CN110207692B - Map-assisted inertial pre-integration pedestrian navigation method - Google Patents

Map-assisted inertial pre-integration pedestrian navigation method Download PDF

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CN110207692B
CN110207692B CN201910393891.4A CN201910393891A CN110207692B CN 110207692 B CN110207692 B CN 110207692B CN 201910393891 A CN201910393891 A CN 201910393891A CN 110207692 B CN110207692 B CN 110207692B
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speed
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navigation
error
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CN110207692A (en
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袁诚
吕品
赖际舟
朱超群
杨子寒
何容
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Nanjing University of Aeronautics and Astronautics
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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
    • G01C21/005—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 with correlation of navigation data from several sources, e.g. map or contour matching
    • 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices

Abstract

The invention discloses a map-assisted inertial pre-integration pedestrian navigation method. Accelerometer data and gyroscope data at the moment k are periodically acquired; predicting navigation information of the carrier at the k moment by utilizing the acquired inertial sensor measurement data pre-integration; judging whether the navigation system is initialized, if so, carrying out map matching detection, if matching is successful, carrying out global position and attitude optimization by combining a map and an inertia error and outputting a carrier navigation message, if matching is failed, carrying out zero-speed detection, if non-zero-speed, carrying out inertia pre-integration to solve the position and attitude, and if zero-speed exists, combining the inertia error and zero-speed to constrain optimization to solve the position and output the carrier navigation message. The invention utilizes the measured value of the inertial sensor to carry out pre-integration optimization solution to output pedestrian navigation information, carries out zero-speed constraint correction optimization, and introduces map information to optimize global trajectory to eliminate accumulated errors.

Description

Map-assisted inertial pre-integration pedestrian navigation method
Technical Field
The invention belongs to the technical field of pedestrian navigation, and particularly relates to an inertia pre-integration pedestrian navigation method.
Background
The pedestrian navigation technology is a great research and application hotspot in the navigation technology field in the society and life at present. The inertial sensor can sense the rotation angular velocity and acceleration information of the inertial sensor, has extremely high autonomy and anti-interference performance, can be applied to various complex environments, and is a technology with wide development prospect and great application potential in the field of navigation.
Most of the existing pedestrian navigation technologies are based on Kalman filtering and extremely derived technologies, and the optimal solution at the current moment is solved in the resolving process, but the optimal solution is not the global optimal condition. Meanwhile, the inertial device is a pure autonomous sensor, and cannot accept external signals to correct the course, so that the course can be corrected by acquiring the prior map information of the current environment when navigating in an indoor environment, and the pedestrian navigation based on the Kalman filtering technology only has simple error average for correcting the course and cannot reflect the real situation, so that the error correction effect is poor, and the precision is reduced.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the invention provides a map-assisted inertial pre-integration pedestrian navigation method, which accurately estimates the accumulated error by using a pre-integration technology in combination with a map optimization framework to obtain global optimal navigation information.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a map-assisted inertial pre-integration pedestrian navigation method, fixing an inertial sensor to a pedestrian foot carrier, the inertial sensor comprising a gyroscope and an accelerometer, comprising the steps of:
(1) accelerometer data and gyroscope data at the moment k are periodically acquired;
(2) predicting navigation information of a carrier at the k moment by utilizing the inertia sensor measurement data obtained in the step (1) to obtain a pre-integral prediction value;
(3) judging whether the navigation system is initialized, if not, initializing to obtain the deviation of the inertial sensor and the estimated value of the gravity component, and jumping to the step (1); if the initialization is finished, entering the step (4);
(4) map matching detection is carried out, if matching is successful, global pose optimization is carried out by combining a map and an inertia error, and the step (6) is skipped; if the matching fails, entering the step (5);
(5) carrying out zero-speed detection, and if the speed is non-zero, carrying out inertia pre-integration to solve the pose; if zero speed exists, the pose is optimally solved by combining inertial error and zero speed constraint;
(6) and (4) outputting carrier navigation information and jumping to the step (1).
Further, the navigation information of the carrier comprises attitude quaternion, three-dimensional position and three-dimensional speed information; the attitude quaternion is used for representing three attitude angles including a roll angle, a pitch angle and a yaw angle, wherein the roll angle is a rotation angle of the carrier around the Y-axis direction of the navigation coordinate system, the pitch angle is a rotation angle of the carrier around the X-axis direction of the navigation coordinate system, the yaw angle is a rotation angle of the carrier around the Z-axis direction of the navigation coordinate system, and the rotation directions of the carrier meet the right-hand rule; the three-dimensional position is the projection of the carrier position in each axis of the navigation system, and the three-dimensional speed is the projection of the carrier speed in each axis of the navigation system.
Further, each coordinate system is defined:
constructing a machine body coordinate system b by taking the position of the carrier at the current moment as an origin, wherein an X axis, a Y axis and a Z axis of the machine body coordinate system b are respectively superposed with the right direction, the front direction and the sky direction of the carrier at the current moment; constructing an inertial coordinate system i by taking the position of the initial time carrier as an origin, wherein the X axis, the Y axis and the Z axis of the inertial coordinate system i are respectively superposed with the right direction, the front direction and the sky direction of a local horizontal plane of the initial time carrier; the navigation coordinate system n is constructed with the same rules as the inertial system.
Further, in step (2), the method for obtaining the pre-integration prediction value is as follows:
in the inertial sensor, based on the assumption of invariance of gravity, the measurement model is as follows:
Figure BDA0002057526980000031
Figure BDA0002057526980000032
in the above formula, the first and second carbon atoms are,
Figure BDA0002057526980000033
and fn(k) Respectively the measured value and the true value of the accelerometer,
Figure BDA0002057526980000034
and
Figure BDA0002057526980000035
measured and true values, eta, respectively, of the gyroscopea(k) Acceleration at time kRandom noise of meter, ηg(k) Random noise of the gyroscope at time k, gnIn order to navigate the weight under the tether,
Figure BDA0002057526980000036
navigation of the rotation matrix of the coordinate system to the body coordinate system for the time k, ba(k) The accelerometer measures the offset for time k, bg(k) The gyroscope measurement deviation at time k is then compared with ba(k) And bg(k) Comprises the following steps:
Figure BDA0002057526980000037
Figure BDA0002057526980000038
wherein the content of the first and second substances,
Figure BDA0002057526980000039
and
Figure BDA00020575269800000310
is b isa(k) And bg(k) A differential of [ (. eta. ])baIs accelerometer white noise, ηbgWhite noise for the gyroscope;
the process of pre-integrating the inertia measurement information is to number the time by two different groups of intervals, wherein the number under the discrete period Δ t is k and k (·), the number under the n discrete periods n Δ t is i, namely, the time i and the time k (i) are represented as the same time, k (i) -k (i-1) ═ n, the elapsed time t (i) -t (i-1) ═ k (i) Δ t- (k (i) -n) Δ t, and t (i) is the total elapsed time to the current time i, then:
Figure BDA00020575269800000311
Figure BDA00020575269800000312
Figure BDA00020575269800000313
in the above formula,. DELTA.Ri-1,iIs a rotation matrix from time i to time i-1, Δ vi-1,iIs the speed variation from time i-1 to time i, Δ pi-1,iFor the amount of change in position from time i-1 to time i, RiA rotation matrix from the machine system to the navigation system at time i,
Figure BDA0002057526980000041
rotation matrix from navigation system to body system at time i-1, viVelocity in the navigation system at time i, vi-1Speed in the navigation system at time i-1, Δ tk(i-1),iIs the time period from time k (i-1) to time i, Δ Rk(i-1),kIs a rotation matrix from time k to time k (i-1), piPosition in the navigation system for time i, pi-1The position in the navigation system at the moment i-1;
Figure BDA0002057526980000042
Exp:R3→ SO (3), representing the exponential projection mapping, will be a pose vector
Figure BDA0002057526980000043
Projecting as a rotation matrix in the lie group; wherein the content of the first and second substances,
Figure BDA0002057526980000044
for any three-dimensional vector, the representation | is restricted to any other continuous range of 2 pi,
Figure BDA0002057526980000045
is a vector
Figure BDA0002057526980000046
Of (3) is a negative symmetry momentArray, I is a unit array, R3Algebraic space, SO (3) lie group space.
Further, in step (3), the initialization process is as follows:
(301) the method comprises the following steps that at the moment k (i), all inertia measurement information at the moment i-1 is obtained, inertia pre-integration is carried out, and a body system at the starting moment is used as a navigation system;
(302) calculating initial deviation of the gyroscope by optimizing a rotation difference value between pre-integral prediction and a static hypothesis by using a zero-speed hypothesis at a static moment, and pre-integrating a measurement value of the gyroscope in an initial zero-speed interval:
Figure BDA0002057526980000047
wherein the continuous variation in the stationary moment is neglected, bg(1)＝bg(2)＝…＝bg(k(1)-1)，
Figure BDA0002057526980000048
Error of gyroscope is represented as bg(1) Time k (1) time to 1 time rotation matrix
Figure BDA0002057526980000049
The partial derivative of (a) of (b),
Figure BDA00020575269800000410
rotating a matrix for k times
Figure BDA0002057526980000051
Relative to gyroscope error bg(1) A derivative;
because the gyroscope is in a static state, the attitude change measurement is a unit array I, and the function is optimized to obtain the initialized gyroscope deviation;
(303) determining the component of the current roll pitch in the navigation system using gravity estimation:
due to the assumption of zero velocity, when the accelerometer measurements are all gravity in the navigation systemProjecting to obtain the initial value of gravity component
Figure BDA0002057526980000052
gbIs the projection of gravity under the machine system;
(304) the gravity is expressed as:
gb＝RbiExp(δθ)gi
≈Rbigi-Rbi(gi)×δθ
wherein R isbiIs the changing relation between the inertia system and the body system (·)×To obtain an inverse symmetric matrix, δ θ ═ δ θx δθy 0]For disturbance of attitude, δ θxFor angular disturbances of rotation about the x-axis, δ θyFor angular disturbances of rotation about the y-axis, giAligning the navigation system with the inertial system for the gravity under the inertial system, so that the gravity component in the navigation system is vertical to the local horizontal plane;
converting the rotation matrix into an attitude quaternion, wherein the conversion process is as follows:
Figure BDA0002057526980000053
Figure BDA0002057526980000054
Figure BDA0002057526980000055
Figure BDA0002057526980000056
Figure BDA0002057526980000057
wherein q is0、q1、q2、q3Is an attitude quaternion, rijIs the element in the ith row and the jth column of the rotation matrix.
Further, in step (4), the method of map matching detection is as follows:
setting an elevation mark point by utilizing a current scene two-dimensional map acquired in advance, projecting the coordinate of the elevation mark point to an inertial coordinate system after setting an initial position and a course, and detecting the elevation change and the angle change of the carrier in the inertial system, wherein the detection equation is as follows:
during the previous movement interval, if the maximum value of the elevation change thereof exceeds a preset threshold value ε h, i.e. if there is a height z at the moment kkChange | z with respect to time k-1k-zk-1If | is greater than ε h, the position of the first zero-velocity point after the motion interval is
Figure BDA0002057526980000061
As a map-matching correction point, and using the velocity v at the current timekThe x, y components of (a) compensate for the position deviation,
Figure BDA0002057526980000062
to compensate for the post-position, vi-1(x, y,0) is the velocity at time (x, y,0) i-1, vi(x, y,0) is the velocity at time i (x, y,0), eliminating the elevation velocity effect, as shown by:
Figure BDA0002057526980000063
further, in the step (4), the method for global pose optimization by combining the map and the inertial error is as follows:
adding the error of the carrier navigation position information at the current moment and the position information matched with the map points into the overall error for optimization, thereby performing overall pose optimization; the optimization target is that the predicted state value χ of the inertia pre-integration in all q zero-speed intervals between the map point successfully matched in the last time and the currently detected map matching point:[x1,x2…xq],
Figure BDA0002057526980000064
Wherein the content of the first and second substances,
Figure BDA0002057526980000065
for the rotation matrix from the machine hierarchy to the navigation hierarchy at time q,
Figure BDA0002057526980000066
for the position of the body at time q in the navigation system,
Figure BDA0002057526980000067
the speed of the body at time q in the navigation system,
Figure BDA0002057526980000068
is the error of the gyroscope at the time q,
Figure BDA0002057526980000069
error of accelerometer at q hours, EIMU(q, q +1) is a pose estimation optimization function at the successful detection moment and the next moment:
Figure BDA00020575269800000610
wherein:
Figure BDA0002057526980000071
Figure BDA0002057526980000072
Figure BDA0002057526980000073
eb＝b(q+1)-b(q)
Figure BDA0002057526980000074
in the above formula, the first and second carbon atoms are,
Figure BDA0002057526980000075
for the current detection of the position of the matching value, sigmaIAnd sigmaRIs an information matrix used for describing the relation between inertia errors, rho is a robust kernel function used for resisting errors caused by error points, eRError in attitude for inertia, evError in velocity for inertia, epError in inertial position, ebFor variations of inertia in error transfer, Δ Rq,q+1(bg(q)) is a gyroscope error of bg(q) rotating the matrix from time q +1 to time q, Δ vq,q+1(bg(q),ba(q)) is a gyroscope error of bg(q) accelerometer error ba(q) a change in speed from time q to time q +1,
Figure BDA0002057526980000076
is the rotation matrix from the inertial system to the body system at time q +1, δ bg(q) is the amount of change in gyroscope error at time q, δ ba(q) is the error variation of the accelerometer at the moment q;
Figure BDA0002057526980000077
representing a logarithmic projection map, transforming the rotation matrix into a rotation angle
Figure BDA0002057526980000078
A rotating shaft unit vector a, R is an arbitrary rotating matrix, and the upper mark is V-shaped to represent that an inverse asymmetric matrix is taken;
eRonly optimizing the difference between the roll and pitch angles estimated by the gravity and the flow type integral measured by the gyroscope in the optimization process;
in performing joint map matchingAfter optimization, the position and the yaw are recurred by using the speed,
Figure BDA0002057526980000079
thereby optimizing the global position and the yaw angle;
and solving the optimization function by using a Newton-column Winberg iteration method, and outputting a solving result of the current global state quantity when an optimal solution is obtained or the iteration number reaches the maximum iteration number.
Further, in step (5), the method of zero-velocity detection is as follows:
zero-speed detection is carried out by utilizing the zero-speed updating of the generalized likelihood ratio test method, and the probability of the pedestrian in the standing phase and the walking phase is estimated, so that the zero-speed state T (z)n) And (3) estimating:
Figure BDA0002057526980000081
wherein N is a sliding window interval omegan＝{k∈N:n≤k≤N-1}，
Figure BDA0002057526980000082
Is the average of the accelerometer outputs over the sliding window interval,
Figure BDA0002057526980000083
is the length of the two-norm modulus,
Figure BDA0002057526980000084
and
Figure BDA0002057526980000085
g represents the local gravity component, which is the noise variance of the accelerometer and gyroscope;
when T (z) is detectedn) And if the speed is less than the threshold value gamma', the standing still phase is considered to be in a zero-speed state, wherein gamma is-2 ln (gamma)/N, and gamma is set according to the actual situation.
Further, in the step (5), the method for solving the pose by combining the inertial error and the zero-speed constraint optimization is as follows:
after the zero speed is detected, comparing the pre-integral attitude value of the current carrier with the zero speed to obtain an error, thereby optimizing the estimation of the inertial error;
taking the current zero-speed interval as q, adding zero-speed constraint between the current zero-speed q and the previous zero-speed q-1, and the optimization target is
Figure BDA0002057526980000086
The optimization function is as follows:
Figure BDA0002057526980000087
and solving the optimization function by adopting a Newton-column Winberg iteration method, and outputting a solving result of the current state quantity when an optimal solution is obtained or the iteration times reach the maximum iteration times.
Adopt the beneficial effect that above-mentioned technical scheme brought:
the invention can effectively correct course and position errors in pedestrian navigation by using the map in an indoor environment, obtains high-reliability and high-precision pedestrian navigation information, and has good application prospect.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
The invention designs a map-assisted inertial pre-integration pedestrian navigation method, as shown in fig. 1, an inertial sensor is fixed on a pedestrian foot carrier, the inertial sensor comprises a gyroscope and an accelerometer, and the method is characterized by comprising the following steps:
step 1: accelerometer data and gyroscope data at the moment k are periodically acquired;
step 2: predicting navigation information of a carrier at the k moment by utilizing the inertia sensor measurement data pre-integration obtained in the step 1 to obtain a pre-integration prediction value;
and step 3: judging whether the navigation system is initialized, if not, initializing to obtain the deviation of the inertial sensor and the estimated value of the gravity component, and skipping to the step 1; if the initialization is finished, entering the step 4;
and 4, step 4: map matching detection is carried out, if matching is successful, global pose optimization is carried out by combining a map and an inertia error, and the step 6 is skipped; if the matching fails, entering step 5;
and 5: carrying out zero-speed detection, and if the speed is non-zero, carrying out inertia pre-integration to solve the pose; if zero speed exists, the pose is optimally solved by combining inertial error and zero speed constraint;
step 6: and outputting carrier navigation information and jumping to the step 1.
In this embodiment, the navigation information of the carrier includes an attitude quaternion, a three-dimensional position, and three-dimensional velocity information; the attitude quaternion is used for representing three attitude angles including a roll angle, a pitch angle and a yaw angle, wherein the roll angle is a rotation angle of the carrier around the Y-axis direction of the navigation coordinate system, the pitch angle is a rotation angle of the carrier around the X-axis direction of the navigation coordinate system, the yaw angle is a rotation angle of the carrier around the Z-axis direction of the navigation coordinate system, and the rotation directions of the carrier meet the right-hand rule; the three-dimensional position is the projection of the carrier position in each axis of the navigation system, and the three-dimensional speed is the projection of the carrier speed in each axis of the navigation system.
In the present embodiment, each coordinate system is defined:
constructing a machine body coordinate system b by taking the position of the carrier at the current moment as an origin, wherein an X axis, a Y axis and a Z axis of the machine body coordinate system b are respectively superposed with the right direction, the front direction and the sky direction of the carrier at the current moment; constructing an inertial coordinate system i by taking the position of the initial time carrier as an origin, wherein the X axis, the Y axis and the Z axis of the inertial coordinate system i are respectively superposed with the right direction, the front direction and the sky direction of a local horizontal plane of the initial time carrier; the navigation coordinate system n is constructed with the same rules as the inertial system.
In this embodiment, step 2 is implemented by the following preferred scheme:
the method for obtaining the pre-integral prediction value is as follows:
in the inertial sensor, based on the assumption of invariance of gravity, the measurement model is as follows:
Figure BDA0002057526980000101
Figure BDA0002057526980000102
in the above formula, the first and second carbon atoms are,
Figure BDA0002057526980000103
and fn(k) Respectively the measured value and the true value of the accelerometer,
Figure BDA0002057526980000104
and
Figure BDA0002057526980000105
measured and true values, eta, respectively, of the gyroscopea(k) Random noise, η, of accelerometers for time kg(k) Random noise of the gyroscope at time k, gnIn order to navigate the weight under the tether,
Figure BDA0002057526980000106
navigation of the rotation matrix of the coordinate system to the body coordinate system for the time k, ba(k) The accelerometer measures the offset for time k, bg(k) The gyroscope measurement deviation at time k is then compared with ba(k) And bg(k) Comprises the following steps:
Figure BDA0002057526980000107
Figure BDA0002057526980000108
wherein the content of the first and second substances,
Figure BDA0002057526980000109
and
Figure BDA00020575269800001010
is b isa(k) And bg(k) A differential of [ (. eta. ])baIs accelerometer white noise, ηbgWhite noise for the gyroscope;
the process of pre-integrating the inertia measurement information is that, the time is numbered by two groups of different intervals, wherein the numbers under the discrete periods Δ t are k and k (·), the numbers under the n discrete periods n Δ t are i, namely the time i and the time k (i) are represented as the same time, k (i) -k (i-1) ═ n, the elapsed time t (i) -t (i-1) ═ k (i) Δ t- (k (i) -n) Δ t, t (i) is the total time elapsed until the current time i, and then:
Figure BDA0002057526980000111
Figure BDA0002057526980000112
Figure BDA0002057526980000113
in the above formula,. DELTA.Ri-1,iIs a rotation matrix from time i to time i-1, Δ vi-1,iIs the speed variation from time i-1 to time i, Δ pi-1,iFor the amount of change in position from time i-1 to time i, RiA rotation matrix from the machine system to the navigation system at time i,
Figure BDA0002057526980000114
rotation matrix from navigation system to body system at time i-1, viVelocity in the navigation system at time i, vi-1Speed in the navigation system at time i-1, Δ tk(i-1),iIs the time period from time k (i-1) to time i, Δ Rk(i-1),kIs a rotation matrix from time k to time k (i-1), piPosition in the navigation system for time i, pi-1The position in the navigation system at the moment i-1;
Figure BDA0002057526980000115
Exp:R3→ SO (3), representing the exponential projection mapping, will be a pose vector
Figure BDA0002057526980000116
Projecting as a rotation matrix in the lie group; wherein the content of the first and second substances,
Figure BDA0002057526980000117
for any three-dimensional vector, the representation | is restricted to any other continuous range of 2 pi,
Figure BDA0002057526980000121
is a vector
Figure BDA0002057526980000122
I is a unit matrix, R3Algebraic space, SO (3) lie group space.
In this embodiment, step 3 is implemented by the following preferred scheme:
the initialization procedure is as follows:
301. the method comprises the following steps that at the moment k (i), all inertia measurement information at the moment i-1 is obtained, inertia pre-integration is carried out, and a body system at the starting moment is used as a navigation system;
302. calculating initial deviation of the gyroscope by optimizing a rotation difference value between pre-integral prediction and a static hypothesis by using a zero-speed hypothesis at a static moment, and pre-integrating a measurement value of the gyroscope in an initial zero-speed interval:
Figure BDA0002057526980000123
wherein the succession in the stationary instants is ignoredVariation of deviation, bg(1)＝bg(2)＝…＝bg(k(1)-1)，
Figure BDA0002057526980000124
Error of gyroscope is represented as bg(1) Time k (1) time to 1 time rotation matrix
Figure BDA0002057526980000125
The partial derivative of (a) of (b),
Figure BDA0002057526980000126
rotating a matrix for k times
Figure BDA0002057526980000127
Relative to gyroscope error bg(1) A derivative;
because the gyroscope is in a static state, the attitude change measurement is a unit array I, and the function is optimized to obtain the initialized gyroscope deviation;
303. determining the component of the current roll pitch in the navigation system using gravity estimation:
due to the assumption of zero velocity, when the measurement values of the accelerometer are all the projections of gravity in the navigation system, the initial values of the gravity components are obtained
Figure BDA0002057526980000128
gbIs the projection of gravity under the machine system;
304. the gravity is expressed as:
gb＝RbiExp(δθ)gi
≈Rbigi-Rbi(gi)×δθ
wherein R isbiIs the changing relation between the inertia system and the body system (·)×To obtain an inverse symmetric matrix, δ θ ═ δ θx δθy 0]For disturbance of attitude, δ θxFor angular disturbances of rotation about the x-axis, δ θyFor angular disturbances of rotation about the y-axis, giAligning the navigation system with the inertial system for gravity under the inertial system so thatThe gravity component in the navigation system is vertical to the local horizontal plane;
converting the rotation matrix into an attitude quaternion, wherein the conversion process is as follows:
Figure BDA0002057526980000131
Figure BDA0002057526980000132
Figure BDA0002057526980000133
Figure BDA0002057526980000134
Figure BDA0002057526980000135
wherein q is0、q1、q2、q3Is an attitude quaternion, rijIs the element in the ith row and the jth column of the rotation matrix.
In this embodiment, step 4 is implemented by using the following preferred scheme:
the map matching detection method comprises the following steps:
setting an elevation mark point by utilizing a current scene two-dimensional map acquired in advance, projecting the coordinate of the elevation mark point to an inertial coordinate system after setting an initial position and a course, and detecting the elevation change and the angle change of the carrier in the inertial system, wherein the detection equation is as follows:
during the previous movement interval, if the maximum value of the elevation change thereof exceeds a preset threshold value ε h, i.e. if there is a height z at the moment kkChange | z with respect to time k-1k-zk-1If | is greater than ε h, the position of the first zero-velocity point after the motion interval is
Figure BDA0002057526980000136
As a map-matching correction point, and using the velocity v at the current timekThe x, y components of (a) compensate for the position deviation,
Figure BDA0002057526980000137
to compensate for the post-position, vi-1(x, y,0) is the velocity at time (x, y,0) i-1, vi(x, y,0) is the velocity at time i (x, y,0), eliminating the elevation velocity effect, as shown by:
Figure BDA0002057526980000141
if at a staircase, there is a change in height | zk-zk-1If | is more than epsilon h, the step at the last step of the staircase can be used as a map mark point, and the height change is from existence to nonexistence, namely | zk-zk-1If the | is less than the epsilon h, the position of the staircase at the moment is taken as a map matching position point.
The method for global pose optimization by combining the map and the inertial error comprises the following steps:
adding the error of the carrier navigation position information at the current moment and the position information matched with the map points into the overall error for optimization, thereby performing overall pose optimization; the optimization target is that the inertia pre-integration prediction state value x in all q zero-speed intervals from the map point successfully matched last time to the map matching point detected now is: [ x: ]1,x2...xq],
Figure BDA0002057526980000142
Wherein the content of the first and second substances,
Figure BDA0002057526980000143
for the rotation matrix from the machine hierarchy to the navigation hierarchy at time q,
Figure BDA0002057526980000144
for q-time machine systemThe position in the navigation system is determined,
Figure BDA0002057526980000145
the speed of the body at time q in the navigation system,
Figure BDA0002057526980000146
is the error of the gyroscope at the time q,
Figure BDA0002057526980000147
error of accelerometer at q hours, EIMU(q, q +1) is a pose estimation optimization function at the successful detection moment and the next moment:
Figure BDA0002057526980000148
wherein:
Figure BDA0002057526980000149
Figure BDA00020575269800001410
Figure BDA00020575269800001411
eb＝b(q+1)-b(q)
Figure BDA0002057526980000151
in the above formula, the first and second carbon atoms are,
Figure BDA0002057526980000152
for the current detection of the position of the matching value, sigmaIAnd sigmaRIs an information matrix for describing the relationship between inertial errors, and is a robust kernel function for resistingError due to error points, eRError in attitude for inertia, evError in velocity for inertia, epError in inertial position, ebFor variations of inertia in error transfer, Δ Rq,q+1(bg(q)) is a gyroscope error of bg(q) rotating the matrix from time q +1 to time q, Δ vq,q+1(bg(q),ba(q)) is a gyroscope error of bg(q) accelerometer error ba(q) a change in speed from time q to time q +1,
Figure BDA0002057526980000153
is the rotation matrix from the inertial system to the body system at time q +1, δ bg(q) is the amount of change in gyroscope error at time q, δ ba(q) is the error variation of the accelerometer at the moment q;
Figure BDA0002057526980000154
representing a logarithmic projection map, transforming the rotation matrix into a rotation angle
Figure BDA0002057526980000155
A rotating shaft unit vector a, R is an arbitrary rotating matrix, and the upper mark is V-shaped to represent that an inverse asymmetric matrix is taken;
eRonly optimizing the difference between the roll and pitch angles estimated by the gravity and the flow type integral measured by the gyroscope in the optimization process;
after the combined map matching optimization is carried out, the position and the yaw are recurred again by using the speed,
Figure BDA0002057526980000156
thereby optimizing the global position and the yaw angle;
and solving the optimization function by using a Newton-column Winberg iteration method such as a graph optimization open source library G2O, GTSAM, Ceres and the like, and outputting a solving result of the current global state quantity when an optimal solution is obtained or the iteration times reach the maximum iteration times.
In this embodiment, step 5 is implemented by the following preferred scheme:
the zero-speed detection method comprises the following steps:
zero-speed detection is carried out by utilizing the zero-speed updating of the generalized likelihood ratio test method, and the probability of the pedestrian in the standing phase and the walking phase is estimated, so that the zero-speed state T (z)n) And (3) estimating:
Figure BDA0002057526980000161
wherein N is a sliding window interval omegan＝{k∈N:n≤k≤N-1}，
Figure BDA0002057526980000162
Is the average of the accelerometer outputs over the sliding window interval,
Figure BDA0002057526980000163
is the length of the two-norm modulus,
Figure BDA0002057526980000164
and
Figure BDA0002057526980000165
g represents the local gravity component, which is the noise variance of the accelerometer and gyroscope;
when T (z) is detectedn) And if the speed is less than the threshold value gamma', the standing still phase is considered to be in a zero-speed state, wherein gamma is-2 ln (gamma)/N, and gamma is set according to the actual situation.
The method for solving the pose by combining inertial error and zero-speed constraint optimization is as follows:
after the zero speed is detected, comparing the pre-integral attitude value of the current carrier with the zero speed to obtain an error, thereby optimizing the estimation of the inertial error;
taking the current zero-speed interval as q, adding zero-speed constraint between the current zero-speed q and the previous zero-speed q-1, and the optimization target is
Figure BDA0002057526980000166
The optimization function is as follows:
Figure BDA0002057526980000167
and solving the optimization function by using a Newton-column Winberg iteration method such as a graph optimization open source library G2O, GTSAM, Ceres and the like, and outputting a solving result of the current state quantity when an optimal solution is obtained or the iteration times reach the maximum iteration times.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.

Claims (7)

1. A map-assisted inertial pre-integration pedestrian navigation method, fixing an inertial sensor to a pedestrian foot carrier, the inertial sensor comprising a gyroscope and an accelerometer, comprising the steps of:
(1) accelerometer data and gyroscope data at the moment k are periodically acquired;
(2) predicting navigation information of a carrier at the k moment by utilizing the inertia sensor measurement data obtained in the step (1) to obtain a pre-integral prediction value;
the method for obtaining the pre-integral prediction value is as follows:
in the inertial sensor, based on the assumption of invariance of gravity, the measurement model is as follows:
Figure FDA0002780115100000011
Figure FDA0002780115100000012
in the above formula, the first and second carbon atoms are,
Figure FDA0002780115100000013
and fn(k) Respectively the measured value and the true value of the accelerometer,
Figure FDA0002780115100000014
and
Figure FDA0002780115100000015
measured and true values, eta, respectively, of the gyroscopea(k) Random noise, η, of accelerometers for time kg(k) Random noise of the gyroscope at time k, gnIn order to navigate the weight under the tether,
Figure FDA0002780115100000016
navigation of the rotation matrix of the coordinate system to the body coordinate system for the time k, ba(k) The accelerometer measures the offset for time k, bg(k) The gyroscope measurement deviation at time k is then compared with ba(k) And bg(k) Comprises the following steps:
Figure FDA0002780115100000017
Figure FDA0002780115100000018
wherein the content of the first and second substances,
Figure FDA0002780115100000019
and
Figure FDA00027801151000000110
is b isa(k) And bg(k) A differential of [ (. eta. ])baIs accelerometer white noise, ηbgWhite noise for the gyroscope;
the process of pre-integrating the inertia measurement information is to number the time by two different groups of intervals, wherein the number under the discrete period Δ t is k and k (·), the number under the n discrete periods n Δ t is i, namely, the time i and the time k (i) are represented as the same time, k (i) -k (i-1) ═ n, the elapsed time t (i) -t (i-1) ═ k (i) Δ t- (k (i) -n) Δ t, and t (i) is the total elapsed time to the current time i, then:
Figure FDA0002780115100000021
Figure FDA0002780115100000022
Figure FDA0002780115100000023
in the above formula,. DELTA.Ri-1,iIs a rotation matrix from time i to time i-1, Δ vi-1,iIs the speed variation from time i-1 to time i, Δ pi-1,iFor the amount of change in position from time i-1 to time i, RiA rotation matrix from the machine system to the navigation system at time i,
Figure FDA0002780115100000024
rotation matrix from navigation system to body system at time i-1, viVelocity in the navigation system at time i, vi-1Speed in the navigation system at time i-1, Δ ti-1,iFor a time period from time i-1 to time i, Δ Rk(i-1),kIs a rotation matrix from time k to time k (i-1), piPosition in the navigation system for time i, pi-1The position in the navigation system at the moment i-1;
Figure FDA0002780115100000025
Exp:R3→ SO (3), representing the exponential projection mapping, will be a pose vector
Figure FDA0002780115100000026
Projecting as a rotation matrix in the lie group; wherein the content of the first and second substances,
Figure FDA0002780115100000027
for any three-dimensional vector, the representation | is restricted to any other continuous range of 2 pi,
Figure FDA0002780115100000028
is a vector
Figure FDA0002780115100000029
I is a unit matrix, R3Is algebraic space, SO (3) is lie group space;
(3) judging whether the navigation system is initialized, if not, initializing to obtain the deviation of the inertial sensor and the estimated value of the gravity component, and jumping to the step (1); if the initialization is finished, entering the step (4);
the initialization procedure is as follows:
(301) the method comprises the following steps that at the moment k (i), all inertia measurement information at the moment i-1 is obtained, inertia pre-integration is carried out, and a body system at the starting moment is used as a navigation system;
(302) calculating initial deviation of the gyroscope by optimizing a rotation difference value between pre-integral prediction and a static hypothesis by using a zero-speed hypothesis at a static moment, and pre-integrating a measurement value of the gyroscope in an initial zero-speed interval:
Figure FDA0002780115100000031
in which the continuous variation of the deviation in the resting moments is ignored, bg(1)＝bg(2)＝…＝bg(k(1)-1)，
Figure FDA0002780115100000032
Figure FDA0002780115100000033
Error of gyroscope is represented as bg(1) Time k (1) time to 1 time rotation matrix
Figure FDA0002780115100000034
The partial derivative of (a) of (b),
Figure FDA0002780115100000035
rotating a matrix for k times
Figure FDA0002780115100000036
Relative to gyroscope error bg(1) A derivative;
because the gyroscope is in a static state, the attitude change measurement is a unit array I, and the function is optimized to obtain the initialized gyroscope deviation;
(303) determining the component of the current roll pitch in the navigation system using gravity estimation:
due to the assumption of zero velocity, when the measurement values of the accelerometer are all the projections of gravity in the navigation system, the initial values of the gravity components are obtained
Figure FDA0002780115100000037
gbIs the projection of gravity under the machine system;
(304) the gravity is expressed as:
gb＝RbiExp(δθ)gi
≈Rbigi-Rbi(gi)×δθ
wherein R isbiIs the changing relation between the inertia system and the body system (·)×To obtain an inverse symmetric matrix, δ θ ═ δ θx δθy 0]For disturbance of attitude, δ θxFor angular disturbances of rotation about the x-axis, δ θyFor angular disturbances of rotation about the y-axis, giAligning the navigation system with the inertial system for the gravity under the inertial system, so that the gravity component in the navigation system is vertical to the local horizontal plane;
converting the rotation matrix into an attitude quaternion, wherein the conversion process is as follows:
Figure FDA0002780115100000041
Figure FDA0002780115100000042
Figure FDA0002780115100000043
Figure FDA0002780115100000044
Figure FDA0002780115100000045
wherein q is0、q1、q2、q3Is an attitude quaternion, rijIs the element of the ith row and the jth column in the rotation matrix;
(4) map matching detection is carried out, if matching is successful, global pose optimization is carried out by combining a map and an inertia error, and the step (6) is skipped; if the matching fails, entering the step (5);
(5) carrying out zero-speed detection, and if the speed is non-zero, carrying out inertia pre-integration to solve the pose; if zero speed exists, the pose is optimally solved by combining inertial error and zero speed constraint;
(6) and (4) outputting carrier navigation information and jumping to the step (1).
2. The map-assisted inertial pre-integration pedestrian navigation method of claim 1, characterized in that the navigation information of the carrier comprises attitude quaternion, three-dimensional position and three-dimensional velocity information; the attitude quaternion is used for representing three attitude angles including a roll angle, a pitch angle and a yaw angle, wherein the roll angle is a rotation angle of the carrier around the Y-axis direction of the navigation coordinate system, the pitch angle is a rotation angle of the carrier around the X-axis direction of the navigation coordinate system, the yaw angle is a rotation angle of the carrier around the Z-axis direction of the navigation coordinate system, and the rotation directions of the carrier meet the right-hand rule; the three-dimensional position is the projection of the carrier position in each axis of the navigation system, and the three-dimensional speed is the projection of the carrier speed in each axis of the navigation system.
3. The map-assisted inertial pre-integration pedestrian navigation method of claim 1, characterized in that each coordinate system is defined:
constructing a machine body coordinate system b by taking the position of the carrier at the current moment as an origin, wherein an X axis, a Y axis and a Z axis of the machine body coordinate system b are respectively superposed with the right direction, the front direction and the sky direction of the carrier at the current moment; constructing an inertial coordinate system i by taking the position of the initial time carrier as an origin, wherein the X axis, the Y axis and the Z axis of the inertial coordinate system i are respectively superposed with the right direction, the front direction and the sky direction of a local horizontal plane of the initial time carrier; the navigation coordinate system n is constructed with the same rules as the inertial system.
4. The map-assisted inertial pre-integration pedestrian navigation method according to claim 1, wherein in step (4), the map matching detection method is as follows:
setting an elevation mark point by utilizing a current scene two-dimensional map acquired in advance, projecting the coordinate of the elevation mark point to an inertial coordinate system after setting an initial position and a course, and detecting the elevation change and the angle change of the carrier in the inertial system, wherein the detection equation is as follows:
during the previous movement interval, if the maximum value of the elevation change thereof exceeds a preset threshold value ε h, i.e. if there is a height z at the moment kkChange | z with respect to time k-1k-zk-1If | is greater than ε h, the position of the first zero-velocity point after the motion interval is
Figure FDA0002780115100000051
As a map-matching correction point, and using the velocity v at the current timekThe x, y components of (a) compensate for the position deviation,
Figure FDA0002780115100000052
to compensate for the post-position, vi-1(x, y,0) is the velocity at time (x, y,0) i-1, vi(x, y,0) is the velocity at time i (x, y,0), eliminating the elevation velocity effect, as shown by:
Figure FDA0002780115100000053
5. the map-assisted inertial pre-integration pedestrian navigation method according to claim 4, wherein in the step (4), the global pose optimization method by combining the map and the inertial error is as follows:
adding the error of the carrier navigation position information at the current moment and the position information matched with the map points into the overall error for optimization, thereby performing overall pose optimization; the optimization target is that the inertia pre-integration prediction state value x in all q zero-speed intervals from the map point successfully matched last time to the map matching point detected now is: [ x: ]1,x2...xq],
Figure FDA0002780115100000054
Wherein the content of the first and second substances,
Figure FDA0002780115100000055
for the rotation matrix from the machine hierarchy to the navigation hierarchy at time q,
Figure FDA0002780115100000056
for the position of the body at time q in the navigation system,
Figure FDA0002780115100000057
is time qThe speed of the body in the navigation system,
Figure FDA0002780115100000061
is the error of the gyroscope at the time q,
Figure FDA0002780115100000062
error of accelerometer at q hours, EIMU(q, q +1) is a pose estimation optimization function at the successful detection moment and the next moment:
Figure FDA0002780115100000063
wherein:
Figure FDA0002780115100000064
Figure FDA0002780115100000065
Figure FDA0002780115100000066
eb＝b(q+1)-b(q)
Figure FDA0002780115100000067
in the above formula, the first and second carbon atoms are,
Figure FDA0002780115100000068
for the current detection of the position of the matching value, sigmaIAnd sigmaRIs an information matrix used for describing the relation between inertia errors, rho is a robust kernel function used for resisting errors caused by error points, eRIs inertia in attitudeError of (e) invError in velocity for inertia, epError in inertial position, ebFor variations of inertia in error transfer, Δ Rq,q+1(bg(q)) is a gyroscope error of bg(q) rotating the matrix from time q +1 to time q, Δ vq,q+1(bg(q),ba(q)) is a gyroscope error of bg(q) accelerometer error ba(q) a change in speed from time q to time q +1,
Figure FDA0002780115100000069
is the rotation matrix from the inertial system to the body system at time q +1, δ bg(q) is the amount of change in gyroscope error at time q, δ ba(q) is the error variation of the accelerometer at the moment q;
Figure FDA00027801151000000610
representing a logarithmic projection map, transforming the rotation matrix into a rotation angle
Figure FDA00027801151000000611
A rotating shaft unit vector a, R is an arbitrary rotating matrix, and the upper mark is V-shaped to represent that an inverse asymmetric matrix is taken;
eRonly optimizing the difference between the roll and pitch angles estimated by the gravity and the flow type integral measured by the gyroscope in the optimization process;
after the combined map matching optimization is carried out, the position and the yaw are recurred again by using the speed,
Figure FDA0002780115100000071
thereby optimizing the global position and the yaw angle;
and solving the optimization function by using a Newton-column Winberg iteration method, and outputting a solving result of the current global state quantity when an optimal solution is obtained or the iteration number reaches the maximum iteration number.
6. The map-assisted inertial pre-integration pedestrian navigation method according to claim 5, wherein in step (5), the method of zero-velocity detection is as follows:
zero-speed detection is carried out by utilizing the zero-speed updating of the generalized likelihood ratio test method, and the probability of the pedestrian in the standing phase and the walking phase is estimated, so that the zero-speed state T (z)n) And (3) estimating:
Figure FDA0002780115100000072
wherein N is a sliding window interval omegan＝{k∈N:n≤k≤N-1}，
Figure FDA0002780115100000073
Is the average of the accelerometer outputs over the sliding window interval,
Figure FDA0002780115100000074
is the length of the two-norm modulus,
Figure FDA0002780115100000075
and
Figure FDA0002780115100000076
g represents the local gravity component, which is the noise variance of the accelerometer and gyroscope;
when T (z) is detectedn) And if the speed is less than the threshold value gamma', the standing still phase is considered to be in a zero-speed state, wherein gamma is-2 ln (gamma)/N, and gamma is set according to the actual situation.
7. The map-assisted inertial pre-integration pedestrian navigation method according to claim 5, wherein in the step (5), the method for solving the pose by combining inertial error and zero-speed constraint optimization is as follows:
after the zero speed is detected, comparing the pre-integral attitude value of the current carrier with the zero speed to obtain an error, thereby optimizing the estimation of the inertial error;
taking the current zero-speed interval as q, adding zero-speed constraint between the current zero-speed q and the previous zero-speed q-1, and the optimization target is
Figure FDA0002780115100000081
The optimization function is as follows:
Figure FDA0002780115100000082
and solving the optimization function by adopting a Newton-column Winberg iteration method, and outputting a solving result of the current state quantity when an optimal solution is obtained or the iteration times reach the maximum iteration times.
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