CN107655476A - Pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation - Google Patents

Pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation Download PDF

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CN107655476A
CN107655476A CN201710716885.9A CN201710716885A CN107655476A CN 107655476 A CN107655476 A CN 107655476A CN 201710716885 A CN201710716885 A CN 201710716885A CN 107655476 A CN107655476 A CN 107655476A
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speed
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CN107655476B (en
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黄欣
熊智
许建新
徐丽敏
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Nanjing University of Aeronautics and Astronautics
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    • 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
    • G01C21/18—Stabilised platforms, e.g. by gyroscope

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Abstract

The invention discloses a kind of pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation, the raw measurement data of collection gyroscope and accelerometer in real time, the error compensation of initial gyroscope is zero, the error compensation of accelerometer is also zero, and strapdown resolving is carried out by strap-down inertial computation；On the basis of the above, structure Kalman filter correction model is filtered amendment, state equation is consistent, and measurement equation adjusts with multidimensional measurement information dynamic, under different multidimensional information detections, algorithm corresponding to structure, measurement equation real-time transform, estimation, amendment navigator fix resultant error and sensor error, return to the error compensation of gyroscope and the error compensation of accelerometer；Finally export navigator fix result, the i.e. position of pedestrian, speed, posture；Using the consumer level sensor chip and Magnetic Sensor of low precision, solve under no global navigation satellite system GNSS environment high-precision pedestrian's orientation problem and it is high long when course divergence problem.

Description

Pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation
Technical field
The present invention relates to a kind of high-precision pedestrian's foot navigation algorithm, more particularly to it is a kind of based on Multi-information acquisition compensation Pedestrian's high accuracy foot navigation algorithm, belongs to pedestrian navigation technical field.
Background technology
At present, the research for pedestrian navigation technology is broadly divided into following a few classes：Wireless aware, pattern-recognition, inertia pass Sensor.Wherein wireless aware technology needs to dispose additional radio frequency equipment, and including WIFI, UWB etc., the scope of application is narrower, signal holds Be vulnerable to block, cost it is higher；And inertial sensor have it is autonomous, not by external interference, lower-cost feature, be adapted to extensive With.But the inertial sensor errors of low cost are larger, if not compensated for or other means aid in, will in the range of several seconds Error more than meter level can be caused.This patent proposes utilize Multi-information acquisition compensation mechanism, designs a kind of based on inertial navigation system Zero-speed Kalman filtering algorithm, the course error for studying magnetic heading stability under pedestrian's initial static are gone from observation algorithm, research Zero-speed course error under people's motion state studies merging based on geomagnetic matching and strap inertial navigation algorithm from observation algorithm Algorithm, it ensure that the high long high accuracy and high reliability at present of pedestrian.This method is applied to pedestrian navigation, solves no global satellite High-precision pedestrian positioning under navigation positioning system GNSS environment, it is independently fixed when can realize that pedestrian is high long using inexpensive sensor Position, has higher engineer applied and commercial value.
The content of the invention
Goal of the invention：The technical problems to be solved by the invention are to be set using the inertial sensor of low precision with Magnetic Sensor Count a kind of Multi-information acquisition backoff algorithm suitable for the navigation of pedestrian's high accuracy foot.
Technical scheme：
A kind of pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation, it is characterised in that：Collection top in real time The raw measurement data of spiral shell instrument and accelerometer, the error compensation of initial gyroscope is zero, and the error compensation of accelerometer is also Zero, strapdown resolving is carried out by strap-down inertial computation；On the basis of the above, Kalman filter correction model is built Amendment is filtered, state equation is consistent, and measurement equation adjusts with multidimensional measurement information dynamic, is examined in different multidimensional information Under survey, algorithm corresponding to structure, measurement equation real-time transform, estimation, amendment navigator fix resultant error and sensor error, return Return the error compensation of gyroscope and the error compensation of accelerometer；Finally export navigator fix result, the i.e. position of pedestrian, speed Degree, posture；
When only zero-speed detection success, calculated using pseudo- measurement information structure based on zero-speed Kalman filtering correction model Method；When having zero-speed detection success and initial magnetic heading error from when observing, magnetic heading error under pedestrian's initial rest state is built From observation algorithm；, from when observing, pedestrian movement's state is built when there is zero-speed course error under zero-speed detection success and dynamical state Lower zero-speed course error is from observation algorithm；When have zero-speed detection success, under motion state zero-speed course error from observing and earth magnetism During matching, the blending algorithm based on geomagnetic matching and strap-down inertial computation is built, wherein the state side of each algorithm Journey and measurement equation collective effect construct Kalman filter correction model.
Further：The strap-down inertial computation is as follows：
Inertial sensor is made up of accelerometer and gyroscope, and accelerometer obtains the ratio force information of motion carrier, passes through Once integration can obtain speed, and position can be obtained by quadratic integral；Gyroscope measuring machine system is relative to inertial system Angular speed, angle can be obtained by once integrating；Most basic strap-down inertial computation includes attitude algorithm, speed Resolve, position resolves；Then following equation calculates posture, speed, position：
Wherein, b is body axis system, and n is navigational coordinate system, and e is terrestrial coordinate system, and i is inertial coodinate system, and f is specific force, G is acceleration of gravity,For the posture transfer matrix of body axis system to navigational coordinate system,For the axle body system phase of x, y, z three The projection fastened for inertial system angular speed in body,For three spindle guides boat, system fastens relative to inertial system angular speed in body Projection,For earth rotation angular speed navigation be under projection,It is navigational coordinate system relative to terrestrial coordinate system The column vector that component of the angular speed in navigational coordinate system axial direction is formed, v is three axle speed vectors, and p is three shaft position vectors；ForOn time t derivative,For vnOn time t derivative,For pnOn time t derivative, therefore above formula is Chang Wei Divide equation, on the basis of known initial attitude, speed, position, iterative.
Yet further：The state equation of the Kalman filtering correction model is as follows：
Kalman filter model selects " northeast day " geographic coordinate system, and it is as follows to build 18 scalariform states models：
Wherein, δ φ=[δ φe δφn δφu] it is platform angle error；δ ν=[δ ve δvn δvu] it is velocity error；δ p= [δ λ δ L δ h] is that site error is longitude, latitude, height error；εb=[εbx εby εbz] it is three axis accelerometer arbitrary constant；εr =[εrx εry εrz] it is three-axis gyroscope single order markoff process,For three axis accelerometer Single order markoff process；
Under different geographic coordinate systemsPosture transfer matrix is different, and the A, G, W coefficient in state equation are also different, Under " northeast day " geographic coordinate system, A, G, W are set as shown in following four formula：A is sytem matrix, and G is system noise matrix, W= [ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz] it is system noise, set according to sensor self character；Its Middle ωgDrifted about for three axis accelerometer random white noise, its mean square deviation is σg, ωrIt is that three axis accelerometer mean square deviation is σrMarkov mistake Journey drives white noise, ωaIt is that three axis accelerometer mean square deviation is σaMarkoff process driving white noise；
It is the matrix of corresponding 9 basic navigation parameters, T is the phase of markoff process Close the time.
Further：It is described as follows based on zero-speed Kalman filtering correction model algorithm：
In the success of only zero-speed detection, the sextuple measurement model under zero-speed state is built using pseudo- measurement information；Order VeloP be 3 × 1 ranks null matrix, posiP (t)=posiN (t-1), then based on zero-speed Kalman filtering measurement model such as following formula It is shown：
Wherein, Z1(t) it is the observed quantity of speed and position, veloN is the speed of SINS real-time resolving, PosiN be SINS real-time resolving position, MvFor velocity error under pedestrian's zero-speed state, MpFor pedestrian's zero-speed state Lower site error, V1To measure noise, H1For measurement matrix, as shown in following two formula：
RmFor meridian circle radius of curvature of the earth, RnFor prime vertical radius of curvature of the earth, L is latitude.
Yet further：Magnetic heading error is as follows from observation algorithm under pedestrian's initial rest state：
Under pedestrian's initial rest state, magnetic heading angle has stronger stability, therefore ought have zero-speed detection successfully and first Beginning magnetic heading error builds one-dimensional measurement equation, is shown below from when observing：
Wherein, Z2(t) it is the observed quantity at initial heading angle, ψINSThe course angle resolved for strapdown, can be by strap-down inertial In computationMatrix carries out trigonometric function conversion and obtained, orderThen ψmgFor magnetic heading angle, it can be resolved and obtained by the magnetic information that Magnetic Sensor measurement obtains,For magnetic heading angle resolution error, V2For Measure noise；
Under pedestrian's initial rest state, the further estimation to sensor error is realized using following formula：
Z3(t) it is the observed quantity of speed, position and initial heading angle.
Further：Zero-speed course error is as follows from observation algorithm under pedestrian movement's state：
Under pedestrian movement's state, each step undergoes one section of zero-speed moment, the zero-speed stage course be basically unchanged, based on zero-speed Steady theory, from when observing, remember the zero-speed of step first when there is zero-speed course error under zero-speed detection success and dynamical state The course angle of moment point is ψk-initial, the course angle for remembering remaining zero-speed moment point of the step is ψk-others；
It is as follows from measurement equation is observed to build one-dimensional zero-speed course：
Wherein：Z4(t) it is the observed quantity of course angle under motion state,For course angle error；Missed for zero-speed course angle Difference, V4To measure noise；Therefore：
θ is the angle of pitch, can be by strap-down inertial computationMatrix carries out trigonometric function conversion and obtained,
Then addition zero-speed course error under motion state can be obtained is from 7 dimension measurement models of observation algorithm：
Wherein, Z5(t) be speed, under position and motion state course angle observed quantity.
Yet further：The blending algorithm based on geomagnetic matching and strap-down navigation computation is as follows：
When being detected simultaneously by zero-speed and geomagnetic matching success, the dimension measurement equation of concentrated filter structure 10, auxiliary are used Correction position error, velocity error and sensor error, as shown in following three formula, wherein posiM is geomagnetic matching position, can be by Geomagnetic matching directly obtains, M6For geomagnetic matching site error, V6For measure noise, posiN be inertial navigation real-time resolving position, δ P is site error, and HI is based on as shown in zero-speed Kalman filtering correction model algorithm：
Z6(t)=[posiN-posiM]=[δ p+M6]=H6(t)X(t)+V6(t)
H6=[03×9 HI 03×9]
Z6(t) it is geomagnetic matching position detection amount, Z7(t) it is course angle and earth magnetism under speed, position, motion state With position observed quantity.
Beneficial effect：
1. using the consumer level sensor chip of low precision, solve under no global navigation satellite system GNSS environment High-precision pedestrian's orientation problem.
2. by using Magnetic Sensor, course divergence problem when solving high long using magnetic heading angle and geomagnetic matching.
3. inertial sensor is low with Magnetic Sensor cost and popularization is wider, the practicality and generalization of algorithm are stronger.
Brief description of the drawings
Fig. 1 is pedestrian's high accuracy foot navigation algorithm FB(flow block) based on Multi-information acquisition compensation.
Embodiment
Further explanation is done to the present invention below in conjunction with the accompanying drawings.
According to following embodiments, the present invention can be better understood from.It is however, as it will be easily appreciated by one skilled in the art that real Apply specific material proportion, process conditions and its result described by example and be merely to illustrate the present invention, without that will not also should limit The present invention described in detail in claims processed.
As shown in figure, on the basis of known pedestrian's initial position, speed, posture, accelerometer and top are gathered in real time Spiral shell instrument information carries out strap-down inertial resolving, obtains speed, position and posture that inertial navigation resolves；Using accelerometer, Gyroscope and magnetometer information carry out zero-speed detection in zero-speed detection module and build pseudo- measurement information, while carry out initial magnetic boat To error from zero-speed course error under observation, dynamical state from observation and geomagnetic matching, when different condition is set up, structure is different Kalman filtering measurement equation, and state equation is consistent；The position estimated, speed, attitude error will be filtered to inertial navigation Position that system obtains, speed, posture compensate, and then obtain final navigator fix result, the i.e. position of pedestrian, speed Degree, posture；The sensor error for filtering estimation is returned into accelerometer, gyroscopes error compensation loop, corrects sensor in real time Error, circulated with this；
When only zero-speed detection success, calculated using pseudo- measurement information structure based on zero-speed Kalman filtering correction model Method；When having zero-speed detection success and initial magnetic heading error from when observing, magnetic heading error under pedestrian's initial rest state is built From observation algorithm；, from when observing, pedestrian movement's state is built when there is zero-speed course error under zero-speed detection success and dynamical state Lower zero-speed course error is from observation algorithm；When have zero-speed detection success, under motion state zero-speed course error from observing and earth magnetism During matching, build the blending algorithm based on geomagnetic matching and strap-down navigation computation, wherein the state equation of each algorithm and Measurement equation collective effect constructs Kalman filter correction model.
The state equation of Kalman filtering correction model：
Kalman filter model selects " northeast day " (ENU) geographic coordinate system, and it is as follows to build 18 scalariform states models：
Wherein, δ φ=[δ φe δφn δφu] it is platform angle error；δ ν=[δ ve δvn δvu] it is velocity error；δ p= [δ λ δ L δ h] is that site error is longitude, latitude, height error；εb=[εbx εby εbz] it is three axis accelerometer arbitrary constant；εr =[εrx εry εrz] it is three-axis gyroscope single order markoff process,For three axis accelerometer Single order markoff process；
Under different coordinatesPosture transfer matrix is different, and the A, G, W coefficient in state equation are also different, in " east Under northern day " geographic coordinate system, A, G, W are set as shown in following four formula：A is sytem matrix, and G is system noise matrix, W=[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz] it is system noise, set according to sensor self character；Wherein ωgFor Three axis accelerometer random white noise drifts about, and its mean square deviation is σg, ωrIt is that three axis accelerometer mean square deviation is σrMarkoff process driving White noise, ωaIt is that three axis accelerometer mean square deviation is σaMarkoff process driving white noise；
It is the matrix of corresponding 9 basic navigation parameters, T is the phase of markoff process Close the time；
Algorithm one：Strap-down inertial computation
Inertial navigation system be it is a kind of independent of any external information, the also self-aid navigation system not to outside emittance System, has good concealment, can in the air, ground, the characteristics of working under the various complex environments such as underwater, be broadly divided into platform-type be used to Guiding systems and the major class of Methods of Strapdown Inertial Navigation System two.SINS develops on the basis of Platform INS Inertial, It is a kind of frameless system.
Inertial sensor is made up of accelerometer and gyroscope, and accelerometer and gyroscope are directly connected on carrier, Gyroscope and accelerometer are respectively used for measuring the angular movement information and line movable information of carrier, and airborne computer is according to these Metrical information calculates course, posture, speed and the position of carrier.Accelerometer obtains the ratio force information of motion carrier, leads to Speed can be obtained by crossing once integration, and position can be obtained by quadratic integral；Gyroscope measuring machine system is relative to inertial system Angular speed, can obtain angle by once integrating.Most basic strap-down inertial computation includes attitude algorithm, speed Degree resolves, position resolves.Then following equation calculates posture, speed, position：
Wherein, b is body axis system, and n is navigational coordinate system, and e is terrestrial coordinate system, and i is inertial coodinate system, and f is specific force, G is acceleration of gravity,For the posture transfer matrix of body axis system to navigational coordinate system,For the axle body system phase of x, y, z three The projection fastened for inertial system angular speed in body,Fastened for three spindle guides boat system relative to inertial system angular speed in body Projection,For earth rotation angular speed navigation be under projection,Angle speed for navigational coordinate system relative to terrestrial coordinate system The column vector that the component in navigational coordinate system axial direction is formed is spent, v is three axle speed vectors, and p is three shaft position vectors,For On time t derivative,For vnOn time t derivative,For pnOn time t derivative, therefore above formula is ordinary differential Equation, on the basis of known initial attitude, speed, position, iterative.
But the inertial sensor noise of low cost is larger, and position error more than meter level can be caused within several seconds, because This need to seek other extra supplementary means amendment navigation positioning errors, suppress error diverging.
Algorithm two：Kalman filtering correction algorithm model based on zero-speed
Kalman filtering correction model, estimated sensor error and navigator fix resultant error are built based on zero-speed, ensured The high long positioning precision at present of pedestrian；In the success of only zero-speed detection, six under zero-speed state are built using pseudo- measurement information Tie up measurement model；Make the null matrix that veloP is 3 × 1 ranks, posiP (t)=posiN (t-1), then Kalman's filter based on zero-speed The continuity equation of ripple measurement model is shown below：
Wherein, Z1(t) it is the observed quantity of speed and position, veloN is the speed of SINS real-time resolving, PosiN be SINS real-time resolving position, MvFor velocity error under pedestrian's zero-speed state, MpFor pedestrian's zero-speed state Lower site error, V1To measure noise, H1For measurement matrix, as shown in following two formula：
RmFor meridian circle radius of curvature of the earth, RnFor prime vertical radius of curvature of the earth, L is latitude.
Here with position, speed virtual measurement information auxiliary amendment sensor error and navigation results error, to maintain The long pedestrian navigation positioning precision at present of height, but course observability is relatively low in algorithm two, course it is whether accurate, can be direct The accuracy of posture is had influence on, need to attempt to build course Correlated Case with ARMA Measurement Information revision course error.
Algorithm three：Magnetic heading error is from observation algorithm under pedestrian's initial rest state
Course precision is to influence the principal element of pedestrian navigation positioning in pedestrian navigation positioning, and magnetic heading angle can be used as absolutely To course information amendment course error.Under pedestrian's initial rest state, magnetic heading angle has stronger stability, therefore ought have zero Speed is detected successfully with initial magnetic heading error from when observing, and is built one-dimensional measurement equation, is shown below：
Wherein, Z2(t) it is the observed quantity at initial heading angle, ψINSThe course angle resolved for strapdown, can be by algorithm oneSquare Battle array carries out trigonometric function conversion and obtained, orderThenψmg, can for magnetic heading angle The magnetic information obtained by Magnetic Sensor measurement, which resolves, to be obtained,For magnetic heading angle resolution error, V2To measure noise.
Under pedestrian's initial rest state, the further estimation to sensor error is realized using following formula：
Z3(t) it is the observed quantity of speed, position and initial heading angle.
Algorithm four：Zero-speed course error is from observation algorithm under pedestrian movement's state
Under pedestrian movement's state, each step undergoes one section of zero-speed moment, the zero-speed stage course be basically unchanged, based on zero-speed Steady theory, from when observing, remember the zero-speed of step first when there is zero-speed course error under zero-speed detection success and dynamical state The course angle of moment point is ψk-initial, the course angle for remembering remaining zero-speed moment point of the step is ψk-others。
It is as follows from measurement equation is observed to build one-dimensional zero-speed course：
Wherein：Z4(t) it is the observed quantity of course angle under motion state,For course angle error；Missed for zero-speed course angle Difference, V4To measure noise；Therefore：
θ is the angle of pitch, can be by algorithm oneMatrix carries out trigonometric function conversion and obtained,
Then addition zero-speed course error under motion state can be obtained is from 7 dimension measurement models of observation algorithm：
Wherein, Z5(t) be speed, under position and motion state course angle observed quantity.
Algorithm five：Blending algorithm based on geomagnetic matching and strap-down navigation computation
Using geomagnetic matching information, increase reliability of positioning, in the case where there is geomagnetic matching, can further ensure pedestrian Navigation and positioning accuracy.When being detected simultaneously by zero-speed and geomagnetic matching success, measurement equation is tieed up using concentrated filter structure 10, Correction position error, velocity error and sensor error are aided in, as shown in following three formula, wherein posiM is geomagnetic matching position, It can be directly obtained by geomagnetic matching, M6For geomagnetic matching site error, V6To measure noise, posiN is the position of inertial navigation real-time resolving Put, δ p are site error, and HI is as shown in algorithm two.
Z6(t)=[posiN-posiM]=[δ p+M6]=H6(t)X(t)+V6(t)
H6=[03×9 HI 03×9]
Z6(t) it is geomagnetic matching position detection amount, Z7(t) it is course angle and earth magnetism under speed, position, motion state With position observed quantity.
So far pedestrian's high accuracy foot navigation algorithm of Multi-information acquisition compensation is constructed, ensures pedestrian's high accuracy, high length When navigate.Wherein algorithm 2345 is in fact to utilize multi-source information, to lift the precision and fault-tolerance of pedestrian navigation positioning.
Algorithm one is most basic strap-down inertial computation, for low cost inertial sensor, its noise compared with Greatly, if do not corrected, position error more than meter level will be caused in a short time.Then use algorithm two, using position, Speed virtual measurement information auxiliary amendment sensor error and navigation results error, to maintain high long pedestrian navigation at present to position Precision, but Kalman filter in algorithm two, course observability is relatively low, and course is closely bound up with posture, need to attempt to build Course Correlated Case with ARMA Measurement Information revision course error；And magnetic heading angle can be used as absolute course information amendment course error, Hang Renchu Under beginning inactive state, magnetic heading angle has stronger stability, therefore adds algorithm three, but pedestrian not necessarily has rest shape State, therefore algorithm four is added, course observability is improved, reduces course error, further improves positioning precision；Algorithm five is profit With earth magnetism match information, increase reliability of positioning, in the case where there is geomagnetic matching, can further ensure pedestrian navigation positioning accurate Degree.
Described above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (7)

  1. A kind of 1. pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation, it is characterised in that：Collection gyro in real time The raw measurement data of instrument and accelerometer, the error compensation of initial gyroscope is zero, and the error compensation of accelerometer is also zero, Strapdown resolving is carried out by strap-down inertial computation；On the basis of the above, structure Kalman filter correction model enters Row filter correction, state equation is consistent, and measurement equation adjusts with multidimensional measurement information dynamic, is detected in different multidimensional information Under, algorithm corresponding to structure, measurement equation real-time transform, estimation, amendment navigator fix resultant error and sensor error, return The error compensation of gyroscope and the error compensation of accelerometer；Finally export navigator fix result, i.e., the position of pedestrian, speed, Posture；
    When only zero-speed detection success, zero-speed Kalman filtering correction model algorithm is based on using pseudo- measurement information structure；When There are zero-speed detection success and initial magnetic heading error to be observed certainly from magnetic heading error under pedestrian's initial rest state when observing, is built Algorithm；, from when observing, zero-speed under pedestrian movement's state is built when there is zero-speed course error under zero-speed detection success and dynamical state Course error is from observation algorithm；When have zero-speed detection success, under motion state zero-speed course error from observing and during geomagnetic matching, The blending algorithm based on geomagnetic matching and strap-down inertial computation is built, wherein the state equation of each algorithm and measurement Equation collective effect constructs Kalman filter correction model.
  2. 2. a kind of pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation according to claim 1, it is special Sign is：The strap-down inertial computation is as follows：
    Inertial sensor is made up of accelerometer and gyroscope, and accelerometer obtains the ratio force information of motion carrier, by once Integration can obtain speed, and position can be obtained by quadratic integral；Gyroscope measuring machine system is fast relative to the angle of inertial system Degree, angle can be obtained by once integrating；Most basic strap-down inertial computation includes attitude algorithm, velocity solution Calculate, position resolves；Then following equation calculates posture, speed, position：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>C</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>b</mi> <mi>n</mi> </msubsup> <mo>=</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <msubsup> <mi>&amp;Omega;</mi> <mrow> <mi>i</mi> <mi>b</mi> </mrow> <mi>b</mi> </msubsup> <mo>-</mo> <msubsup> <mi>Q</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> <mi>b</mi> </msubsup> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mover> <mi>v</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>n</mi> </msup> <mo>=</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> <msup> <mi>f</mi> <mi>b</mi> </msup> <mo>-</mo> <mo>&amp;lsqb;</mo> <mrow> <mo>(</mo> <mn>2</mn> <msubsup> <mi>&amp;omega;</mi> <mrow> <mi>i</mi> <mi>e</mi> </mrow> <mi>n</mi> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;omega;</mi> <mrow> <mi>e</mi> <mi>n</mi> </mrow> <mi>n</mi> </msubsup> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msup> <mi>v</mi> <mi>n</mi> </msup> <mo>-</mo> <mi>g</mi> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <msup> <mover> <mi>p</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>n</mi> </msup> <mo>=</mo> <msup> <mi>v</mi> <mi>n</mi> </msup> </mtd> </mtr> </mtable> </mfenced>
    Wherein, b is body axis system, and n is navigational coordinate system, and e is terrestrial coordinate system, and i is inertial coodinate system, and f is specific force, and g is Acceleration of gravity,For the posture transfer matrix of body axis system to navigational coordinate system,For x, y, z three, axle body system is relative In the projection that inertial system angular speed is fastened in body,Fastened for three spindle guides boat system relative to inertial system angular speed in body Projection,For earth rotation angular speed navigation be under projection,Angle for navigational coordinate system relative to terrestrial coordinate system The column vector that component of the speed in navigational coordinate system axial direction is formed, v is three axle speed vectors, and p is three shaft position vectors；ForOn time t derivative,For vnOn time t derivative,For pnOn time t derivative, therefore above formula is Chang Wei Divide equation, on the basis of known initial attitude, speed, position, iterative.
  3. 3. a kind of pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation according to claim 1, it is special Sign is that the state equation of the Kalman filtering correction model is as follows：
    Kalman filter model selects " northeast day " geographic coordinate system, and it is as follows to build 18 scalariform states models：
    <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mover> <mi>X</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>A</mi> <mi>X</mi> <mo>+</mo> <mi>G</mi> <mi>W</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>X</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>&amp;delta;</mi> <mi>&amp;phi;</mi> </mrow> </mtd> <mtd> <mrow> <mi>&amp;delta;</mi> <mi>v</mi> </mrow> </mtd> <mtd> <mrow> <mi>&amp;delta;</mi> <mi>p</mi> </mrow> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mi>b</mi> </msub> </mtd> <mtd> <msub> <mi>&amp;epsiv;</mi> <mi>r</mi> </msub> </mtd> <mtd> <msub> <mo>&amp;dtri;</mo> <mi>r</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced>
    Wherein, δ φ=[δ φe δφn δφu] it is platform angle error；δ ν=[δ ve δvn δvu] it is velocity error；δ p=[δ λ δ L δ h] it is that site error is longitude, latitude, height error；εb=[εbx εby εbz] it is three axis accelerometer arbitrary constant；εr= [εrx εry εrz] it is three-axis gyroscope single order markoff process, ▽r=[▽rx ▽ry ▽rz] it is three axis accelerometer single order Markoff process；
    Under different geographic coordinate systemsPosture transfer matrix is different, and the A, G, W coefficient in state equation are also different, in " east Under northern day " geographic coordinate system, A, G, W are set as shown in following four formula：A is sytem matrix, and G is system noise matrix, W=[ωgx ωgy ωgz ωrx ωry ωrz ωax ωay ωaz] it is system noise, set according to sensor self character；Wherein ωgFor Three axis accelerometer random white noise drifts about, and its mean square deviation is σg, ωrIt is that three axis accelerometer mean square deviation is σrMarkoff process driving White noise, ωaIt is that three axis accelerometer mean square deviation is σaMarkoff process driving white noise；
    <mrow> <mi>G</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>9</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>9</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>9</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>I</mi> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>I</mi> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
    <mrow> <mi>A</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mrow> <mi>I</mi> <mi>N</mi> <mi>S</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mn>9</mn> <mo>&amp;times;</mo> <mn>9</mn> </mrow> </msub> </mtd> <mtd> <msub> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mrow> <mi>s</mi> <mi>g</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mn>9</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>9</mn> <mo>&amp;times;</mo> <mn>9</mn> </mrow> </msub> </mtd> <mtd> <msub> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mrow> <mi>I</mi> <mi>M</mi> <mi>U</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mn>9</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
    <mrow> <msub> <mi>A</mi> <mrow> <mi>I</mi> <mi>M</mi> <mi>U</mi> </mrow> </msub> <mo>=</mo> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow> <mi>r</mi> <mi>y</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow> <mi>r</mi> <mi>z</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow> <mi>a</mi> <mi>y</mi> </mrow> </msub> </mfrac> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <msub> <mi>T</mi> <mrow> <mi>a</mi> <mi>z</mi> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
    <mrow> <msub> <mi>A</mi> <mrow> <mi>s</mi> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> </mrow> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msubsup> <mi>C</mi> <mi>b</mi> <mi>n</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
    It is the matrix of corresponding 9 basic navigation parameters, when T is the correlation of markoff process Between.
  4. 4. a kind of pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation according to claim 1, it is special Sign is, described as follows based on zero-speed Kalman filtering correction model algorithm：
    In the success of only zero-speed detection, the sextuple measurement model under zero-speed state is built using pseudo- measurement information；The veloP is made to be The null matrix of 3 × 1 ranks, posiP (t)=posiN (t-1), then the Kalman filtering measurement model based on zero-speed be shown below：
    <mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <mtable> <mtr> <mtd> <mrow> <mi>v</mi> <mi>e</mi> <mi>l</mi> <mi>o</mi> <mi>N</mi> <mo>-</mo> <mi>v</mi> <mi>e</mi> <mi>l</mi> <mi>o</mi> <mi>P</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>p</mi> <mi>o</mi> <mi>s</mi> <mi>i</mi> <mi>N</mi> <mo>-</mo> <mi>p</mi> <mi>o</mi> <mi>s</mi> <mi>i</mi> <mi>P</mi> </mrow> </mtd> </mtr> </mtable> <mo>&amp;rsqb;</mo> <mo>=</mo> <mo>&amp;lsqb;</mo> <mtable> <mtr> <mtd> <mrow> <mi>&amp;delta;</mi> <mi>v</mi> <mo>+</mo> <msub> <mi>M</mi> <mi>v</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;delta;</mi> <mi>p</mi> <mo>+</mo> <msub> <mi>M</mi> <mi>p</mi> </msub> </mrow> </mtd> </mtr> </mtable> <mo>&amp;rsqb;</mo> <mo>=</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>X</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>V</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow>
    Wherein, Z1(t) it is the observed quantity of speed and position, veloN is the speed of SINS real-time resolving, and posiN is victory Join the position of inertial navigation system real-time resolving, MvFor velocity error under pedestrian's zero-speed state, MpMissed for position under pedestrian's zero-speed state Difference, V1To measure noise, H1For measurement matrix, as shown in following two formula：
    <mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>I</mi> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>3</mn> </mrow> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>12</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>6</mn> </mrow> </msub> </mtd> <mtd> <mrow> <mi>H</mi> <mi>I</mi> </mrow> </mtd> <mtd> <msub> <mn>0</mn> <mrow> <mn>3</mn> <mo>&amp;times;</mo> <mn>9</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
    <mrow> <mi>H</mi> <mi>I</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>R</mi> <mi>m</mi> </msub> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>R</mi> <mi>n</mi> </msub> <mi>cos</mi> <mi> </mi> <mi>L</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow>
    RmFor meridian circle radius of curvature of the earth, RnFor prime vertical radius of curvature of the earth, L is latitude.
  5. 5. a kind of pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation according to claim 4, it is special Sign is：Magnetic heading error is as follows from observation algorithm under pedestrian's initial rest state：
    Under pedestrian's initial rest state, magnetic heading angle has stronger stability, therefore working as has zero-speed detection successful and initial magnetic Course error builds one-dimensional measurement equation, is shown below from when observing：
    Wherein, Z2(t) it is the observed quantity at initial heading angle, ψINSThe course angle resolved for strapdown, can be resolved by strap-down inertial In algorithmMatrix carries out trigonometric function conversion and obtained, orderThenψmgFor Magnetic heading angle, it can be resolved and obtained by the magnetic information that Magnetic Sensor measurement obtains,For magnetic heading angle resolution error, V2Made an uproar to measure Sound；
    Under pedestrian's initial rest state, the further estimation to sensor error is realized using following formula：
    <mrow> <msub> <mi>Z</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>&amp;rsqb;</mo> </mrow>
    Z3(t) it is the observed quantity of speed, position and initial heading angle.
  6. 6. a kind of pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation according to claim 4, it is special Sign is：Zero-speed course error is as follows from observation algorithm under pedestrian movement's state：
    Under pedestrian movement's state, each step undergoes one section of zero-speed moment, the zero-speed stage course be basically unchanged, based on zero-speed course Constant theory, from when observing, remember the step the first zero-speed moment when there is zero-speed course error under zero-speed detection success and dynamical state The course angle of point is ψk-initial, the course angle for remembering remaining zero-speed moment point of the step is ψk-others；
    It is as follows from measurement equation is observed to build one-dimensional zero-speed course：
    Wherein：Z4(t) it is the observed quantity of course angle under motion state,For course angle error；For zero-speed course angle error, V4 To measure noise；Therefore：
    θ is the angle of pitch, can be by strap-down inertial computationMatrix carries out trigonometric function conversion and obtained,
    Then addition zero-speed course error under motion state can be obtained is from 7 dimension measurement models of observation algorithm：
    <mrow> <msub> <mi>Z</mi> <mn>5</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>&amp;rsqb;</mo> </mrow>
    Wherein, Z5(t) be speed, under position and motion state course angle observed quantity.
  7. 7. a kind of pedestrian's high accuracy foot navigation algorithm based on Multi-information acquisition compensation according to claim 4, it is special Sign is：The blending algorithm based on geomagnetic matching and strap-down navigation computation is as follows：
    When being detected simultaneously by zero-speed and geomagnetic matching success, the dimension measurement equation of concentrated filter structure 10, auxiliary amendment are used Site error, velocity error and sensor error, as shown in following three formula, wherein posiM is geomagnetic matching position, can be by earth magnetism Matching directly obtains, M6For geomagnetic matching site error, V6To measure noise, posiN is the position of inertial navigation real-time resolving, and δ p are Site error, HI is based on as shown in zero-speed Kalman filtering correction model algorithm：
    Z6(t)=[posiN-posiM]=[δ p+M6]=H6(t)X(t)+V6(t)
    H6=[03×9 HI 03×9]
    <mrow> <msub> <mi>Z</mi> <mn>7</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Z</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>&amp;rsqb;</mo> </mrow>
    Z6(t) it is geomagnetic matching position detection amount, Z7(t) it is course angle and geomagnetic matching position under speed, position, motion state Put observed quantity.
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