CN110793519A - Incomplete measurement collaborative navigation positioning method - Google Patents

Incomplete measurement collaborative navigation positioning method Download PDF

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CN110793519A
CN110793519A CN201911175384.XA CN201911175384A CN110793519A CN 110793519 A CN110793519 A CN 110793519A CN 201911175384 A CN201911175384 A CN 201911175384A CN 110793519 A CN110793519 A CN 110793519A
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navigation
platform
collaborative
positioning
relative
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陈红梅
常林江
吴才章
王慧娟
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Henan University of Technology
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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
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • G01S19/47—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/024—Guidance services
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management

Abstract

The invention discloses a collaborative navigation positioning method for incomplete measurement, which aims at solving the incomplete measurement problems of measurement data randomness packet loss and the like of a networking communication link in a relative navigation platform and establishes a collaborative navigation positioning filter under a Bayesian framework. Comprises two steps: modeling a collaborative navigation positioning system into a plurality of mobile nodes and a plurality of anchor points, wherein each mobile node utilizes an own inertial sensor to carry out strapdown calculation, and corrects navigation errors calculated by an INS (inertial navigation system) by using GPS (global positioning system) signals; step two, collaborative navigation positioning networking communication, wherein each mobile node utilizes observable anchor points and UWB relative ranging of other mobile nodes to conduct collaborative navigation positioning; when the networking communication link is incompletely measured, the incomplete measurement is used for compensating in cooperation with a navigation estimation filter, and navigation parameters are output; the invention is suitable for collaborative navigation positioning when random packet loss occurs in the networking communication link.

Description

Incomplete measurement collaborative navigation positioning method
Technical Field
The invention belongs to the technical field of collaborative navigation, and particularly relates to a collaborative navigation positioning method considering incomplete measurement.
Background
The collaborative navigation is a technology for interactively utilizing navigation information among platforms in collaborative networking formation, resolving and correcting navigation information such as self position, speed and attitude in real time, and guaranteeing that collaborative formation is maintained, formation reconstruction and subsequent collaborative tasks are smoothly completed. If the accurate navigation information of the collaborative platform cannot be obtained or the acquired relative navigation accuracy is reduced, the control accuracy of formation is deteriorated, and the task execution effect is reduced or even wrong.
The collaborative navigation positioning under the Bayesian framework mainly comprises an absolute navigation platform and a relative navigation platform. Absolute navigation GPS update rate is lower, and UWB is introduced in relative navigation, has the high-frequency high accuracy characteristics, can reach GPS ten times's frequency, and the UWB precision can reach centimetre level simultaneously, and UWB's introduction makes navigation positioning accuracy in coordination promote greatly. However, when UWB is located through wireless communication, when there are many obstacles in the location area, the influence of multipath effect and shadowing effect needs to be considered to cause the problem of random packet loss of UWB measurement data. Therefore, the problem of improving the navigation and positioning accuracy of the system by designing the incomplete measurement collaborative filter is very important in researching the incomplete measurement collaborative navigation and positioning technology.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problem of poor positioning accuracy caused by the fact that the information of the collaborative platform is lost in incomplete measurement, a collaborative navigation positioning algorithm of incomplete measurement is provided, a collaborative filter of incomplete measurement is established, and an efficient and stable collaborative navigation positioning method is provided.
The technical scheme is as follows: a collaborative navigation positioning method for incomplete measurement is characterized by comprising the following specific steps:
modeling a collaborative navigation positioning system into a plurality of mobile nodes and a plurality of anchor points, wherein each mobile node utilizes an own inertial sensor to carry out strapdown calculation, and corrects navigation errors calculated by an INS (inertial navigation system) by using GPS (global positioning system) signals;
step two, collaborative navigation positioning networking communication, wherein each mobile node utilizes observable anchor points and UWB relative ranging of other mobile nodes to conduct collaborative navigation positioning; when the networking communication link generates incomplete measurement of collaborative data, an incomplete measurement estimation filter is established according to a system collaborative model, a sensor error estimation and speed and position compensation absolute navigation filter is carried out, and navigation parameters are output.
The invention has the advantages that
(1) The invention considers the measurement of different platforms and adopts a dynamic relative navigation collaborative modeling mode.
(2) The invention considers the measurement noise estimation of the problem of incomplete measurement of the networking communication link, approximates the state variable estimation by the confidence estimation of relative navigation, and can effectively solve the precision influence caused by incomplete measurement.
(3) The working modes of all the platforms are the same, and when some platform generates random incomplete measurement, the precision of the whole system is not influenced.
Drawings
FIG. 1 is a flow chart of a collaborative filter for absolute and relative navigation according to the present invention;
FIG. 2 shows a system p (x) according to the invention(0:2)|z(0:2)) A factor graph;
FIG. 3 is a collaboration information interaction factor graph of incomplete measurement according to the present invention;
FIG. 4 is a flow chart of collaboration information interaction for incomplete measurement in accordance with the present invention.
Detailed Description
The invention is further explained below with reference to the drawings.
The present invention will be better understood from the following examples. As shown in fig. 1, the invention is a collaborative navigation positioning method for incomplete measurement, which comprises the following specific steps:
1. a collaborative navigation positioning method considering incomplete measurement is characterized in that the collaborative navigation method comprises the following specific steps:
modeling a collaborative navigation positioning system into a plurality of mobile nodes and a plurality of anchor points, wherein each mobile node utilizes an own inertial sensor to carry out strapdown calculation, corrects navigation errors calculated by an INS (inertial navigation system) by using GPS (global positioning system) signals and carries out feedback correction;
step two, collaborative navigation positioning networking communication, as shown in figure 2, each mobile node utilizes observable anchor points and UWB relative ranging of other mobile nodes to carry out collaborative navigation positioning; when the networking communication link is subjected to incomplete measurement of collaborative data, an incomplete measurement estimation filter is established according to a system collaborative model, a sensor error estimation and speed position compensation absolute navigation filter is carried out, and navigation parameters are output.
2. Step one, correcting INS errors by using the GPS, wherein a specific model is as follows:
Figure BDA0002289818040000021
in the formula:
Figure BDA0002289818040000022
is a vector of the states of the memory cells,
Figure BDA0002289818040000023
is an observation vector, and f (-) and h (-) correspond to a system state equation and an observation equation respectively; w is a(t-1)Is a sequence of noise in the process of the system,
Figure BDA0002289818040000024
is the system observation noise sequence; subscript k denotes the platform number; the superscript t indicates the current time.
3. Step two, the UWB relatively measures the distance and carries on the navigation positioning of coordination, specifically:
Figure BDA0002289818040000025
the collaborative navigation system utilizes the communication link of the navigation platform to carry out networking and relativeRanging, exchanging platform navigation information, navigation platform xkThe state vector of the cooperative platform with the neighbor on the communication link is
Figure BDA0002289818040000026
Networking neighbor set Nk＝{l1，l2，…，l|Nk|The K belongs to {1,2, L, K }, L belongs to {1,2, L, K } \ { K }, { K, L }, belongs to epsilon, K represents the total number of the collaborative navigation platform, and the collaborative navigation filter establishes the posterior probability of Bayesian estimation;
Figure BDA0002289818040000027
establishing a confidence approximation method by using a factor graph transmitted by the BP message, wherein p represents the interactive iteration times of the message;
Figure BDA0002289818040000028
measurements of collaborative relative navigation filters
Figure BDA0002289818040000029
The abbreviation is:representing an observed quantity communicated with a navigation platform k; the measured values are constituted by the measured data of the corresponding platform/associated with the navigation platform k:
Figure BDA00022898180400000211
Figure BDA00022898180400000212
is abbreviated as
Figure BDA00022898180400000213
Satisfies g (x)k,xl)＝g(xl,xk)。
4. The measurement values for the incomplete measurement collaborative navigation mainly include the following two cases:
case 1, navigation platform k and anchor point li(Anchor) UWB communication ranging measurements
Figure BDA0002289818040000031
Wherein
Figure BDA0002289818040000032
Representing the location and anchor point (l) of agent navigation platform k via INS solution or GPS/INS integrated navigation solutioni) The relative distance measurement specifically comprises:
wherein
Figure BDA0002289818040000034
Representing agent navigation platform k via UWB and anchor point liThe UWB ranging method comprises the following steps that (1) UWB ranging is carried out, wherein a navigation platform k provides high-precision positioning through UWB, and the positioning can be obtained after compensation is carried out on positions calculated by INS or GPS/INS integrated navigation, and specifically the UWB ranging method comprises the following steps:
case 2, UWB of agent navigation platform k and UWB of collaborative navigation platform l communicate a distance measurement value; (k, l) epsilon ∈ epsilon, (l, k) epsilon ∈ epsilon
Figure BDA0002289818040000036
Wherein
Figure BDA0002289818040000037
The relative distance measurement of the positions of agent navigation platforms k and l calculated by the INS or the GPS/INS integrated navigation is specifically as follows:
Figure BDA0002289818040000038
wherein
Figure BDA0002289818040000039
The method is characterized in that agent navigation platform k and platform l are measured by UWB, the navigation platform provides high-precision positioning by UWB, and the positioning can be obtained after position compensation is carried out on the position resolved by INS or GPS/INS combined navigation, and the method specifically comprises the following steps:
Figure BDA00022898180400000310
5. the state variables of the navigation platform randomly walk and are independently and equally distributed among all nodes;
Figure BDA00022898180400000311
the measurement values of the absolute navigation and the relative navigation are independent from each other, and satisfy the following relation:
Figure BDA00022898180400000312
navigation data zkIn the transmission process, when data is transmitted by a node with high priority when transmission is attempted, the sensor gives up the transmission; or zkHas been sent but is lost during transmission; both cases indicate random loss of data packets, which do not completely measure the measurements received by the system filter
Figure BDA00022898180400000313
The subscript rel may be omitted and is described by the following model:
y(n)＝(1-r(n))z(n)+r(n)z(n-1)n＝0:T,y(1)＝z(1)(8)
wherein z is(n)∈RmOutputting ideal measurement for the system; y is(n)∈RmIs the actual measured value of the system; r is(n)To satisfy Bernouli distributionThe values of the sequence of (1) are 0 and 1, and the incomplete measurement probability is: p is a radical of(n)Is composed of
Figure BDA00022898180400000314
When r is(n)When the value is 0, the representation system obtains a real observed quantity, and the observed noise is Rv(ii) a When r iskWhen the measured value is 1, the system does not obtain a true observed quantity, and the system is replaced by the measured value at the previous moment, so that the collaborative navigation system not only needs to estimate x at n moments(n)There is also a need to estimate the observation noise v(n)。
Figure BDA0002289818040000041
Figure BDA0002289818040000042
6. The measurement of the relative navigation is independently and equally distributed and is related to the state and the noise of the adjacent time of every two nodes where the measurement occurs, wherein, the subscript l/k represents the number of the adjacent navigation platform, (l, k) is epsilon,
Figure BDA0002289818040000043
indicating that platform k receives the neighbor platform j information,
Figure BDA0002289818040000045
representing the relative range observations that platform k received platform j;
defining state dimensions for relative navigation:
Figure BDA0002289818040000046
(11) simplified to
Figure BDA0002289818040000047
7. Confidence of relative navigation for collaborative navigation positioning filter
Figure BDA0002289818040000048
Estimating the pdf of the approximated state variable:
Figure BDA0002289818040000049
wherein
Figure BDA00022898180400000410
All collaborative state variables representing interaction of the kth navigation platform, in particular
Figure BDA00022898180400000411
Figure BDA00022898180400000412
State variables representing a first one of the collaboration platforms adjacent to the kth platform,
Figure BDA00022898180400000413
to represent
Figure BDA00022898180400000414
Removing
Figure BDA00022898180400000415
The latter vector;
Figure BDA00022898180400000416
wherein
Figure BDA00022898180400000417
When the information interaction of the relative navigation is uncertain and random packet loss occurs, the relative positioning is completed by adopting the following mode shown in the attached figure 3
Figure BDA00022898180400000418
Wherein
Its initial value
Figure BDA00022898180400000420
Figure BDA00022898180400000421
If it is
Figure BDA00022898180400000422
Then there is
Figure BDA00022898180400000423
Then (16)
Bringing formula (16) into (17)
Wherein
Figure BDA0002289818040000051
Bringing formula (16) into (18)
Figure BDA0002289818040000052
Wherein (22) therein
Figure BDA0002289818040000053
Determined according to (15), in the formula (20)
Figure BDA0002289818040000054
According to the determination of (21),
Figure BDA0002289818040000055
for middle use
Figure BDA0002289818040000056
Correspond to
Figure BDA0002289818040000057
Updating navigation platform information
Figure BDA0002289818040000058
8. The collaborative navigation method for incomplete measurement is characterized in that:
Figure BDA0002289818040000059
9. (14) navigation platform information interaction
Figure BDA00022898180400000510
Can be expressed in terms of mean and variance
Figure BDA00022898180400000511
Figure BDA00022898180400000512
Updating navigation platform informationCan be expressed in terms of mean and variance.
10. Navigation platform information interaction
Figure BDA00022898180400000514
Estimation, as shown in FIG. 4, the observed noise sequence is used as a state variable to expand dimensions
Figure BDA00022898180400000515
And discretizing a continuous system into
Figure BDA00022898180400000516
It is composed of
Figure BDA00022898180400000517
Satisfy the requirement of
Figure BDA0002289818040000061
Wherein
Figure BDA0002289818040000062
Initial value of collaboration platform
Figure BDA0002289818040000063
Figure BDA0002289818040000064
Updating navigation platform information with (27)
Figure BDA0002289818040000065
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (10)

1. A collaborative navigation positioning method considering incomplete measurement is characterized in that the collaborative navigation method comprises the following specific steps:
modeling a collaborative navigation positioning system into a plurality of mobile nodes and a plurality of anchor points, wherein each mobile node utilizes an own inertial sensor to carry out strapdown calculation, corrects navigation errors calculated by an INS (inertial navigation system) by using GPS (global positioning system) signals and carries out feedback correction;
step two, collaborative navigation positioning networking communication, wherein each mobile node utilizes observable anchor points and UWB relative ranging of other mobile nodes to conduct collaborative navigation positioning; when the networking communication link is subjected to incomplete measurement of collaborative data, an incomplete measurement estimation filter is established according to a system collaborative model, a sensor error estimation and speed position compensation absolute navigation filter is carried out, and navigation parameters are output.
2. The collaborative navigation method with incomplete measurement taken into account as claimed in claim 1, wherein step one corrects the INS error by using GPS, and the specific model is as follows:
in the formula:
Figure FDA0002289818030000012
is a vector of the states of the memory cells,
Figure FDA0002289818030000013
is an observation vector, and f (-) and h (-) correspond to a system state equation and an observation equation respectively; w is a(t-1)Is a sequence of noise in the process of the system,
Figure FDA0002289818030000014
is the system observation noise sequence; subscript k denotes the platform number; the superscript t indicates the current time.
3. The collaborative navigation method considering incomplete measurement according to claim 1, wherein in step two, the UWB relative ranging performs collaborative navigation positioning, specifically:
Figure FDA0002289818030000015
the collaborative navigation system utilizes the communication link of the navigation platform to carry out networking and relative distance measurement, exchanges platform navigation information, and the navigation platform xkThe state vector of the cooperative platform with the neighbor on the communication link isNetworking neighbor set Nk＝{l1，l2，…，l|Nk|The K belongs to {1,2, L, K }, L belongs to {1,2, L, K } \ { K }, { K, L }, belongs to epsilon, K represents the total number of the collaborative navigation platform, and the collaborative navigation filter establishes the posterior probability of Bayesian estimation;
Figure FDA0002289818030000017
establishing a confidence approximation method by using a factor graph transmitted by the BP message, wherein p represents the interactive iteration times of the message;
Figure FDA0002289818030000018
measurements of collaborative relative navigation filtersThe abbreviation is:
Figure FDA00022898180300000110
representing an observed quantity communicated with a navigation platform k; the measured values are constituted by the measured data of the corresponding platform/associated with the navigation platform k:
Figure FDA0002289818030000021
Figure FDA0002289818030000022
is abbreviated as
Figure FDA0002289818030000023
Satisfies g (x)k,xl)＝g(xl,xk)。
4. The method of claim 3, wherein the measurement values mainly include the following two situations:
case 1, navigation platform k and anchor point li(Anchor) UWB communication ranging measurements
Wherein
Figure FDA0002289818030000025
Representing the location and anchor point (l) of agent navigation platform k via INS solution or GPS/INS integrated navigation solutioni) The relative distance measurement specifically comprises:
Figure FDA0002289818030000026
wherein
Figure FDA0002289818030000027
Representing agent navigation platform k via UWB and anchor point liThe UWB ranging method comprises the following steps that (1) UWB ranging is carried out, wherein a navigation platform k provides high-precision positioning through UWB, and the positioning can be obtained after compensation is carried out on positions calculated by INS or GPS/INS integrated navigation, and specifically the UWB ranging method comprises the following steps:
Figure FDA0002289818030000028
case 2, UWB of agent navigation platform k and UWB of collaborative navigation platform l communicate a distance measurement value;
(k,l)∈ε,(l,k)∈ε
Figure FDA0002289818030000029
wherein
Figure FDA00022898180300000210
The relative distance measurement of the positions of agent navigation platforms k and l calculated by the INS or the GPS/INS integrated navigation is specifically as follows:
wherein
Figure FDA00022898180300000212
The method is characterized in that agent navigation platform k and platform l are measured by UWB, the navigation platform provides high-precision positioning by UWB, and the positioning can be obtained after position compensation is carried out on the position resolved by INS or GPS/INS combined navigation, and the method specifically comprises the following steps:
5. the collaborative navigation method with consideration of incomplete measurement according to claim 3, wherein the navigation platform state variables are randomly walked and independently and identically distributed among the nodes;
Figure FDA00022898180300000214
the measurement values of the absolute navigation and the relative navigation are independent from each other, and satisfy the following relation:
Figure FDA00022898180300000215
navigation data zkIn the transmission process, when data is transmitted by a node with high priority when transmission is attempted, the sensor gives up the transmission; or zkHas been sent but is lost during transmission; both cases indicate random loss of data packets, the incomplete measurement systemMeasured values received by the filter
Figure FDA0002289818030000031
The subscript rel may be omitted and is described by the following model:
y(n)＝(1-r(n))z(n)+r(n)z(n-1)n＝0:T,y(1)＝z(1)(8)
wherein z is(n)∈RmOutputting ideal measurement for the system; y is(n)∈RmIs the actual measured value of the system; r is(n)In order to satisfy the sequence of Bernouli distribution, the values are 0 and 1, and the probability of incomplete measurement is as follows: p is a radical of(n)Is composed of
Figure FDA0002289818030000032
When r is(n)When the value is 0, the representation system obtains a real observed quantity, and the observed noise is Rv(ii) a When r iskWhen the measured value is 1, the system does not obtain a true observed quantity, and the system is replaced by the measured value at the previous moment, so that the collaborative navigation system not only needs to estimate x at n moments(n)There is also a need to estimate the observation noise v(n)；
Figure FDA0002289818030000033
Figure FDA0002289818030000034
6. The collaborative navigation method considering incomplete measurement according to claim 5, wherein the measurements of relative navigation are independently identically distributed with respect to states and noises at adjacent times of two nodes where the measurements occur, wherein a subscript l/k denotes an adjacent navigation platform number, (l, k) e,
Figure FDA0002289818030000035
Figure FDA0002289818030000036
indicating that platform k receives the neighbor platform j information,
Figure FDA0002289818030000037
representing the relative range observations that platform k received platform j;
defining state dimensions for relative navigation:
Figure FDA0002289818030000038
(11) simplified to
Figure FDA0002289818030000039
7. The method of claim 3, wherein the collaborative navigation positioning filter uses confidence of relative navigation
Figure FDA00022898180300000310
Estimating the pdf of the approximated state variable:
Figure FDA00022898180300000311
wherein
Figure FDA00022898180300000312
All collaborative state variables representing interaction of the kth navigation platform, in particular
Figure FDA00022898180300000313
Figure FDA00022898180300000314
Representing a first collaboration platform adjacent to a kth platformThe state variable of (a) is changed,
Figure FDA00022898180300000315
to represent
Figure FDA00022898180300000316
Removing
Figure FDA00022898180300000317
The latter vector;
Figure FDA00022898180300000318
wherein
Figure FDA0002289818030000041
When the information interaction of the relative navigation generates uncertain random packet loss, the relative positioning is completed by adopting the following mode
Figure FDA0002289818030000042
Wherein
Its initial value
Figure FDA0002289818030000044
If it is
Figure FDA0002289818030000046
Then there is
Figure FDA0002289818030000047
Then (16)
Figure FDA0002289818030000048
Bringing formula (16) into (17)
Wherein
Figure FDA00022898180300000410
Bringing formula (16) into (18)
Figure FDA00022898180300000411
Wherein (22) therein
Figure FDA00022898180300000412
Determined according to (15), in the formula (20)
Figure FDA00022898180300000413
According to the determination of (21),
Figure FDA00022898180300000414
for middle use
Figure FDA00022898180300000415
Correspond toUpdating navigation platform information
Figure FDA00022898180300000417
8. The collaborative navigation method with incomplete measurement taken into account of claim 1, wherein:
step 1: giving an initial value
Figure FDA00022898180300000418
Probability of incomplete measurement p(0)
step 2：for n＝1:T
step 3: absolute navigation platform parallel operation start k is 1: n is a radical ofk
Figure FDA00022898180300000419
step 4: parallel operation ending end of absolute navigation platform
step 5: relative navigation platform cooperative operation start k is 1: n is a radical ofk
step 6: initialization
Figure FDA00022898180300000420
step 7：for p＝1:NiterInformation interaction
step 8: broadcast transmission of navigation platform information
Figure FDA0002289818030000051
step 9: receiving neighborhood navigation platform information
step 10: (16) formula adjacent navigation platform carries out information interaction
Figure FDA0002289818030000053
step 11: (18) updating method
Figure FDA0002289818030000054
Correspond to
Figure FDA0002289818030000055
Updating navigation platform information
Figure FDA0002289818030000056
step 12: end of information interaction
step 13: collaborative navigation positioning confidence update for relative navigation platform
Figure FDA0002289818030000057
Navigation data update
step 14: and finishing the cooperative operation.
9. The collaborative navigation method with incomplete measurement taken into account of claim 7, wherein (14) navigation platform information interactionCan be expressed in terms of mean and variance
Updating navigation platform information
Figure FDA00022898180300000511
Can be expressed in terms of mean and variance.
10. The collaborative navigation method in accordance with claim 9, wherein navigation platform information interaction is performedEstimating, expanding dimensions with observation noise sequences as state variables
Figure FDA00022898180300000513
And discretizing a continuous system into
Figure FDA00022898180300000514
It is composed ofSatisfy the requirement of
Figure FDA00022898180300000516
Wherein
Initial value of collaboration platform
Figure FDA00022898180300000518
Figure FDA0002289818030000061
Updating navigation platform information with (27)
Figure FDA0002289818030000062
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CN112325880A (en) * 2021-01-04 2021-02-05 中国人民解放军国防科技大学 Distributed platform relative positioning method and device, computer equipment and storage medium
CN112836418A (en) * 2021-01-15 2021-05-25 中国人民解放军91550部队 Aircraft real-time positioning method and system based on incomplete measurement
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CN112325880A (en) * 2021-01-04 2021-02-05 中国人民解放军国防科技大学 Distributed platform relative positioning method and device, computer equipment and storage medium
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