Disclosure of Invention
In view of the above analysis, the present invention aims to disclose a pseudo satellite navigation positioning method under a weak geometry, which improves the accuracy of solving parameter positions under the weak geometry, and enhances the availability of positioning services.
The invention discloses a pseudo satellite navigation positioning method under a weak geometric configuration, which comprises the following steps:
s1, fixing a motion track of a pseudo satellite receiver, and under the condition that the layout of the pseudo satellite base station is limited and is in a weak geometric configuration, after the motion track of the pseudo satellite receiver is folded, laying the pseudo satellite base station along the folding track;
s2, when the pseudolite receiver moves to one track line segment in the broken line track, a first error equation set of pseudolite positioning is established according to signals which are simultaneously received by the pseudolite receiver and transmitted by a plurality of foundation pseudolite base stations arranged on the track line segment;
s3, adding a motion track horizontal error equation at the approximate coordinates of the pseudo satellite receiver into the first error equation set by taking the track equation of the track line segment as a motion constraint condition to obtain a second pseudo satellite positioning error equation set;
and S4, iteratively solving a second error equation set to obtain a pseudo satellite single-point positioning result, calculating an HDOP value of the second error equation set, and evaluating the horizontal positioning precision.
Further, for pseudolite receivers moving at a fixed altitude;
In step S3, a trajectory equation of the trajectory segment is used as a motion constraint condition, and a motion trajectory level and a height error equation at an approximate coordinate of a pseudo satellite receiver are added into a first error equation set to obtain a third error equation set of pseudo satellite positioning;
in step S4, after the third error equation set is solved iteratively, a single-point positioning result of the pseudolite is obtained, each DOP value of the third error equation set is calculated, and the overall, horizontal and height positioning accuracy is evaluated.
Further, according to signals transmitted by a plurality of pseudolite base stations which are simultaneously received by a pseudolite receiver, a first error equation set of pseudolite positioning is established as follows:
Wherein, (N0,E0,U0) is the approximate coordinates of the pseudolite receiver, (Ni,ei,ui) is the accurate coordinates of the ith pseudolite base station from which the pseudolite receiver can receive the transmitted signal, (vi is the residual error of the ith pseudolite base station signal received by the pseudolite receiver, (i=1., N is the number of received pseudolite base stations;
ρi,0 is a geometric distance initial value based on the coordinate initial value;
(dN, dE, dU) is the initial value correction of the coordinates of the pseudolite receiver to be solved, dtr is the initial value correction of the clock difference of the pseudolite receiver to be solved, c is the light speed, Pi is the observation value of the pseudolite receiver to the ith pseudolite base station, ρi is the true geometric distance between the pseudolite receiver and the ith pseudolite base station, Ti is the clock difference of the ith pseudolite base station, and Ti is the tropospheric delay on the signal propagation path of the ith pseudolite base station.
Further, adding the motion track horizontal error equation into the first error equation set to obtain a second error equation set of pseudo satellite positioning, wherein the second error equation set is as follows:
v' is a pseudo satellite receiver horizontal position residual error on a motion track; The horizontal accurate coordinates of the j1 th pseudolite base station on the track line segment; The horizontal accurate coordinates of the j2 th pseudolite base station on the track line segment, j1≠j2.
Further, the weight array PP of the second error equation set of the pseudo satellite positioning after the motion track horizontal error equation is added is as follows:
Wherein P is a weight matrix corresponding to a first error equation set of pseudo satellite positioning, and P' is a weight matrix corresponding to a horizontal error equation of a motion track;
Is the variance of the weights of the units,Horizontal variance of the pseudolite receiver.
Further, for the pseudolite receiver moving at a fixed altitude, adding the motion track level and altitude error equation into the first error equation set to obtain a third error equation set of pseudolite positioning, wherein the third error equation set is as follows:
Wherein Ur0 is the height of the pseudolite receiver, v '' is the vertical position residual error of the pseudolite receiver on the motion trail.
Further, for the pseudo satellite receiver with elevation change, adding the motion track level and the elevation error equation into the first error equation set to obtain a fourth error equation set of pseudo satellite positioning, wherein the fourth error equation set is as follows:
wherein v '' is a pseudolite receiver vertical position residual error on the motion trail; The accurate coordinates of the1 th pseudolite base station on the track line segment; The accurate coordinates of the j2 th pseudolite base station on the track line segment, j1≠j2.
Further, the weight array PP of the third error equation set or the fourth error equation set of the pseudo satellite positioning after adding the horizontal and vertical error equations of the motion track is:
Wherein P is a weight matrix corresponding to a first error equation set of pseudo satellite positioning, and P' is a weight matrix corresponding to a horizontal error equation of a motion track;
p' is a weight matrix corresponding to a motion track vertical error equation;
Wherein, theIs the variance of the weights of the units,The horizontal variance of the pseudolite receiver,Is the elevation variance of the pseudolite receiver.
Further, after the pseudo satellite base stations are distributed at the inflection points of the folding lines of the motion track, the pseudo satellite base stations are uniformly distributed on the folding line sections according to the lengths of the folding line sections, so that the shape of the folding lines of the whole track can be fitted by fewer base stations;
When the number of the folding line segments is M, using M+1 pseudo satellite base stations to be positioned on the starting point, the inflection point and the end point of the whole folding line, the pseudo satellite base stations at the inflection point of the track folding line are named as STAm in sequence, wherein m=0, 1,2······m, the distances between two adjacent inflection point pseudolite base stations are calculated respectively and are recorded as DDmm, respectively calculating the false points of two adjacent inflection points the inter-satellite base station distance is denoted as DDmm.
Further, according to the pseudolite base station arranged at the inflection point, judging whether the pseudolite receiver moves from the current inflection line segment to the next inflection line segment, so as to update a track constraint equation, wherein the method comprises the following steps:
1) When the pseudo satellite receiver moves on the j th folding line segment, a track constraint equation is obtained by fitting coordinates of an inflection point pseudo satellite base station STAj-1 and a pseudo satellite base station STAj;
2) Respectively calculating the distance of a pseudo satellite receiver according to the positioning result of each epoch, and calculating the plane distance between two pseudo satellite base stations STAj-1、STAj of the broken line segment Duan Liangduan;
3) Determining that the pseudolite receiver moves to the next broken line segment when the distance between the pseudolite receiver and the pseudolite base station STAj-1 at the head end of the broken line segment is larger than the plane distance between the two pseudolite base stations of the broken line segment Duan Liangduan and the shortest plane distance DMIN between the current epoch pseudolite receiver and the current broken line segment is consistent with the plane distance between the pseudolite receiver and the pseudolite base station STAj at the tail end of the broken line segment;
4) And updating a track constraint equation, wherein the track constraint equation is obtained by fitting coordinates of the inflection point pseudolite base station STAj and the pseudolite base station STAj+1.
The invention can realize one of the following beneficial effects:
The invention discloses a pseudo satellite navigation positioning method under a weak geometry, which aims at the problems that the condition of a deployment site of a ground pseudo satellite positioning system is limited, for example, the weak geometry exists in base stations in areas such as urban canyons, narrow strip-shaped spaces and the like, a positioning method equation has singular or approximate pathological conditions, so that coordinate parameter calculation accuracy is low and is not stable. And the functional relation which is met by the motion trail is used as a constraint condition to constrain the process of positioning the user, so that the aims of obtaining a guaranteed positioning result, improving the precision of parameter position solving and enhancing the usability of positioning service are fulfilled.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
An embodiment of the invention discloses a pseudo satellite navigation positioning method under a weak geometric configuration, as shown in fig. 1, comprising the following steps:
s1, fixing a motion track of a pseudo satellite receiver, and under the condition that the layout of the pseudo satellite base station is limited and is in a weak geometric configuration, after the motion track of the pseudo satellite receiver is folded, laying the pseudo satellite base station along the folding track;
s2, when the pseudolite receiver moves to one track line segment in the broken line track, a first error equation set of pseudolite positioning is established according to signals which are simultaneously received by the pseudolite receiver and transmitted by a plurality of foundation pseudolite base stations arranged on the track line segment;
s3, adding a motion track horizontal error equation at the approximate coordinates of the pseudo satellite receiver into the first error equation set by taking the track equation of the track line segment as a motion constraint condition to obtain a second pseudo satellite positioning error equation set;
and S4, iteratively solving a second error equation set to obtain a pseudo satellite single-point positioning result, calculating an HDOP value of the second error equation set, and evaluating the horizontal positioning precision.
The proposal is suitable for the application scene without the requirement on the vertical positioning precision, and after the proposal is further optimized under the application scene with the requirement on the vertical positioning precision or the pseudolite receiver moving at a fixed height,
In step S3, a trajectory equation of the trajectory segment is used as a motion constraint condition, and a motion trajectory level and a height error equation at an approximate coordinate of a pseudo satellite receiver are added into a first error equation set to obtain a third error equation set of pseudo satellite positioning;
in step S4, after the third error equation set is solved iteratively, a single-point positioning result of the pseudolite is obtained, each DOP value of the third error equation set is calculated, and the overall, horizontal and height positioning accuracy is evaluated.
A flow chart of a pseudolite navigation positioning method for a pseudolite receiver moving at a fixed altitude is shown in fig. 2.
In the navigation application scenes, the layout of the foundation pseudolite base station is affected by the environment, and the foundation pseudolite base station is difficult to be laid into ideal distribution positions and has the characteristic of weak geometric configuration;
However, in the above application scenario, the motion track of the pseudolite receiver is also mostly constrained by the environment, and can only move on a fixed track with straight line or broken line characteristics.
For example, the tunnel application scene is limited by tunnel space, and the pseudo satellite base stations can only be distributed in a strip shape along the tunnel, so that the geometric configuration in the plane direction is poor, and a weak plane geometric configuration is formed.
However, the movement track of the vehicle or other equipment to be positioned in the tunnel is also limited in the tunnel space by the tunnel constraint and moves along the tunnel.
Based on the characteristics of the navigation application scene, in the embodiment, on the premise of obtaining the motion trail of the pseudo satellite receiver in advance, after the motion trail of the pseudo satellite receiver is folded, a foundation pseudo satellite base station is arranged along the folding trail of the satellite receiver.
After the motion track is folded, a plurality of pseudo satellite base stations which also have the same trend are correspondingly arranged on each linear track segment;
and the coordinates of the pseudolite base stations are precisely measured in advance, and time synchronization is carried out among the pseudolite base stations so as to reduce the clock error among the pseudolites.
Specifically, in step S2, when the pseudolite receiver moves to one track segment in the broken line track, a plurality of pseudolite base stations arranged on the track segment can be received simultaneously;
After linearization at the pseudolite receiver approximate coordinates (N0,E0,U0), the pseudolite positioning error equation can be written as:
Wherein vi is the residual error of the ith pseudolite base station signal received by the pseudolite receiver, (ni,ei,ui) is the accurate coordinate of the ith pseudolite base station of the transmitted signal received by the pseudolite receiver, i=1, n is the number of the received pseudolite base stations;
ρi,0 is a geometric distance initial value based on the coordinate initial value;
(dN, dE, dU) is an initial value correction of a satellite receiver coordinate to be solved, dtr is an initial value correction of a satellite receiver clock error to be solved, c is a light speed, Pi is an observation value of the satellite receiver to an ith pseudolite base station, ρi is a true geometric distance between the satellite receiver and the ith pseudolite base station, Ti is the clock error of the ith pseudolite base station, Ti is tropospheric delay on a signal propagation path of the ith pseudolite base station, Ti can be ignored after accurate time synchronization is carried out between the pseudolite base stations, and tropospheric delay Ti of base station propagation can be ignored under the condition of limited height of the pseudolite base station.
According to signals transmitted by a plurality of pseudolite base stations which are simultaneously received by a pseudolite receiver, a first error equation set of pseudolite positioning is established as follows:
Writing a first error equation set of pseudo satellite positioning into a matrix form:
V=BX-L;
in the formula,
V=[v1 … vi … vn]T,
X=[dN dE dU c·dtr]T,
The design matrix B is:
the optimal estimation of the parameter X by using the weight matrix P corresponding to the matrix B is as follows:
X=(BTPB)-1BTPL
the coordinates of the pseudolite receiver are:
And taking the obtained coordinates as new initial coordinates, and carrying out iterative calculation until the parameters are converged.
The accuracy of pseudolite positioning depends in part on the strength of the geometry between the user and the pseudolite, and a precision factor DOP (Dilution of Precision) is commonly used in single point positioning to quantitatively reflect the geometry strength. The precision factor is found from the inverse of the normal coefficient matrix, which can be expressed as:
three-dimensional accuracy factor PDOP (Position Dilution of Precision), plane accuracy factor HDOP (Horizontal Dilution of Precision), and elevation positioning accuracy factor VDOP Vertical Dilution of Precision) are defined as:
aiming at the weak plane geometry of the pseudolite base station of the tunnel application scene, in step S3 of one scheme of the embodiment, the horizontal track error equation of the track line segment is added into a first error equation set as motion constraint based on the application condition that the pseudolite base station and a user are not on the same horizontal plane,
In the process of establishing a motion trail horizontal error equation at the approximate coordinates of the pseudo satellite receiver, the method comprises the following steps:
1) Selecting two foundation pseudolite base stations arranged on the track line segment, and taking the plane relation between the pseudolite base stations into consideration, wherein the horizontal accurate coordinate of the jth1 pseudolite base stations on the track line segment isThe horizontal accurate coordinate of the jth2 pseudolite base station on the track line segment is
The horizontal plane linear equation through the two pseudolite base stations is:
Preferably, the two pseudolite base stations for establishing the plane linear equation are two pseudolite base stations arranged at two ends of the tunnel plane linear segment, namely, the j1 th pseudolite base station is the 1 st pseudolite base station on the track line segment, and the j2 th pseudolite base station is the last 1 pseudolite base station on the track line segment.
2) Writing the plane linear equation at the approximate plane coordinates (N0,E0) of the pseudo satellite receiver into a motion track horizontal error equation, wherein the motion track horizontal error equation is as follows:
v' is the pseudo satellite receiver horizontal position residual error on the motion trail;
The corresponding weight is P':
Is the variance of the weights of the units,Horizontal variance of the pseudolite receiver.
3) Adding the motion track horizontal error equation into the first error equation set to obtain a second error equation set of pseudo satellite positioning, wherein the second error equation set is as follows:
The weight matrix corresponding to the first error equation set of pseudo satellite positioning is P, and the weight matrix PP of the second error equation set of pseudo satellite positioning after adding the constraint equation is:
wherein P is a weight matrix corresponding to a first error equation set of pseudo satellite positioning, and P' is a weight matrix corresponding to a horizontal error equation of a motion track.
Specifically, in step S4, the pseudo satellite single-point positioning result after adding the constraint equation can be obtained by using the least square method to iteratively solve the two error equation sets, and meanwhile, the HDOP value after adding the constraint equation can be calculated, so as to evaluate the overall and horizontal positioning accuracy.
In another scheme, step S3, the horizontal error equation of the track line segment is added into a first error equation set as a motion constraint, and the altitude error equation is also added into the first error equation set to obtain a third error equation set of pseudo satellite positioning;
Specifically, for the altitude error equation at the pseudo-satellite receiver approximate coordinates, the altitude of the pseudo-satellite receiver is assumed to be Ur0 and its variance isThe equations satisfied by the pseudolite receiver elevation can be written:
U=Ur0
The form written as error equation is:
v′′=1·dU-Ur0
v″ is a pseudolite receiver vertical position residual error on the motion trajectory;
the corresponding weights P' are:
Wherein, theIs the unit weight variance.
Then, adding the motion track level and height error equation into the first error equation set to obtain a third error equation set of pseudo satellite positioning, wherein the third error equation set is as follows:
The weight array PP of the third error equation set of the pseudo satellite positioning after the horizontal and vertical error equations of the motion track are added is as follows:
wherein P is the weight matrix corresponding to the first error equation set of pseudo satellite positioning, P ' is the weight matrix corresponding to the horizontal error equation of the motion trail, and P ' ' is the weight matrix corresponding to the vertical error equation of the motion trail.
Specifically, in step S4, the single-point positioning result of the pseudolite after adding the constraint equation can be obtained by using the least square method to iteratively solve the two error equation sets, and meanwhile, each DOP value after adding the constraint equation can be calculated to evaluate the overall, horizontal and height positioning accuracy.
More preferably, in this embodiment, after the pseudolite base station is arranged at the inflection point of the motion trajectory broken line, the pseudolite base station is uniformly arranged on the broken line section according to the length of the broken line section, so that the shape of the whole trajectory broken line can be fitted by using fewer base stations;
When the number of the folding line segments is M, using M+1 pseudo satellite base stations to be positioned on the starting point, the inflection point and the end point of the whole folding line, the pseudo satellite base stations at the inflection point of the track folding line are named as STAm in sequence, wherein m=0, 1,2······m, the distances between two adjacent inflection point pseudolite base stations are calculated respectively and are recorded as DDmm, respectively calculating the false points of two adjacent inflection points the inter-satellite base station distance is denoted as DDmm.
In the embodiment, whether the pseudolite receiver moves from the current folding line segment to the next folding line segment is judged according to the base station of the inflection point pseudolite so as to update a track constraint equation;
In particular, the method comprises the steps of,
1) When the pseudo satellite receiver moves on the j th folding line segment, a track constraint equation is obtained by fitting coordinates of an inflection point pseudo satellite base station STAj-1 and a pseudo satellite base station STAj;
2) Calculating the pseudo satellite receiver distance according to the positioning result of each epoch (generally 0.1 second) and calculating the plane distance between two pseudo satellite base stations (STAj-1 and STAj) of the broken line segment Duan Liangduan;
3) Determining that the pseudolite receiver moves to the next broken line segment when the distance between the pseudolite receiver and the pseudolite base station STAj-1 at the head end of the broken line segment is larger than the plane distance between the two pseudolite base stations (STAj-1 and STAj) of the broken line segment Duan Liangduan and the shortest plane distance DMIN of the current epoch pseudolite receiver from the current broken line segment is consistent with the plane distance between the pseudolite receiver and the pseudolite base station STAj at the tail end of the broken line segment;
4) And updating a track constraint equation, wherein the track constraint equation is obtained by fitting coordinates of the inflection point pseudolite base station STAj and the pseudolite base station STAj+1.
In a more preferred scheme, the method can also be performed on a pseudolite receiver with elevation change, and in the process of establishing the three-dimensional motion trail at the approximate coordinates of the pseudolite receiver, the method comprises the following steps:
1) Selecting two foundation pseudolite base stations arranged on the track line segment, and taking the three-dimensional position relation between the pseudolite base stations into consideration, wherein the horizontal accurate coordinate of the jth1 pseudolite base stations on the track line segment isThe horizontal accurate coordinate of the jth2 pseudolite base station on the track line segment is
The linear equation through the two pseudolite base stations is:
Preferably, the two pseudolite base stations for establishing the linear equation are two pseudolite base stations arranged at two ends of the linear section of the tunnel, namely, the j1 th pseudolite base station is the 1 st pseudolite base station on the track line section, and the j2 th pseudolite base station is the last 1 pseudolite base station on the track line section.
2) Writing the linear equation at the approximate three-dimensional coordinate (N0,E0,U0) of the pseudo satellite receiver into a horizontal error equation and a vertical error equation of a motion track, wherein the horizontal error equation and the vertical error equation are as follows:
v' is the residual error of the horizontal position of the pseudolite receiver on the motion trail, v″ is the residual error of the vertical position of the pseudolite receiver on the motion trail;
Its corresponding weight isWherein, theIs the variance of the weights of the units,The horizontal variance of the pseudolite receiver; Is the elevation variance of the pseudolite receiver.
3) Adding the motion track level and the error equation into the first error equation set to obtain a fourth error equation set of pseudo satellite positioning, wherein the fourth error equation set is as follows:
Obtaining a constraint equation of the coordinates of the pseudo satellite receiver established by obtaining a linear track based on the coordinates of projection points projected onto the motion track of the user by the 2 pseudo satellite base stations, adding the constraint equation into a first error equation set, and at the moment, a fourth error equation set of pseudo satellite positioning is as follows:
The weight array PP of the third error equation set of the pseudo satellite positioning after the horizontal and vertical error equations of the motion track are added is as follows:
wherein P is the weight matrix corresponding to the first error equation set of pseudo satellite positioning, P ' is the weight matrix corresponding to the horizontal error equation of the motion trail, and P ' ' is the weight matrix corresponding to the vertical error equation of the motion trail.
In summary, the core of the present invention is the improvement of the existing pseudolite positioning model. The traditional pseudolite positioning model can obtain accurate positioning results when the geometry of the pseudolite base station is good. However, when the positioning model is used alone in a scenario that some pseudo satellite base stations are in weak geometric configuration, the positioning method equation is odd or nearly ill-conditioned, and accurate positioning results are difficult to obtain. We consider adding more information to the positioning model making the positioning model more robust. In the method, a situation that a pseudo satellite base station is in a weak geometric configuration is considered to be a limited space, and in the limited space, the motion trail of a user is constrained by the space to be in accordance with a corresponding rule curve to a certain extent, in this case, the motion trail of the user is taken as a constraint condition, and a mathematical function model and a random model based on the constraint condition of the trail are established, so that the condition number of a normal equation in parameter solving is improved, and the accuracy of parameter position solving is improved. This improvement is effective.
Example two
In this embodiment, taking a tunnel scene as an example, performing effect verification of a pseudo satellite navigation positioning method under a weak geometry configuration;
As shown in fig. 3, a pseudo satellite positioning test line with a weak geometry (tunnel scene) in the embodiment is shown in fig. 4, and in this tunnel scene, a plane geometry precision factor HDOP of the test trolley on the test line before and after the linear track constraint is added.
In fig. 4, fig. 4a shows that the HDOP value of the test trolley on the test line is greater than 40 when the linear track constraint is not added;
In fig. 4, fig. 4b shows that after the linear track constraint is added, the HDOP value of the test trolley on the test line is lower than 3 in all areas;
by comparing fig. 4a and fig. 4b, it can be seen that the present embodiment greatly reduces the HDOP value by increasing the linear track constraint.
Fig. 5 shows a positioning result diagram of the test trolley after the linear track constraint is added in the tunnel scene. From the figure, the positioning result of the test trolley is basically on a line segment, and the test trolley has good conformity with the path in the actual tunnel.
FIG. 6 shows PDOP after increasing three-dimensional linear trajectory constraint under weak geometry, with all regions below 3.5;
fig. 7 is a schematic diagram of a positioning result of a tunnel pseudo satellite system. The positioning result of the test trolley is basically on a three-dimensional line segment, and the degree of coincidence with the path in the actual tunnel is good.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.