CN114184190A - Inertial/odometer integrated navigation system and method - Google Patents

Inertial/odometer integrated navigation system and method Download PDF

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CN114184190A
CN114184190A CN202111271351.2A CN202111271351A CN114184190A CN 114184190 A CN114184190 A CN 114184190A CN 202111271351 A CN202111271351 A CN 202111271351A CN 114184190 A CN114184190 A CN 114184190A
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odometer
time
navigation
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inertial
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邓继权
郭玉胜
邹思远
刘洋
周亚男
王海军
庄广琛
裴新凯
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Beijing Automation Control Equipment Institute BACEI
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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
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/183—Compensation of inertial measurements, e.g. for temperature effects
    • 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

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Abstract

The invention provides an inertia/mileometer integrated navigation system and a method thereof, which establish an inertia/mileometer integrated navigation state equation, establish an inertia/mileometer integrated navigation observation equation, utilize the inertia/mileometer integrated navigation observation equation and carry out Kalman filtering. According to the method, the difference value of the inertial navigation speed increment and the odometer speed increment is used as the Kalman filtering observed quantity, and the influence of the odometer speed error on the inertial/odometer integrated navigation is restrained by adopting a state delay Kalman filtering algorithm, so that the accurate estimation of each error of the inertial navigation system is realized.

Description

Inertial/odometer integrated navigation system and method
Technical Field
The invention relates to an inertia/odometer integrated navigation system and a method, in particular to an inertia/odometer integrated navigation system and a method for track detection, belonging to the technical field of track detection application.
Background
Along with the continuous development of railway construction in China, more and more reconstruction, extension and new construction projects of the existing line are provided, and line mapping plays a decisive role in engineering construction, which directly influences the quality, cost and construction period of the engineering. The inertial navigation system can continuously provide high-precision position, speed, attitude and other information, but errors of the inertial navigation system are accumulated along with time, and the error increase of the inertial navigation system is restrained by means of auxiliary information such as a milemeter, satellite positioning and the like for long-time engineering measurement.
The odometer is arranged on a wheel of the track detection system, the running speed in the test process is obtained by measuring the rotating speed of the wheel, and various states of the detection system such as movement, stop and the like in the measurement process can be accurately reflected. And the speed of the odometer does not depend on external information, and the odometer can also provide accurate speed measurement information even in areas with serious satellite signal shielding, such as tunnels, jungles and the like.
The inertia/milemeter combined navigation uses the high-precision speed information of the milemeter to inhibit the error accumulation of an inertia navigation system, and is a common measurement mode for the track detection system at the present stage. The inertia/mileometer combined navigation maps observation data to a state space according to a physical model of a system and the noise statistical characteristics of a sensor, establishes a system state equation and an observation equation according to the motion rule of a track detection system, and obtains the optimal estimation of a system state variable through a Kalman filtering estimation algorithm.
And the difference value between the measurement speed of the odometer for the inertia/odometer combined navigation and the inertial navigation speed is used as Kalman filtering inertial measurement, and each error of the inertial navigation system is accurately estimated through a filtering algorithm. Therefore, the speed measurement error of the odometer can have serious influence on the integrated navigation precision, and how to inhibit the influence of the speed measurement error of the odometer on the integrated navigation precision is a key technology of the inertia/odometer integrated navigation. The existing common method mainly models and estimates the speed measurement error of the odometer, and estimates the scale coefficient, installation error and other main error sources of the odometer through Kalman filtering, the estimation precision depends on the modeling accuracy, and the general modeling is general rather than aiming at a single product, so that the estimation precision is not high.
Disclosure of Invention
The present invention is directed to overcoming one of the deficiencies of the prior art and providing an inertial/odometer integrated navigation system and method.
The technical solution of the invention is as follows: an inertia/odometer combined navigation method comprises the following steps:
establishing an inertia/mileometer integrated navigation state equation;
establishing an inertia/mileometer combined navigation observation equation,
Zk＝HkXk+LkXk-1+Vk
wherein Z iskIs tkThe observed quantity of the moment takes the difference value of the inertial navigation speed increment and the odometer speed increment as the combined navigation observed quantity of the inertial navigation/odometer, HkIs tkTime state variable XkCorresponding observation matrix, LkIs tk-1Time state variable Xk-1Corresponding observation matrix, VkIs tkA time observation noise;
and (4) performing Kalman filtering by using an inertia/milemeter combined navigation observation equation.
An inertia/mileometer combined navigation system comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the inertia/mileometer combined navigation method when executing the computer program.
Compared with the prior art, the invention has the beneficial effects that:
(1) according to the method, the difference value of the inertial navigation speed increment and the odometer speed increment is used as Kalman filtering observed quantity, and a state delay Kalman filtering algorithm is adopted to inhibit the influence of the odometer speed increment error on the inertial/odometer integrated navigation, so that the accurate estimation of each error of an inertial navigation system is realized;
(2) the invention eliminates the influence of speed measurement errors of the odometer by using the speed increment of two adjacent measurement results of the speed of the odometer, improves the position and posture measurement precision of the inertia/odometer combined navigation and further improves the detection precision of the geometrical parameters of the track.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The present invention will be described in detail with reference to the following examples and accompanying drawings.
The invention provides an inertia/mileometer combined navigation method as shown in figure 1, which comprises the following steps:
establishing an inertia/mileometer integrated navigation state equation,
Figure BDA0003328088720000031
wherein X (t) is a state variable at the time t, and a north speed error delta V is selectedNSpeed error delta V in the direction of the skyUEast velocity error δ VELatitude error delta L, altitude error delta h, longitude error delta lambda, north misalignment angle phiNAngle of vertical misalignment phiUEast misalignment angle phiETriaxial gyro drift
Figure BDA0003328088720000032
Triaxial accelerometer zero position
Figure BDA0003328088720000033
Figure BDA0003328088720000034
As state variables for the inertial/odometer combination navigation;
f is a state transition matrix of a continuous state equation corresponding to the state variable at the time t;
w (t) is the systematic random noise vector at time t.
The method comprises the following specific steps:
1. selecting a north direction speed error delta VNSpeed error delta V in the direction of the skyUEast velocity error δ VELatitude error delta L, altitude error delta h, longitude error delta lambda, north misalignment angle phiNAngle of vertical misalignment phiUDong (east)Angle of disclination phiETriaxial gyro drift
Figure BDA0003328088720000035
Triaxial accelerometer zero position
Figure BDA0003328088720000036
As the state variable of the inertia/mileometer combination navigation, obtaining the state variable,
Figure BDA0003328088720000037
2. establishing an inertia/mileometer integrated navigation state equation,
Figure BDA0003328088720000038
wherein, x (t) is a state variable at the time t, F is a state transition matrix of a continuous state equation corresponding to the state variable at the time t, and w (t) is a system random noise vector at the time t.
Discretization can result in:
Xk＝Φk,k-1Xk-1+Γk-1Wk-1
in the formula (I), the compound is shown in the specification,
Figure BDA0003328088720000041
is tk-1Time tkA system one-step state transition matrix of time of day, wherein
Figure BDA0003328088720000042
T is the filter period, TnFor discrete periods, FiIs a system matrix; gamma-shapedk-1I is the noise driving matrix of the system; wkSatisfies E [ W ] for the excitation noise sequence of the systemk]＝0，
Figure BDA0003328088720000043
Wherein when k is j, δk,j1, otherwise 0, QkIs WkThe variance matrix of (a), assuming non-negative determinism.
Establishing an inertia/mileometer combined navigation observation equation,
Zk＝HkXk+LkXk-1+Vk
wherein Z iskIs tkThe observed quantity of the moment takes the difference value of the inertial navigation speed increment and the odometer speed increment as the inertial/odometer combined navigation observed quantity;
Hkis tkTime state variable XkThe corresponding observation matrix is used for observing,
Figure BDA0003328088720000044
Lkis tk-1Time state variable Xk-1The corresponding observation matrix is used for observing,
Figure BDA0003328088720000045
Vkis tkThe time of day observer noise.
The method comprises the following specific steps:
1. selecting a difference value delta V between the inertial navigation speed increment and the speedometer speed incrementIns-ΔVdObtaining a filtering observed quantity Z as an inertia/mileometer combined navigation observed quantityk，
Zk＝ΔVIns(k)-ΔVd(k)
Wherein Z iskIs tkFiltering the observed quantity of the moment observed quantity;
ΔVIns(k)is tkThe observed quantity inertial navigation speed increment of the moment;
ΔVd(k)is tkThe observed quantity at that moment is the odometer speed increment.
(1)tkOdometer speed delta V at timed(k)And (4) obtaining.
Comprehensively considering error sources such as scale coefficients and installation errors of the odometer, the output speed of the odometer is expressed by the following formula:
Vd＝vr+vc+δvd
wherein, VdIndicating odometer output speed, vrFor the true speed of the track-detection system, vcThe speed measurement error of the odometer is shown, and the delta v is the speed measurement noise of the odometer.
The speed increment can be obtained by differentiating the speeds of two adjacent mileometers
ΔVd(k)＝Vd(k)-Vd(k-1)
＝vr(k)+vc(k)+δvd(k)-vr(k-1)-vc(k-1)-δvd(k-1)
Wherein, Vd(k)Is tkOutput speed, V, of a time odometerd(k-1)Is tk-1Output speed, v, of a time odometerr(k)Is tkTrue velocity, v, of time-of-day track detection systemr(k-1)Is tk-1True velocity, v, of time-of-day track detection systemc(k)Is tkVelocity measurement error of time odometer, vc(k-1)Is tk-1Speed measurement error of time odometer, delta vd(k)Is tkSpeed noise, δ v, of time odometerd(k-1)Is tk-1The time odometer measures speed noise.
The filtering period of the inertia/odometer combined navigation Kalman filtering is usually not more than 1 second, and the odometer speed error can be considered to be unchanged in a short time, so that the method can obtain,
ΔVd(k)＝vr(k)+δvd(k)-vr(k-1)-δvd(k-1)
after the speed difference of the odometer, the influence of the speed measurement error of the odometer is eliminated.
(2)tkMoment inertial navigation velocity increment delta VIns(k)And (4) obtaining.
Inertial navigation speed increment at adjacent filtering calculation time
ΔVIns(k)＝(vIns(k)-vIns(k-1))+(δvIns(k)-δvIns(k-1))
Wherein v isIns(k)Is tkVelocity of inertial navigation at time vIns(k-1)Is tk-1Moment of inertia velocity, δ vIns(k)Is tkMoment of inertia velocity noise, δ vIns(k-1)Is tk-1Moment inertial navigation speed noise.
(3) Taking the difference value of the inertial navigation speed increment and the odometer speed increment as the inertial/odometer combined navigation observed quantity to obtain Zk＝ΔVIns(k)-ΔVd(k)。
2. The inertial odometer combines the navigation observation equation,
Zk＝HkXk+LkXk-1+Vk
wherein Z iskIs tkObserved quantity of time, HkIs tkTime state variable XkCorresponding observation matrix, LkIs tk-1Time state variable Xk-1Corresponding observation matrix, VkIs the observed quantity noise.
Figure BDA0003328088720000061
Figure BDA0003328088720000062
And (5) Kalman filtering.
Kalman filtering, t, in which Kalman filtering is performed with state delaykThe observation equation of the time contains tk-1State variable X of timek-1Term, i.e. tkObserved value of time and tk-1The state quantity at the moment is relevant.
Adjusting the Kalman filter according to the inertial odometer combined navigation observation equation to obtain the Kalman filtering with state delay, which comprises the following steps:
let tkThe estimated state of the time instant is subjected to a system noise sequence Wk-1Drive, the equation of state is described by
Xk＝Φk,k-1Xk-1+Γk-1Wk-1
For XkSatisfies the following relationship
Zk＝HkXk+LkXk-1+Vk
In the formula phik,k-1Is tk-1Time tkMoment system one-step state transition matrix, Γk-1For the noise-driven matrix of the system, WkFor the excitation noise sequence of the system, HkIs the observation matrix of the system, LkIs a delay state observation matrix, V, corresponding to the state at the last moment of the systemkIs the system observation noise sequence.
At the same time, WkAnd VkSatisfy the following relationship
E[Wk]＝0，
Figure BDA0003328088720000071
E[Vk]＝0，
Figure BDA0003328088720000072
Figure BDA0003328088720000073
In the formula, QkIs WkThe variance matrix of (a), assuming non-negative determinants,
Figure BDA0003328088720000074
is VkThe variance matrix of (a) is assumed to be positive.
Corresponding filtering algorithm based on delay state can be obtained
State one-step prediction
Figure BDA0003328088720000075
One-step prediction mean square error array
Figure BDA0003328088720000076
Filter gain
Figure BDA0003328088720000077
Figure BDA0003328088720000078
State estimation
Figure BDA0003328088720000079
Estimating mean square error matrix
Figure BDA00033280887200000710
Other kalman filtering in this step is well known in the art.
The invention further provides a system for realizing the inertia/odometer combined navigation method, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the inertia/odometer combined navigation when executing the computer program.
The invention has not been described in detail and is in part known to those of skill in the art.

Claims (10)

1. An inertia/odometer combined navigation method is characterized by comprising the following steps:
establishing an inertia/mileometer integrated navigation state equation;
establishing an inertia/mileometer combined navigation observation equation,
Zk＝HkXk+LkXk-1+Vk
wherein Z iskIs tkObservation of time of dayMeasuring, using the difference value of inertial navigation speed increment and odometer speed increment as inertial/odometer combined navigation observed quantity, HkIs tkTime state variable XkCorresponding observation matrix, LkIs tk-1Time state variable Xk-1Corresponding observation matrix, VkIs tkA time observation noise;
and (4) performing Kalman filtering by using an inertia/milemeter combined navigation observation equation.
2. The combined inertial/odometer navigation method according to claim 1, characterized in that: the inertial/odometer combined navigation observation equation is established as follows,
step 1, selecting a difference value delta V between an inertial navigation speed increment and a speedometer speed incrementIns-ΔVdObtaining a filtering observed quantity Z as an inertia/mileometer combined navigation observed quantityk，
Zk＝ΔVIns(k)-ΔVd(k)
Wherein Z iskIs tkThe observations at a time filter the observations, Δ VIns(k)Is tkObserved inertial navigation velocity delta at time, Δ Vd(k)Is tkThe speed increment of the milemeter of the observed quantity at the moment;
and 2, establishing an inertial odometer integrated navigation observation equation.
3. An inertia/odometer combined navigation method according to claim 2, characterized in that: step 1 filtering observation quantity ZkIt is determined that the following is true,
(1)tkodometer speed delta V at timed(k)The method comprises the steps of (1) obtaining,
ΔVd(k)＝Vd(k)-Vd(k-1)
＝vr(k)+vc(k)+δvd(k)-vr(k-1)-vc(k-1)-δvd(k-1)
wherein, Vd(k)Is tkOutput speed, V, of a time odometerd(k-1)Is tk-1Output speed, v, of a time odometerr(k)Is tkTrue velocity, v, of time-of-day track detection systemr(k-1)Is tk-1True velocity, v, of time-of-day track detection systemc(k)Is tkVelocity measurement error of time odometer, vc(k-1)Is tk-1Speed measurement error of time odometer, delta vd(k)Is tkSpeed noise, δ v, of time odometerd(k-1)Is tk-1Measuring speed noise of the moment odometer;
and δ vd(k)≈δvd(k-1)
Thus, Δ V is obtainedd(k)＝vr(k)+δvd(k)-vr(k-1)-δvd(k-1)；
(2)tkMoment inertial navigation velocity increment delta VIns(k)The method comprises the steps of (1) obtaining,
ΔVIns(k)＝(vIns(k)-vIns(k-1))+(δvIns(k)-δvIns(k-1))
wherein v isIns(k)Is tkVelocity of inertial navigation at time vIns(k-1)Is tk-1Moment of inertia velocity, δ vIns(k)Is tkMoment of inertia velocity noise, δ vIns(k-1)Is tk-1Moment inertial navigation speed noise;
(3) taking the difference value of the inertial navigation speed increment and the odometer speed increment as the inertial/odometer combined navigation observed quantity to obtain Zk＝ΔVIns(k)-ΔVd(k)。
4. The combined inertial/odometer navigation method according to claim 1, characterized in that: the above-mentioned
Figure FDA0003328088710000025
5. The combined inertial/odometer navigation method according to claim 1, characterized in that: the inertia/mileometer combined navigation state equation is
Figure FDA0003328088710000021
Wherein X (t) is a state variable at the time t, and a north speed error delta V is selectedNSpeed error delta V in the direction of the skyUEast velocity error δ VELatitude error delta L, altitude error delta h, longitude error delta lambda, north misalignment angle phiNAngle of vertical misalignment phiUEast misalignment angle phiETriaxial gyro drift
Figure FDA0003328088710000022
Triaxial accelerometer zero position
Figure FDA0003328088710000023
Figure FDA0003328088710000024
As state variables for the inertial/odometer combination navigation;
f is a state transition matrix of a continuous state equation corresponding to the state variable at the time t;
w (t) is the systematic random noise vector at time t.
6. The combined inertial/odometer navigation method according to claim 1, characterized in that: the inertia/odometer integrated navigation state equation establishing steps are as follows,
step 1, selecting a north direction speed error delta VNSpeed error delta V in the direction of the skyUEast velocity error δ VELatitude error delta L, altitude error delta h, longitude error delta lambda, north misalignment angle phiNAngle of vertical misalignment phiUEast misalignment angle phiETriaxial gyro drift
Figure FDA0003328088710000031
Triaxial accelerometer zero position
Figure FDA0003328088710000032
As the state variable of the inertia/mileometer combination navigation, obtaining the state variable,
Figure FDA0003328088710000033
step 2, establishing an inertia/mileometer integrated navigation state equation,
Figure FDA0003328088710000034
wherein, X (t) is a state variable at the time t, F is a state transition matrix of a continuous state equation corresponding to the state variable at the time t, and w (t) is a system random noise vector at the time t;
the method is obtained by discretization, and the method comprises the following steps of,
Xk＝Φk,k-1Xk-1+Γk-1Wk-1
in the formula (I), the compound is shown in the specification,
Figure FDA0003328088710000035
is tk-1Time tkA system one-step state transition matrix of time of day, wherein
Figure FDA0003328088710000036
T is the filter period, TnFor discrete periods, FiIs a system matrix; gamma-shapedk-1I is the noise driving matrix of the system; wkSatisfies E [ W ] for the excitation noise sequence of the systemk]＝0，
Figure FDA0003328088710000037
Wherein when k is j, δk,j1, otherwise 0, QkIs WkThe variance matrix of (a), assuming non-negative determinism.
7. The combined inertial/odometer navigation method according to claim 1, characterized in that: the Kalman filteringKalman filtering as state delay, tkThe observation equation of the time contains tk-1State variable X of timek-1Term, i.e. tkObserved value of time and tk-1The state quantity at the moment is relevant.
8. An inertia/odometer combined navigation method according to claim 7, characterized in that: the state-delayed kalman filter is as follows,
let tkThe estimated state of the time instant is subjected to a system noise sequence Wk-1Drive, the equation of state is described by
Xk＝Φk,k-1Xk-1+Γk-1Wk-1
For XkSatisfies the following relationship
Zk＝HkXk+LkXk-1+Vk
In the formula phik,k-1Is tk-1Time tkMoment system one-step state transition matrix, Γk-1For the noise-driven matrix of the system, WkFor the excitation noise sequence of the system, HkIs the observation matrix of the system, LkIs a delay state observation matrix, V, corresponding to the state at the last moment of the systemkIs the system observation noise sequence;
Wkand VkThe following relationship is satisfied,
E[Wk]＝0，
Figure FDA0003328088710000041
E[Vk]＝0，
Figure FDA0003328088710000042
Figure FDA0003328088710000043
in the formula, QkIs WkThe variance matrix of (a), assuming non-negative determinants,
Figure FDA0003328088710000044
is VkThe variance matrix of (a), assumed to be positive;
and obtaining corresponding Kalman filtering based on the delay state.
9. An inertia/odometer combined navigation method according to claim 9, characterized in that: the time-delay state-based Kalman filtering,
state one-step prediction
Figure FDA0003328088710000045
One-step prediction mean square error array
Figure FDA0003328088710000046
Filter gain
Figure FDA0003328088710000047
Figure FDA0003328088710000051
State estimation
Figure FDA0003328088710000052
Estimating mean square error matrix
Figure FDA0003328088710000053
10. An inertial/odometer combination navigation system comprising a memory and a processor, characterized in that: the memory stores a computer program which, when executed by the processor, implements the combined inertial/odometer navigation method of any one of claims 1 to 9.
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Cited By (3)

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Publication number Priority date Publication date Assignee Title
CN114923479A (en) * 2022-04-19 2022-08-19 北京自动化控制设备研究所 Inertial/odometer combined navigation error compensation method
CN114993296A (en) * 2022-04-19 2022-09-02 北京自动化控制设备研究所 High-dynamic combined navigation method for guided projectile
CN114993296B (en) * 2022-04-19 2024-03-15 北京自动化控制设备研究所 High dynamic integrated navigation method for guided projectile

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