing the results, wherein the method comprises the following specific steps:
first, deriving formula 1:
secondly, carrying out error disturbance on the formula 6:
the derivation of the above formula applies to the following properties:
wherein a represents that the disturbance value of the projection vector of the b system relative to the angular velocity of the i system is equal to the true value thereof plus the error term thereof; b represents that the disturbance value of the projection vector of the angular velocity of the n system relative to the i system in the n system is equal to the true value thereof plus the error term thereof; c has the same meaning as formula 1; the left side of the equal sign of d and e contains two small amounts so that their product is approximately equal to 0;
therefore equation 8 can be reduced to:
the third step, the other 7 and 9 are equal:
and (3) finishing to obtain:
upper two-side right-hand rideDue to->Is an identity orthogonal matrix, so the above is further simplified into:
and (3) further finishing to obtain:
the method comprises the following steps:
thus, formula 10 is further simplified as:
due toTherefore, the formula (11) can be simplified as:
writing 12 into vector form has:
due toWherein:
in the above, δr N 、δr D And δr E Respectively representing a north position error under a local horizontal coordinate system, an east position error under the local horizontal coordinate system and a vertical position error under the local horizontal coordinate system; omega e Is the rotation angular velocity of the earth; h is the elevation of the carrier;is the latitude of the carrier; r is R M Representing the radius of curvature, R, of the meridian N Representing the radius of curvature, v of the circle of mortise and tenon N 、υ D And v E Respectively, the north direction speed, the east direction speed and the vertical direction speed in the local horizontal coordinate system.
Modeling a speed error differential equation, wherein the target form is as follows:
the above expression is to represent the velocity error as a form of a first order linear differential equation, with the known condition:
in the above formula, the left side of the equal sign represents the projection of the first derivative of the velocity vector under the n-series, f b Representing the projection of the inertial navigation measured specific force in the b system; the first term in brackets represents 2 times the projection of the angular velocity of the e-system relative to the i-system (the angular velocity of earth rotation) under the n-system; the second term in brackets represents the projection of the angular velocity of the n-series relative to the e-series under the n-series; upsilon (v) n Representation ofSpeed in a local horizontal coordinate system; g p The expansion of (2) is:
in the above formula, g represents a gravity vector; omega ie An angular velocity vector representing the e-system relative to the i-system; r represents the position vector of the carrier; thus, there are:
the deduction thinking is to carry out disturbance analysis on the 14-type, and the 14-type disturbance is obtained after the 14-type disturbance is expanded item by item, and the deduction process is as follows:
the superscript "≡" indicates disturbance of the corresponding physical quantity, the symbol "δ" indicates error of the corresponding physical quantity, and disturbance values of the rest physical quantities except for the attitude disturbance are equal to true values plus the error thereof; the derivation of equation 17 above uses the following properties:
neglecting the second order small in equation 17 is:
the binding 14, in turn, includes:
in the above, ω en An angular velocity of n series relative to e series; δω en An angular velocity error of n series relative to e series is represented; upsilon (v) n Representing a velocity vector in a local horizontal coordinate system; delta v n Representing a velocity error vector in a local horizontal coordinate system; δg p Is representative of local gravity error; and (3) further finishing to obtain:
equation 18 is the differential equation of the velocity error of inertial navigation.
Modeling a position error equation of inertial navigation, wherein the form of the position error differential equation in the high-longitude and latitude sense is as follows:
in the above-mentioned method, the step of,is the latitude of the carrier; λ is the longitude where the carrier is located; h is the elevation of the carrier; each component on the left side of the equal sign is a respective derivative; the meaning of the remaining components has been explained above and is not described in detail herein;
the disturbance analysis of the derivative of latitude is as follows:
disturbance analysis of the derivative of longitude is:
the disturbance analysis of the derivative of the elevation is as follows:
modeling an inertial navigation position error differential equation under an n system, the model is as follows:
in the above-mentioned method, the step of,is the latitude of the carrier; h is the elevation of the carrier; r is R M Representing the radius of curvature, R, of the meridian N Representing the radius of curvature, v of the circle of mortise and tenon N 、υ E And v D Respectively representing the north speed, the east speed and the vertical speed under the n series; the disturbance analysis of the derivative of latitude is as follows: delta v N Is north velocity error, delta v E For east speed error δv D Represents the vertical speed error, and the left side of the equal sign represents the corresponding delta v respectively N 、δυ E And δv D And (5) derivative is obtained.
Preferably, the sensor error modeling is divided into the following two steps:
first, accelerometer error model:
in the above formula 20, the left side of the equal sign indicates the actual specific force measurement output of the accelerometer; f (f) b Representing the theoretical output of the accelerometer; i is a unit vector; s is S a Is the scale factor error of the accelerometer, b g Zero offset for the accelerometer; omega a White noise representing accelerometer measurements; 21, δf b Representing accelerometer measurement errors;
second step, gyroscope error model
In equation 23, the left side of the equal sign indicates the actual angular velocity measurement output, ω, of the gyro ib b The theoretical angular velocity in the b system; s is S g Is the scale factor error of the gyroscope, b g Zero offset of the gyroscope; w (w) g White noise representing gyroscope measurements; δω ib b Representing gyroscope measurement errors; the accelerometer zero bias, the gyroscope zero bias, the proportional factor error of the accelerometer and the proportional factor error of the gyroscope are modeled as a first-order Gaussian Markov process, and the method comprises the following steps:
/>
in the above, T gb 、T ab 、T gs And T as Respectively representing the related time of the gyro zero bias, the accelerometer zero bias, the gyro scale factor and the accelerometer scale factor; omega gb 、ω ab 、ω gs And omega as The method respectively represents gyro zero bias driving white noise, accelerometer zero bias driving white noise, gyro scale factor driving white noise and accelerometer scale factor driving white noise.
The modeling mode of the inertial navigation system state error differential equation is as follows: the state error differential equation modeling of the inertial navigation system is carried out by combining the structures of state vector determination, attitude error differential equation modeling, speed error differential equation modeling, inertial navigation position error differential equation modeling and sensor error modeling, and comprises the following steps:
wherein F (t) represents a system matrix; g (t) represents an input equation; ω (t) represents continuous-time system gaussian white noise; further deriving an error state extrapolation equation from 29 has:
δx k ＝Φ k,k-1 δx k-1 +ω k-1
wherein:
in the above, phi k,k-1 Representing a state transition matrix, ω k-1 For linear transformation of the system gaussian white noise omega (t),
note the discretization time interval Δt=t k -t k-1 F (t) is at time interval [ t ] when Δt is relatively small k-1 ，t k ]The internal changes were not large, and at this time, there were:
Φ k,k-1 ＝exp(F(t k-1 )Δt)≈I+F(t k-1 )Δt
omega can be demonstrated k-1 Is a zero-mean white noise sequence, and meets the following conditions:
ω k ～N(0,Q k )
in the above, Q k The method for calculating the system state noise covariance matrix comprises the following steps:
in the above formula, q (t) is a power spectrum density matrix, is a constant matrix and is related to sensor error model parameters; when G (t) is at time interval t k-1 ，t k ]Q when the internal change is not large k The calculation can be as follows:
the above equation uses a trapezoidal integral formula calculation.
The modeling of the UWB position error observation equation comprises the following steps:
s0, fixing UWB labels at the central position of a carrier, fixing UWB base stations on the ground with known positions (longitude, latitude and elevation), wherein the number of the base stations is set to be 4, and the base stations are marked as a No. 1 base station, a No. 2 base station, a No. 3 base station and a No. 4 base station;
s1, determining the distance between manually set road mark points by using a binocular distance measurement principle, thereby determining the absolute position of a carrier, wherein the specific distance measurement mode is as follows:
in the above, T 14 Representing the time interval from the transmission of the request to the receipt of the feedback signal by the tag; t (T) 23 Representing a time interval from receiving the request to transmitting the feedback signal by the base station; t represents a time-of-flight interval; the superscript indicates the corresponding base station number;
s2, calculating the distance between the tag and each base station, wherein the calculation formula is as follows:
D 1 ＝cT 1
D 2 ＝cT 2
D 2 ＝cT 3
D 4 ＝cT 4
in the above formula, c is the light velocity, D 1 、D 2 、D 3 And D 4 The distances from the labels on the carrier to the 4 base stations respectively;
s3, calculating the coordinates of the label on the carrier relative to the base station, setting the coordinates of the No. 1 base station as (x 1, y1 and z 1), the coordinates of the No. 2 base station as (x 2, y2 and z 2), the coordinates of the No. 3 base station as (x 3, y3 and z 3), the coordinates of the No. 4 base station as (x 4, y4 and z 4), and marking the label as r UWB = (x, y, z), then there is the following relation:
the coordinates of the tag relative to the base station can be obtained by using a least square method;
s4, UWB error observation equation modeling
In the above, δr UWB For UWB position observation errors, the superscript "≡" indicates the position of the UWB tag calculated by inertial navigation, and the superscript "-" indicates the position of the UWB tag with errors calculated by the UWB tag itself.
Kalman cycle positioning: the system consists of an error state extrapolation equation, an error state covariance extrapolation equation, a Kalman gain equation, a UWB error state updating equation and an error state covariance updating equation; the above equations are derived from an error state extrapolation equation and a UWB position error observation equation; the invention fuses the IMU and UWB multi-source data, takes the IMU as a main sensor for deducing an error state equation, and takes UWB observation data as a sensor for deducing an observation equation.
Embodiment one:
this is a description of an IMU (inertial measurement unit) and UWB (ultra wide band) based high precision positioning algorithm that includes steps and equations for determining the state vector of the system, modeling the differential equation model for attitude error, velocity error and position error in inertial navigation, modeling sensor errors, system state error and UWB position error observations, and the like. Finally, a Kalman cyclic positioning method is adopted to carry out position estimation, and the following implementation steps of the algorithm are as follows:
1. determination of a state vector: state vectors in the kalman filter equation are determined, including a navigation state error vector and a sensor state.
2. Modeling a speed error differential equation: a relationship is established between the first derivative of the velocity vector in the local horizontal coordinate system and the specific force error measured by the accelerometer. The equation describes the variation of the speed error.
3. Modeling an inertial navigation position error differential equation: and establishing a differential equation of the position error under the n system, wherein factors such as latitude and elevation of the carrier are considered.
4. Modeling sensor errors: errors of the accelerometer and the gyroscope are modeled, including scale factor errors, zero bias, measurement noise, and the like.
5. Modeling a state error differential equation of the inertial navigation system: and combining the results of the previous steps, establishing a differential equation of the state error of the inertial navigation system, and describing the evolution of the state error.
6. Modeling a UWB position error observation equation: based on the time-of-flight principle between the UWB tag and the base station, a relationship between UWB position observation errors and state errors is established.
7. Kalman cycle positioning: the Kalman filtering method is adopted, and the method comprises the steps of state extrapolation, covariance extrapolation, kalman gain calculation, state updating, covariance updating and the like, and the IMU and UWB data are fused to perform position estimation.
The key idea of the algorithm is to utilize multi-source data (IMU and UWB) to perform positioning, and perform state estimation and error correction through Kalman filtering so as to improve the positioning accuracy and robustness.
The above is a specific workflow of the present invention, and the next time the present invention is used, the process is repeated.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
The invention and its embodiments have been described above with no limitation, and the actual construction is not limited to the embodiments of the invention as shown in the drawings. In summary, if one of ordinary skill in the art is informed by this disclosure, a structural manner and an embodiment similar to the technical solution should not be creatively devised without departing from the gist of the present invention.
Claims (6)
1. A four-way shuttle high-precision positioning algorithm based on multi-sensor fusion comprises state vector determination, attitude error differential equation modeling, speed error differential equation modeling, position error differential equation modeling, sensor error modeling, inertial navigation system state error differential equation modeling, UWB position error observation equation modeling and Kalman cyclic positioning; the determination of the state vector is to determine the state vector in a Kalman filtering equation, and the state vector comprises a navigation state error vector and a sensor:
δx＝[δr n δv n φ b g b a s g s a ]
in the above formula, δx represents a state error, δr n Representing the projection of the inertial navigation position error vector in the n-system (local horizontal coordinate system), δv n Representing the projection of the inertial navigation speed error vector under the n system, the third term on the right of the equal sign represents the inertial navigation attitude error vector, b g Representing zero deflection of triaxial gyroscope，b a Representing the zero deflection of the triaxial accelerometer, s g Representing the scale factor error vector of the triaxial gyroscope, s a Representing the triaxial accelerometer scale factor error vector, each term on the right of the equal sign is a three-dimensional column vector, so δx has 21 dimensions in total; the attitude error differential equation is modeled as:
in the above-mentioned method, the step of,derivative, phi, representing the attitude error of inertial navigation np The attitude error of inertial navigation is represented, and the superscript n represents the projection of each physical quantity under an n system (local horizontal coordinate system); the superscript b denotes the projection of each physical quantity under the b system (carrier coordinate system); omega in Representing the angular velocity of the n-system (local horizontal coordinate system) relative to the i-system (practical inertial system); δω in Representing the angular velocity error of the n-system (local horizontal coordinate system) relative to the i-system (practical inertial system); δω ib An angular velocity error of the b-system (carrier coordinate system) with respect to the i-system (practical inertial system); />A direction cosine matrix of a b system relative to an n system where inertial navigation is located is represented; the velocity error differential equation is modeled as:
in the above formula, the left side of the equal sign represents the first derivative of the velocity vector in the local horizontal coordinate system, δf b Representing the projection of the specific force error measured by the accelerometer in the b system; f (f) n Representing a projection of the specific force measured by the accelerometer in the n-series; omega ie Representing the angular velocity of the e-system (geocentric-earth-fixed coordinate system) relative to the i-system; δω ie Representing the relative of the e-system (geocentric and geodetic coordinates)Angular velocity error at i; omega en An angular velocity of n series relative to e series; δω en An angular velocity error of n series relative to e series is represented; upsilon (v) n Representing a velocity vector in a local horizontal coordinate system; delta v n Representing a velocity error vector in a local horizontal coordinate system; δg p Is representative of local gravity error; the expansion of local gravity is:
in the above formula, g represents a gravity vector; omega ie An angular velocity vector representing the e-system relative to the i-system; r represents the position vector of the carrier; thus, there are:
in the above formula, the superscript n denotes a projection in the n system.
2. A multi-sensor fusion based four-way shuttle high precision positioning algorithm as claimed in claim 1, wherein: the kalman cycle positioning: the system consists of an error state extrapolation equation, an error state covariance extrapolation equation, a Kalman gain equation, a UWB error state updating equation and an error state covariance updating equation; the above equations are derived from an error state extrapolation equation and a UWB position error observation equation; the invention fuses the IMU and UWB multi-source data, takes the IMU as a main sensor for deducing an error state equation, and takes the UWB observation data as a sensor for deducing an observation equation.
3. A multi-sensor fusion based four-way shuttle high precision positioning algorithm as claimed in claim 1, wherein: the UWB position error observation equation modeling comprises the following steps: fixing UWB labels at the central position of a carrier, fixing UWB base stations on the ground with known positions (longitude, latitude and elevation), wherein the number of the base stations is set to be 4, and the base stations are marked as a No. 1 base station, a No. 2 base station, a No. 3 base station and a No. 4 base station; the distance from the UWB tag to the UWB base station is determined by utilizing the time-of-flight principle, so that the absolute position of the carrier is determined, and the specific ranging mode is as follows:
in the above, T 14 Representing the time interval from the transmission of the request to the receipt of the feedback signal by the tag; t (T) 23 Representing a time interval from receiving the request to transmitting the feedback signal by the base station; t represents a time-of-flight interval; the superscript indicates the corresponding base station number; then, the distance between the tag and each base station is calculated, and the calculation formula is as follows:
D 1 ＝cT 1
D 2 ＝CT 2
D 3 ＝cT 3
D 4 ＝CT 4
in the above formula, c is the light velocity, D 1 、D 2 、D 3 And D 4 The distances from the labels on the carrier to the 4 base stations respectively; calculating the coordinates of the label on the carrier relative to the base station, setting the coordinates of the No. 1 base station as (x 1, y1 and z 1), the coordinates of the No. 2 base station as (x 2, y2 and z 2), the coordinates of the No. 3 base station as (x 3, y3 and z 3), the coordinates of the No. 4 base station as (x 4, y4 and z 4), and the label sitting mark as r UWB = (x, y, z), then there is the following relation:
the coordinates of the tag relative to the base station can be obtained by using a least square method; based on the above steps, the UWB error observation equation is modeled as:
in the above, δr UWB For UWB position observation errors, the superscript "≡" indicates the position of the UWB tag calculated by inertial navigation, and the superscript "-" indicates the position of the UWB tag with errors calculated by the UWB tag itself.
4. A multi-sensor fusion based four-way shuttle high precision positioning algorithm as claimed in claim 1, wherein: the position error differential equation is modeled as a position error differential equation form under an n system:
in the above-mentioned method, the step of,is the latitude of the carrier; h is the elevation of the carrier; r is R M Representing the radius of curvature, R, of the meridian N Representing the radius of curvature, v of the circle of mortise and tenon N 、υ E And v D Respectively representing the north speed, the east speed and the vertical speed under the n series; the disturbance analysis of the derivative of latitude is as follows: delta v N Is north velocity error, delta v E For east speed error δv D Represents the vertical speed error, and the left side of the equal sign represents the corresponding delta v respectively N 、δυ E And δv D And (5) derivative is obtained.
5. A multi-sensor fusion based four-way shuttle high precision positioning algorithm as claimed in claim 1, wherein: the sensor error modeling is as follows:
first, modeling accelerometer errors:
in the formula 1 above, the left side of the equal sign represents the actual specific force measurement output of the accelerometer; f (f) b Representing the theoretical output of the accelerometer; i is a unit vector; s is S a Is the scale factor error of the accelerometer, b g Zero offset for the accelerometer; omega a Representing accelerometer measurementsWhite noise of (a); in formula 2, δf b Representing accelerometer measurement errors;
secondly, modeling gyroscope errors:
in the formula 3, the left side of the equal sign represents the actual angular velocity measurement output omega of the gyro ib b The theoretical angular velocity in the b system; s is S g Is the scale factor error of the gyroscope, b g Zero offset of the gyroscope; w (w) g White noise representing gyroscope measurements; δω ib b Representing gyroscope measurement errors; the accelerometer zero bias, the gyroscope zero bias, the scale factor error of the accelerometer and the scale factor error of the gyroscope are modeled as a first order Gaussian Markov process, which has:
in the above, T gb 、T ab 、T gs And T as Respectively represent zero offset of gyroscope and zero offset of accelerometerThe relative times of the screw scale factor and the accelerometer scale factor; omega gb 、ω ab 、ω gs And omega as The method respectively represents gyro zero bias driving white noise, accelerometer zero bias driving white noise, gyro scale factor driving white noise and accelerometer scale factor driving white noise.
6. A multi-sensor fusion based four-way shuttle high precision positioning algorithm as claimed in claim 1, wherein: the inertial navigation system state error differential equation modeling comprises the following specific steps:
firstly, combining the results of state vector determination, attitude error differential equation modeling, speed error differential equation modeling, position error differential equation modeling and sensor error modeling, a system state error differential equation of inertial navigation can be constructed, which comprises:
wherein F (t) represents a system matrix; g (t) represents an input equation; ω (t) represents continuous-time system gaussian white noise; δx (t) represents a state error at time t;
and then, further deducing an error state extrapolation equation according to the differential equation, wherein the error state extrapolation equation comprises the following steps:
δx k ＝Φ k，k-1 δx k-1 +ω k-1
wherein:
in the above, phi k,k-1 Representing a state transition matrix, ω k-1 Delta is the linear transformation of system Gaussian white noise omega (t)x k A state error at time k; δx k-1 A state error at time k-1; note the discretization time interval Δt=t k -t k-1 F (t) is at time interval [ t ] when Δt is relatively small k-1 ，t k ]The internal changes are not great, and at this time, there are:
Φ k，k-1 ≈I+F(t k-1 )Δt
omega can be demonstrated k-1 Is a zero-mean white noise sequence, and meets the following conditions:
ω k ～N(0，Q k )
in the above formula, the symbol "N" represents a Gaussian distribution, and the symbols "to" represent compliance, i.e., ω k-1 Obeys Gaussian distribution, Q k The method for calculating the system state noise covariance matrix comprises the following steps:
in the above, Q k The calculation of (1) uses the Le trapezoidal integral formula.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311402686.2A CN117433517A (en) | 2023-10-27 | 2023-10-27 | Four-way shuttle high-precision positioning algorithm based on multi-sensor fusion |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202311402686.2A CN117433517A (en) | 2023-10-27 | 2023-10-27 | Four-way shuttle high-precision positioning algorithm based on multi-sensor fusion |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN117433517A true CN117433517A (en) | 2024-01-23 |
Family
ID=89545695
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202311402686.2A Pending CN117433517A (en) | 2023-10-27 | 2023-10-27 | Four-way shuttle high-precision positioning algorithm based on multi-sensor fusion |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117433517A (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116182867A (en) * | 2023-02-22 | 2023-05-30 | 东南大学 | INS/UWB unmanned aerial vehicle positioning method based on tight combination in complex indoor environment |
| CN117289322A (en) * | 2023-11-24 | 2023-12-26 | 江苏领创星通卫星通信科技有限公司 | High-precision positioning algorithm based on IMU, GPS and UWB |
-
2023
- 2023-10-27 CN CN202311402686.2A patent/CN117433517A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116182867A (en) * | 2023-02-22 | 2023-05-30 | 东南大学 | INS/UWB unmanned aerial vehicle positioning method based on tight combination in complex indoor environment |
| CN117289322A (en) * | 2023-11-24 | 2023-12-26 | 江苏领创星通卫星通信科技有限公司 | High-precision positioning algorithm based on IMU, GPS and UWB |
Non-Patent Citations (4)
| Title |
|---|
| 余航: "超宽带/GNSS/SINS融合定位模型与方法研究", 《中国博士学位论文全文数据库信息科技辑》, 15 July 2021 (2021-07-15), pages 15 - 24 * |
| 曹琢健: "基于 GNSS/INS/UWB 组合的室内外无缝定位方法研究", 《中国优秀硕士学位论文全文数据库信息科技辑》, 15 February 2022 (2022-02-15) * |
| 王长强: "多源信息融合无缝定位理论和方法研究", 《中国博士学位论文全文数据库信息科技辑》, 15 July 2023 (2023-07-15), pages 32 - 40 * |
| 许海: "基于UWB/MEMS组合的室内定位算法研究", 《中国优秀硕士学位论文全文数据库信息科技辑》, 15 August 2023 (2023-08-15), pages 13 - 38 * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109556632B (en) | INS/GNSS/polarization/geomagnetic integrated navigation alignment method based on Kalman filtering | |
| CN107655476B (en) | Pedestrian high-precision foot navigation method based on multi-information fusion compensation | |
| CN109974697B (en) | High-precision mapping method based on inertial system | |
| CN104736963B (en) | mapping system and method | |
| CN106289246B (en) | A kind of flexible link arm measure method based on position and orientation measurement system | |
| CN111156994B (en) | INS/DR & GNSS loose combination navigation method based on MEMS inertial component | |
| CN102169184B (en) | Method and device for measuring installation misalignment angle of double-antenna GPS (Global Position System) in integrated navigation system | |
| CN103196445B (en) | Based on the carrier posture measuring method of the earth magnetism supplementary inertial of matching technique | |
| CN106842271B (en) | Navigation positioning method and device | |
| CN109186597B (en) | Positioning method of indoor wheeled robot based on double MEMS-IMU | |
| CN107270893A (en) | Lever arm, time in-synchronization error estimation and the compensation method measured towards real estate | |
| CN109870173A (en) | A kind of track correct method of the submarine pipeline inertial navigation system based on checkpoint | |
| CN110221332A (en) | A kind of the dynamic lever arm estimation error and compensation method of vehicle-mounted GNSS/INS integrated navigation | |
| CN101173858A (en) | Three-dimensional posture fixing and local locating method for lunar surface inspection prober | |
| CN111399023B (en) | Inertial basis combined navigation filtering method based on lie group nonlinear state error | |
| CN113916222B (en) | Combined navigation method based on Kalman filtering estimation variance constraint | |
| CN110207691A (en) | A kind of more unmanned vehicle collaborative navigation methods based on data-link ranging | |
| CN102879779A (en) | Rod arm measurement and compensation method based on synthetic aperture radar (SAR) remote sensing imaging | |
| CN108873034A (en) | A kind of implementation method of inertial navigation subcarrier ambiguity resolution | |
| CN109931952A (en) | The direct analytic expression coarse alignment method of inertial navigation under the conditions of unknown latitude | |
| CN103207388A (en) | Method for calibrating airborne interference synthesis aperture radar (SAR) under squint condition | |
| CN109084755B (en) | Accelerometer zero offset estimation method based on gravity apparent velocity and parameter identification | |
| CN116482735A (en) | High-precision positioning method for inside and outside of limited space | |
| CN114909608B (en) | Non-excavation pipeline positioning method based on MIMU/mileage wheel/photoelectric speed measurement module combination | |
| CN109827572A (en) | A kind of method and device of detection truck position prediction |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |