Pseudo-satellite navigation positioning method under weak geometric configuration

Abstract

The invention relates to a pseudo satellite navigation and positioning method under weak geometric configuration, and belongs to the technical field of pseudo satellite positioning, and the method comprises the following steps: under the condition that the layout of a pseudo satellite base station is limited and is in weak geometric configuration, after the fixed motion track of a pseudo satellite receiver is broken, laying the pseudo satellite base station along the broken line track; when the pseudo-satellite receiver moves to one track line segment in the broken line track, establishing a pseudo-satellite positioning first error equation set according to signals transmitted by a plurality of ground-based pseudo-satellite base stations which are received at the same time; taking the trajectory equation of the trajectory line segment as a motion constraint condition, and adding a motion trajectory horizontal error equation at the approximate coordinate of the pseudo satellite receiver into the first error equation set to obtain a pseudo satellite positioning second error equation set; and iteratively solving the second error equation set to obtain a pseudo-satellite single-point positioning result, and calculating an HDOP value of the second error equation set. According to the method, the parameter position solving precision is improved under the weak geometric configuration, and the availability of the positioning service is enhanced.

Description

Technical Field

[0001] The present invention belongs to the technical field of pseudolite navigation, and particularly relates to a pseudolite navigation and positioning method under a weak geometric configuration. Background Art

[0002] The positioning, navigation and timing (PNT) services provided by the Global Navigation Satellite System (GNSS) have been integrated into various fields of the national economy, national defense construction and social development. However, the GNSS system has an inherent "vulnerability", with weak signals, being easily interfered with, deceived, and having poor penetrability, and cannot benefit the navigation and positioning in underground, underwater and other shielded areas.

[0003] As a navigation means other than GNSS technology, the Pseudolite System can provide positioning services independently or be integrated with GNSS to enhance GNSS positioning. The application fields of pseudolites are constantly expanding with the progress of technology. In actual application scenarios of pseudolites such as urban canyons and long and narrow tunnels, since the positions of ground-based pseudolite base stations are generally fixed, affected by the terrain environment of the base station layout area, a distribution situation of weak geometric configuration is likely to be formed, thus affecting the positioning performance of the pseudolite positioning system.

[0004] The geometric configuration refers to the position distribution of visible satellites of a ground receiver relative to itself at a certain moment, which has an important impact on the positioning accuracy, and the degree of influence can be measured by the Dilution of Precision (DOP). The lower the DOP value, the better the geometric configuration and the higher the positioning accuracy. The so-called "weak geometric configuration" means that the distribution position of satellites in the sky is not ideal, with a large DOP value and low positioning accuracy. It can be subdivided into two types - weak vertical geometric configuration and weak horizontal geometric configuration. The weak vertical and weak horizontal geometric configurations refer to the situation where the Vertical Dilution of Precision (VDOP) and Horizontal Dilution of Precision (HDOP) of user elevation in the service area of the pseudolite positioning system are abnormally large.

[0005] However, the application scenarios where the weak geometric configuration appears are exactly the scenarios where the positioning difficulties most need to be solved. Therefore, aiming at the current problems, there is an urgent need for a pseudolite navigation and positioning method under a weak geometric configuration to obtain guaranteed positioning results and improve the availability of positioning services. Summary of the Invention

[0006] In view of the above analysis, the present invention aims to disclose a pseudo-satellite navigation and positioning method under a weak geometric configuration, which improves the accuracy of parameter position solution under a weak geometric configuration and enhances the availability of positioning services.

[0007] The present invention discloses a pseudo-satellite navigation and positioning method under a weak geometric configuration, comprising:

[0008] Step S1: The movement trajectory of the pseudo-satellite receiver is fixed. Under the condition that the layout of the pseudo-satellite base stations is restricted and presents a weak geometric configuration, after the movement trajectory of the pseudo-satellite receiver is folded into a polyline, pseudo-satellite base stations are arranged along the polyline trajectory.

[0009] Step S2: When the pseudo-satellite receiver moves to a trajectory segment in the polyline trajectory, according to the signals simultaneously received by the pseudo-satellite receiver from multiple ground-based pseudo-satellite base stations arranged on the trajectory segment, a first error equation set for pseudo-satellite positioning is established.

[0010] Step S3: Taking the trajectory equation of the trajectory segment as a movement constraint condition, a horizontal error equation of the movement trajectory at the approximate coordinates of the pseudo-satellite receiver is added to the first error equation set to obtain a second error equation set for pseudo-satellite positioning.

[0011] Step S4: After iteratively solving the second error equation set, a pseudo-satellite single-point positioning result is obtained, and the HDOP value of the second error equation set is calculated to evaluate the horizontal positioning accuracy.

[0012] Further, for a pseudo-satellite receiver moving at a fixed altitude;

[0013] In step S3, taking the trajectory equation of the trajectory segment as a movement constraint condition, a horizontal and altitude error equation of the movement trajectory at the approximate coordinates of the pseudo-satellite receiver is added to the first error equation set to obtain a third error equation set for pseudo-satellite positioning.

[0014] In step S4, after iteratively solving the third error equation set, a pseudo-satellite single-point positioning result is obtained, and the DOP values of the third error equation set are calculated to evaluate the overall, horizontal, and altitude positioning accuracies.

[0015] Further, the first error equation set for pseudo-satellite positioning established according to the signals simultaneously received by the pseudo-satellite receiver from multiple pseudo-satellite base stations is:

[0016]

[0017] where, (N0, E0, U0) are the approximate coordinates of the pseudo-satellite receiver, and (n i , e i , u i ) are the exact coordinates of the i-th pseudo-satellite base station from which the pseudo-satellite receiver can receive the transmitted signal; vi is the residual of the signal of the i-th pseudolite base station received by the pseudolite receiver; i = 1, …, n; n is the number of received pseudolite base stations;

[0018] ρ i,0 is the initial geometric distance based on the initial coordinates;

[0019]

[0020] (dN, dE, dU) is the correction of the initial coordinates of the pseudolite receiver to be solved, dt r is the correction of the initial clock error of the pseudolite receiver to be solved; c is the speed of light, P i is the observation value of the pseudolite receiver for the i-th pseudolite base station; ρ i is the true geometric distance between the pseudolite receiver and the i-th pseudolite base station; t i is the clock error of the i-th pseudolite base station, T i is the tropospheric delay on the signal propagation path of the i-th pseudolite base station.

[0021] Furthermore, adding the horizontal error equation of the motion trajectory to the first error equation set, the second error equation set for pseudolite positioning is obtained as:

[0022]

[0023] where v′ is the horizontal position residual of the pseudolite receiver on the motion trajectory; is the horizontal precise coordinate of the j1-th pseudolite base station on the trajectory segment; is the horizontal precise coordinate of the j2-th pseudolite base station on the trajectory segment; j1 ≠ j2.

[0024] Furthermore, the weight matrix PP of the second error equation set for pseudolite positioning after adding the horizontal error equation of the motion trajectory is:

[0025]

[0026] where P is the weight matrix corresponding to the first error equation set for pseudolite positioning, and P′ is the weight matrix corresponding to the horizontal error equation of the motion trajectory;

[0027]

[0028] is the variance of unit weight, the horizontal variance of the pseudolite receiver.

[0029] Further, for the pseudolite receiver moving at a fixed altitude, the horizontal and altitude error equations of the movement trajectory are added to the first error equation set to obtain the third error equation set for pseudolite positioning as follows:

[0030]

[0031] where U r0 is the altitude of the pseudolite receiver; v″ is the vertical position residual of the pseudolite receiver on the movement trajectory;.

[0032] Further, for the pseudolite receiver with changing elevation, the horizontal and altitude error equations of the movement trajectory are added to the first error equation set to obtain the fourth error equation set for pseudolite positioning as follows:

[0033]

[0034] where v″ is the vertical position residual of the pseudolite receiver on the movement trajectory; is the precise coordinate of the j1-th pseudolite base station on the trajectory line segment; is the precise coordinate of the j2-th pseudolite base station on the trajectory line segment; j1≠j2.

[0035] Further, the weight matrix P of the third error equation set or the fourth error equation set for pseudolite positioning after adding the horizontal and vertical error equations of the movement trajectory is:

[0036]

[0037] where P is the weight matrix corresponding to the first error equation set for pseudolite positioning, and P′ is the weight matrix corresponding to the horizontal error equation of the movement trajectory;

[0038]

[0039] P″ is the weight matrix corresponding to the vertical error equation of the movement trajectory;

[0040]

[0041] where is the variance of unit weight, is the horizontal variance of the pseudolite receiver, is the elevation variance of the pseudolite receiver.

[0042] Further, first deploy pseudolite base stations at the inflection points of the movement trajectory polyline, and then, according to the length of the polyline segment, evenly deploy pseudolite base stations on the polyline segment, so that the shape of the entire trajectory polyline can be fitted with fewer base stations;

[0043] When the number of broken line segments is M, M + 1 pseudo-satellite base stations are used and located at the starting point, inflection points and end point of the whole broken line. Name these pseudo-satellite base stations at the inflection points of the trajectory broken line in sequence as STA m , where m = 0, 1, 2 ··· M, and calculate the distances between adjacent two inflection point pseudo-satellite base stations respectively and record them as DD mm , where mm = 1, 2 ··· M.

[0044] Furthermore, according to the pseudo-satellite base stations set at the inflection points, judge whether the pseudo-satellite receiver has moved from the current broken line segment to the next broken line segment; to update the trajectory constraint equation; including:

[0045] 1) When the pseudo-satellite receiver is moving on the j-th broken line segment, the trajectory constraint equation is obtained by fitting the coordinates of the inflection point pseudo-satellite base station STA j-1 and the pseudo-satellite base station STA j .

[0046] 2) Calculate the planar distances between the pseudo-satellite receiver and the two pseudo-satellite base stations STA j-1 , STA j at both ends of the current broken line segment respectively according to the positioning results of each epoch;

[0047] 3) Judge that the distance between the pseudo-satellite receiver and the pseudo-satellite base station STA j-1 at the start end of the current broken line segment is greater than the planar distance between the two pseudo-satellite base stations at both ends of the current broken line segment, and when the shortest planar distance D MIN of the pseudo-satellite receiver from the current broken line segment in the current epoch is consistent with the planar distance between the pseudo-satellite receiver and the pseudo-satellite base station STA j at the end of the current broken line segment, it is determined that the pseudo-satellite receiver has moved to the next broken line segment;

[0048] 4) Update the trajectory constraint equation, which is obtained by fitting the coordinates of the inflection point pseudo-satellite base station STA j and the pseudo-satellite base station STA j+1 .

[0049] One of the beneficial effects that can be achieved by the present invention is:

[0050] The pseudo-satellite navigation and positioning method disclosed in the present invention under weak geometric configurations aims at the problem that the deployment site conditions of the ground pseudo-satellite positioning system are limited. For example, in areas such as urban canyons and narrow strip spaces, there are weak geometric configurations in the base station layout, and the positioning normal equation is singular or nearly ill-conditioned, resulting in low accuracy and instability in the solution of coordinate parameters. For the first time, it is proposed to add the navigation trajectory as a constraint condition to the pseudo-satellite positioning under weak geometric configurations; the present invention takes into account that the movement of pseudo-satellite users under weak geometric configurations in a restricted space is often not completely random movement, but is restricted by the space environment. The lines in these spaces can be abstracted into several straight lines connected with curves. Therefore, the movement trajectory of the user on the line conforms to the corresponding regular curve to a certain extent. Taking the functional relationship satisfied by this movement trajectory as a constraint condition, the process of user positioning is constrained to achieve the purpose of obtaining a guaranteed positioning result, improving the accuracy of parameter position solution, and enhancing the availability of positioning services. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained according to the provided drawings;

[0052] Figure 1 It is a flowchart of a pseudo-satellite navigation and positioning method under weak geometric configurations provided by an example of the present invention;

[0053] Figure 2 It is a flowchart of another pseudo-satellite navigation and positioning method under weak geometric configurations provided by an example of the present invention;

[0054] Figure 3 It is a pseudo-satellite positioning test line diagram of a weak geometric configuration (tunnel scene) provided by an example of the present invention;

[0055] Figure 4a It is an HDOP example diagram of a weak plane geometric configuration provided by an example of the present invention;

[0056] Figure 4b It is an HDOP example diagram of adding a plane trajectory constraint to a weak plane geometric configuration provided by an example of the present invention;

[0057] Figure 5 It is a plane schematic diagram of the positioning result of a tunnel pseudo-satellite system provided by an example of the present invention;

[0058] Figure 6 It is a PDOP example diagram of adding a three-dimensional straight line trajectory constraint under a weak geometric configuration provided by an example of the present invention;

[0059] Figure 7 3D schematic diagram of the positioning result of the tunnel pseudolite system provided by the embodiment of the present invention. Detailed implementation manners

[0060] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0061] Embodiment 1

[0062] An embodiment of the present invention discloses a pseudolite navigation and positioning method under weak geometric configurations, as Figure 1 shown, including:

[0063] Step S1: The movement trajectory of the pseudolite receiver is fixed. Under the condition that the layout of the pseudolite base stations is restricted and presents a weak geometric configuration, after the movement trajectory of the pseudolite receiver is folded into a broken line, the pseudolite base stations are arranged along the broken line trajectory.

[0064] Step S2: When the pseudolite receiver moves to a trajectory segment in the broken line trajectory, a first error equation set for pseudolite positioning is established according to the signals simultaneously received by the pseudolite receiver from multiple ground-based pseudolite base stations arranged on the trajectory segment.

[0065] Step S3: Taking the trajectory equation of the trajectory segment as a movement constraint condition, a horizontal error equation of the movement trajectory at the approximate coordinates of the pseudolite receiver is added to the first error equation set to obtain a second error equation set for pseudolite positioning.

[0066] Step S4: After iteratively solving the second error equation set, the pseudolite single-point positioning result is obtained, and the HDOP value of the second error equation set is calculated to evaluate the horizontal positioning accuracy.

[0067] The above solution is applicable to application scenarios with no requirement for vertical positioning accuracy. For a pseudolite receiver moving at a fixed height or for application scenarios with a requirement for vertical positioning accuracy, after further optimizing the above solution,

[0068] In step S3, taking the trajectory equation of the trajectory segment as a movement constraint condition, a horizontal and height error equation of the movement trajectory at the approximate coordinates of the pseudolite receiver is added to the first error equation set to obtain a third error equation set for pseudolite positioning.

[0069] In step S4, after iteratively solving the third error equation set, the pseudo-satellite single-point positioning result is obtained, and the DOP values of each of the third error equation set are calculated to evaluate the overall, horizontal, and altitude positioning accuracies.

[0070] The flowchart of the pseudo-satellite navigation and positioning method for a pseudo-satellite receiver moving at a fixed altitude is as Figure 2 shown.

[0071] Specifically, in step S1, the involved navigation application scenarios include urban canyons, narrow strip spaces, and tunnel scenarios, etc.; in these navigation application scenarios, the layout of the ground-based pseudo-satellite base stations is affected by the environment, and it is difficult to arrange them in ideal distribution positions, showing the characteristics of a weak geometric configuration;

[0072] However, in the above application scenarios, the movement trajectories of the pseudo-satellite receivers are also mostly restricted by the environment and can only move on fixed trajectories showing linear or polyline characteristics.

[0073] For example, in the tunnel application scenario, due to the limitation of the tunnel space, the pseudo-satellite base stations can only be arranged in a strip along the tunnel, resulting in a poor geometric configuration in the plane direction and forming a weak planar geometric configuration; at the same time, the height in the tunnel space is limited, and the height difference between the arranged pseudo-satellite base stations is small, which also results in a poor geometric configuration in the elevation direction and forms a weak vertical geometric configuration.

[0074] However, the movement trajectories of the vehicles or other devices to be positioned in the tunnel are also restricted by the tunnel and are limited within the tunnel space, moving along the tunnel direction.

[0075] Based on the characteristics of the above navigation application scenarios, in this embodiment, on the premise of obtaining the movement trajectory of the pseudo-satellite receiver in advance, after linearizing the movement trajectory of the pseudo-satellite receiver, the ground-based pseudo-satellite base stations are arranged along the polyline trajectory of the satellite receiver.

[0076] After linearizing the movement trajectory, on each linear trajectory segment, multiple pseudo-satellite base stations with the same orientation are correspondingly arranged;

[0077] Moreover, the coordinates of the pseudo-satellite base stations are accurately measured in advance, and time synchronization is performed between the pseudo-satellite base stations to reduce the clock difference between the pseudo-satellites.

[0078] Specifically, in step S2, when the pseudo-satellite receiver moves to a trajectory segment in the polyline trajectory, it can simultaneously receive multiple pseudo-satellite base stations arranged on this trajectory segment;

[0079] After linearization at the approximate coordinates (N0, E0, U0) of the pseudo-satellite receiver, the pseudo-satellite positioning error equation can be written as:

[0080]

[0081] where \(v\) i is the residual of the \(i\)-th pseudolite base station signal received by the pseudolite receiver, \((n i , e i , u i ) is the exact coordinate of the \(i\)-th pseudolite base station from which the pseudolite receiver can receive the transmitted signal; \(i = 1,\ldots,n\); \(n\) is the number of received pseudolite base stations;

[0082] \(\rho\) i,0 is the initial geometric distance based on the initial coordinates;

[0083]

[0084] (\(dN\), \(dE\), \(dU\)) is the correction of the initial coordinates of the pseudolite receiver to be solved, \(dt r is the correction of the initial clock error of the pseudolite receiver to be solved; \(c\) is the speed of light, \(P i is the observation value of the \(i\)-th pseudolite base station by the pseudolite receiver; \(\rho i is the true geometric distance between the pseudolite receiver and the \(i\)-th pseudolite base station; \(t i is the clock error of the \(i\)-th pseudolite base station, \(T i is the tropospheric delay on the signal propagation path of the \(i\)-th pseudolite base station; after precise time synchronization is performed between pseudolite base stations, \(t i can be ignored, and under the condition that the height of the pseudolite base station is limited, the tropospheric delay \(T i of the base station propagation can be ignored.

[0085] Based on the signals transmitted by multiple pseudolite base stations simultaneously received by the pseudolite receiver, the first pseudolite positioning error equation set is established as:

[0086]

[0087] Writing the first pseudolite positioning error equation set in matrix form:

[0088] \(V = BX - L\);

[0089] where

[0090] \(V=[v_1\ldots v i \ldots v n T ,

[0091] \(X = [dN\ dE\ dU\ c\cdot dt r T ,

[0092]

[0093] The design matrix \(B\) is:​​

[0094]

[0095] Using the weight matrix P corresponding to matrix B, the optimal estimate of parameter X is:

[0096] X = (B T PB) -1 B T PL

[0097] The coordinates of the pseudolite receiver are:

[0098]

[0099] Take the obtained coordinates as the new initial coordinates and perform iterative calculation until the parameters converge.

[0100] The accuracy of pseudolite positioning depends partly on the strength of the geometric figure between the user and the pseudolites. In single-point positioning, the Dilution of Precision (DOP) is commonly used to quantitatively reflect the strength of the geometric figure. The DOP is obtained from the inverse matrix of the normal equation coefficient matrix, and the inverse matrix can be expressed as:

[0101]

[0102] The definitions of the three-dimensional Position Dilution of Precision (PDOP), the Horizontal Dilution of Precision (HDOP), and the Vertical Dilution of Precision (VDOP) are:

[0103]

[0104] For the weak horizontal geometric configuration of the pseudolite base station in the tunnel application scenario, in step S3 of a solution in this embodiment, based on the application condition that the pseudolite base station and the user are not on the same horizontal plane, the horizontal trajectory error equation of the trajectory segment is used as a motion constraint and added to the first error equation set.

[0105] In the process of establishing the horizontal trajectory error equation of the motion trajectory at the approximate coordinates of the pseudolite receiver, it includes:

[0106] 1) Select two ground-based pseudolite base stations arranged on the trajectory segment. Considering the planar relationship between the pseudolite base stations, among them, the horizontal precise coordinates of the j1-th pseudolite base station on the trajectory segment are The horizontal precise coordinates of the j2-th pseudolite base station on the trajectory segment are

[0107] Then the horizontal straight-line equation passing through the two pseudolite base stations is:

[0108]

[0109] Preferably, the two pseudolite base stations for establishing the plane straight-line equation are two pseudolite base stations arranged at both ends of the straight-line segment on the tunnel plane; that is, the j1th pseudolite base station is the first pseudolite base station on the trajectory segment; the j2th pseudolite base station is the last pseudolite base station on the trajectory segment.

[0110] 2) Write the above plane straight-line equation in the form of the horizontal error equation of the motion trajectory at the approximate plane coordinates (N0, E0) of the pseudolite receiver as:

[0111]

[0112] v′ is the horizontal position residual of the pseudolite receiver on the motion trajectory;

[0113] Its corresponding weight P′ is:

[0114]

[0115] is the variance of unit weight, the horizontal variance of the pseudolite receiver.

[0116] 3) Add the horizontal error equation of the motion trajectory to the first error equation set to obtain the second error equation set for pseudolite positioning as:

[0117]

[0118] The weight matrix corresponding to the first error equation set for pseudolite positioning is P, and the weight matrix PP of the second error equation set for pseudolite positioning after adding the constraint equation is:

[0119]

[0120] where P is the weight matrix corresponding to the first error equation set for pseudolite positioning, and P′ is the weight matrix corresponding to the horizontal error equation of the motion trajectory.

[0121] Specifically, in step S4, using the least squares method, iteratively solve the two error equation sets to obtain the pseudolite single-point positioning result after adding the constraint equation. At the same time, the HDOP value after adding the constraint equation can also be calculated to evaluate the overall and horizontal positioning accuracy.

[0122] In a more preferred embodiment, for a pseudolite receiver moving at a fixed height; in step S3 of another embodiment, the horizontal error equation of the trajectory segment is added as a motion constraint to the first error equation set, and the height error equation is also added to the first error equation set to obtain a third error equation set for pseudolite positioning;

[0123] Specifically, for the height error equation at the approximate coordinates of the pseudolite receiver, the elevation of the pseudolite receiver is assumed to be U r0 and its variance is The equation satisfied by the elevation of the pseudolite receiver can be written as:

[0124] U = U r0

[0125] Written in the form of an error equation as:

[0126] v″ = 1·dU - U r0

[0127] v″ is the vertical position residual of the pseudolite receiver on the motion trajectory;

[0128] Its corresponding weight P″ is:

[0129]

[0130] where is the unit weight variance.

[0131] Then, by adding the horizontal and height error equations of the motion trajectory to the first error equation set, the third error equation set for pseudolite positioning obtained is:

[0132]

[0133] The weight matrix PP of the third error equation set for pseudolite positioning after adding the horizontal and vertical error equations of the motion trajectory is:

[0134]

[0135] where P is the weight matrix corresponding to the first error equation set for pseudolite positioning, P′ is the weight matrix corresponding to the horizontal error equation of the motion trajectory; P″ is the weight matrix corresponding to the vertical error equation of the motion trajectory.

[0136] Specifically, in step S4, using the least squares method, after iteratively solving the two error equation sets, the pseudolite single-point positioning result after adding the constraint equation can be obtained. At the same time, the DOP values after adding the constraint equation can also be calculated to evaluate the overall, horizontal, and height positioning accuracies.

[0137] More preferably, in this embodiment, after arranging the pseudolite base stations at the inflection points of the movement trajectory polyline first, and then arranging the pseudolite base stations evenly on the polyline according to the length of the polyline segment, the shape of the entire trajectory polyline can be fitted with fewer base stations;

[0138] When the number of polyline segments is M, M + 1 pseudolite base stations are used at the starting point, inflection point and end point of the entire polyline. The pseudolite base stations at the inflection points of the trajectory polyline are named STA m in sequence, where m = 0, 1, 2 ··· M, and the distances between adjacent two inflection point pseudolite base stations are calculated and denoted as DD mm , where mm = 1, 2 ··· M.

[0139] In this embodiment, it is also determined whether the pseudolite receiver moves from the current polyline segment to the next polyline segment according to the pseudolite base stations at the inflection points; so as to update the trajectory constraint equation;

[0140] Specifically,

[0141] 1) When the pseudolite receiver moves on the j-th polyline segment, the trajectory constraint equation is fitted by the coordinates of the inflection point pseudolite base station STA j-1 and the pseudolite base station STA j ;

[0142] 2) According to the positioning results of each epoch (generally 0.1 second), the planar distances between the pseudolite receiver and the two pseudolite base stations (STA j-1 and STA j ) at both ends of the polyline segment are calculated respectively;

[0143] 3) It is judged that the distance between the pseudolite receiver and the pseudolite base station STA j-1 at the head end of the polyline segment is greater than the planar distance between the two pseudolite base stations (STA j-1 and STA j ) at both ends of the polyline segment, and when the shortest planar distance D MIN of the pseudolite receiver from the current polyline segment in the current epoch is consistent with the planar distance between the pseudolite receiver and the pseudolite base station STA j at the end of the polyline segment, it is determined that the pseudolite receiver moves to the next polyline segment;

[0144] 4) Update the trajectory constraint equation, which is fitted by the coordinates of the inflection point pseudolite base station STA j and the pseudolite base station STA j+1 .

[0145] In a more preferred solution, it can also be performed for the pseudolite receiver with elevation change; in the process of establishing the three-dimensional movement trajectory at the approximate coordinates of the pseudolite receiver, it includes:

[0146] 1) Select two ground-based pseudolite base stations deployed on the trajectory segment. Considering the three-dimensional position relationship between the pseudolite base stations, among them, the horizontal precise coordinates of the j1-th pseudolite base station on the trajectory segment are The horizontal precise coordinates of the j2-th pseudolite base station on the trajectory segment are

[0147] Then the straight-line equation passing through the two pseudolite base stations is:

[0148]

[0149] Preferably, the two pseudolite base stations for establishing the straight-line equation are two pseudolite base stations deployed at both ends of the straight segment of the tunnel; that is, the j1-th pseudolite base station is the first pseudolite base station on the trajectory segment; the j2-th pseudolite base station is the last pseudolite base station on the trajectory segment.

[0150] 2) Substitute the above straight-line equation at the approximate three-dimensional coordinates (N0, E0, U0) of the pseudolite receiver to obtain the horizontal and vertical error equations of the motion trajectory as:

[0151]

[0152] v′ is the horizontal position residual of the pseudolite receiver on the motion trajectory; v″ is the vertical position residual of the pseudolite receiver on the motion trajectory;

[0153] Its corresponding weight is Among them, is the unit weight variance, The horizontal variance of the pseudolite receiver; is the elevation variance of the pseudolite receiver.

[0154] 3) Add the horizontal and error equations of the motion trajectory to the first error equation set to obtain the fourth error equation set for pseudolite positioning as:

[0155] Obtain the constraint equation for establishing the coordinates of the pseudolite receiver based on the projection point coordinates of these 2 pseudolite base stations projected onto the user's motion trajectory to obtain a linear trajectory, and add this constraint equation to the first error equation set. At this time, the fourth error equation set for pseudolite positioning is:

[0156]

[0157] The weight matrix PP of the third error equation set for pseudolite positioning after adding the horizontal and vertical error equations of the motion trajectory is:

[0158]

[0159] Among them, \(P\) is the weight matrix corresponding to the first error equation system of pseudolite positioning, \(P'\) is the weight matrix corresponding to the horizontal error equation of the motion trajectory; \(P''\) is the weight matrix corresponding to the vertical error equation of the motion trajectory.

[0160] To sum up, the core of the present invention lies in the improvement of the existing pseudolite positioning model. For the traditional pseudolite positioning model, accurate positioning results can be obtained when the geometric configuration of the pseudolite base stations is good. However, in some scenarios where the pseudolite base stations have a weak geometric configuration, when only using this positioning model, the positioning normal equation will be singular or nearly ill-conditioned, and it is difficult to obtain accurate positioning results. Therefore, we consider adding more information to the positioning model to make the positioning model more robust. We consider that the scenarios where the pseudolite base stations have a weak geometric configuration are generally restricted spaces, and in restricted spaces, the motion trajectory of the user is constrained by the space and to a certain extent conforms to the corresponding regular curve. In this case, taking the motion trajectory of the user as a constraint condition, a mathematical function model and a stochastic model based on the trajectory constraint condition are established, so as to improve the condition number of the normal equation in parameter solving and improve the accuracy of parameter position solving. This improvement is effective.

[0161] Embodiment 2

[0162] In this embodiment, taking the tunnel scenario as an example, the effect of the pseudolite navigation and positioning method under weak geometric configuration is verified;

[0163] As Figure 3 shown, it is the pseudolite positioning test line under weak geometric configuration (tunnel scenario) in the embodiment. As shown in Figure 4, it is the horizontal dilution of precision HDOP of the test vehicle on the test line before and after adding the straight-line trajectory constraint in this tunnel scenario.

[0164] In Figure 4, Figure 4a is the HDOP value of the test vehicle on the test line without adding the straight-line trajectory constraint, and most areas exceed 40;

[0165] In Figure 4, Figure 4b is the HDOP value of the test vehicle on the test line after adding the straight-line trajectory constraint, and all areas are lower than 3;

[0166] By Figure 4a and Figure 4b comparison, it can be seen that the scheme of this embodiment greatly reduces the HDOP value by adding the straight-line trajectory constraint.

[0167] Figure 5 shows the positioning result diagram of the test vehicle after adding the straight-line trajectory constraint in this tunnel scenario. It can be seen from the figure that the positioning results of the test vehicle are basically on a line segment, and the degree of coincidence with the actual path in the tunnel is relatively good.

[0168] Figure 6 The PDOP after adding the three-dimensional straight-line trajectory constraint in the weak geometric configuration; it is below 3.5 in all regions;

[0169] Figure 7 It is a schematic diagram of the positioning result of the tunnel pseudolite system. The positioning result of the test vehicle is basically on a three-dimensional line segment, and the degree of coincidence with the actual path in the tunnel is relatively good.

[0170] As mentioned above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A pseudo-satellite navigation positioning method under weak geometric configuration, characterized in that: include: Step S1, the pseudo-satellite receiver motion trajectory is fixed, and under the condition that the pseudo-satellite base station deployment is limited and presents a weak geometric configuration, the pseudo-satellite receiver motion trajectory is folded, and the pseudo-satellite base stations are deployed along the folded trajectory; Step S2, when the pseudolite receiver moves to a track segment in the broken line track, a first set of pseudolite positioning error equations is established based on signals transmitted by a plurality of ground-based pseudolite base stations arranged on the track segment and received simultaneously by the pseudolite receiver; Step S3, taking the trajectory equation of the trajectory segment as a motion constraint condition, adding the horizontal error equation of the motion trajectory at the approximate coordinates of the pseudolite receiver to the first error equation group, and obtaining a second error equation group for pseudolite positioning; Step S4, after iteratively solving the second error equation group, the pseudolite single point positioning result is obtained, and the HDOP value of the second error equation group is calculated to evaluate the horizontal positioning accuracy.

2. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 1, characterized in that: For pseudo-satellite receivers moving at a fixed altitude; In step S3, the trajectory equation of the trajectory segment is used as a motion constraint condition, and the horizontal and height error equations of the motion trajectory at the approximate coordinates of the pseudolite receiver are added to the first error equation group to obtain a third error equation group for pseudolite positioning; In step S4, the pseudolite single point positioning result is obtained by iteratively solving the third error equation group, and each DOP value of the third error equation group is calculated to evaluate the overall, horizontal and altitude positioning accuracy.

3. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 1 or 2, characterized in that: According to the signals transmitted by multiple pseudo-satellite base stations received simultaneously by the pseudo-satellite receiver, the first error equation group of pseudo-satellite positioning is established as follows: Among them, (N0, E0, U0) are the approximate coordinates of the pseudo-satellite receiver, (n i , e i ,u i ) is the precise coordinates of the ith pseudo-satellite base station whose transmission signal can be received by the pseudo-satellite receiver; v i is the residual of the received signal of the ith pseudo-satellite base station; i = 1,…,n; n is the number of pseudo-satellite base stations received; ρ i,0 is the initial value of geometric distance based on the initial value of coordinates; (dN, dE, dU) are the initial correction values ​​of the pseudo-satellite receiver coordinates to be solved, dt r is the initial value correction of the pseudo-satellite receiver clock error to be solved; c is the speed of light, P i is the observation value of the pseudo-satellite receiver to the i-th pseudo-satellite base station; ρ i is the true geometric distance between the pseudo-satellite receiver and the ith pseudo-satellite base station; t i is the clock error of the ith pseudo-satellite base station, T i is the tropospheric delay on the signal propagation path of the i-th pseudo-satellite base station.

4. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 3, characterized in that: Adding the horizontal error equation of the motion trajectory to the first error equation group, the second error equation group of pseudolite positioning is obtained: Among them, v ′ is the horizontal position residual of the pseudo-satellite receiver on the motion trajectory; is the precise horizontal coordinate of the j1th pseudo-satellite base station on the trajectory segment; is the precise horizontal coordinate of the j2th pseudo-satellite base station on the trajectory segment; j1≠j2.

5. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 4, characterized in that: The weight matrix PP of the second error equation group of pseudo-satellite positioning after adding the horizontal error equation of the motion trajectory is: Among them, P is the weight matrix corresponding to the first error equation group of pseudo-satellite positioning, P ′ is the weight matrix corresponding to the horizontal error equation of the motion trajectory; is the unit weight variance, Horizontal variance of the pseudolite receiver.

6. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 4, characterized in that: For a pseudolite receiver moving at a fixed altitude, the horizontal and altitude error equations of the motion trajectory are added to the first error equation group, and the third error equation group for pseudolite positioning is obtained as follows: Among them, U r0 is the height of the pseudo-satellite receiver; v″ is the vertical position residual of the pseudo-satellite receiver on the motion trajectory.

7. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 4, characterized in that: For pseudolite receivers with varying elevations, the horizontal and height error equations of the motion trajectory are added to the first error equation group, and the fourth error equation group for pseudolite positioning is obtained as follows: Where v″ is the vertical position residual of the pseudo-satellite receiver on the motion trajectory; is the precise coordinate of the j1th pseudo-satellite base station on the trajectory segment; are the precise coordinates of the j2th pseudo-satellite base station on the trajectory segment; j1≠j2.

8. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 6 or 7, characterized in that: The weight matrix PP of the third error equation group or the fourth error equation group of pseudo-satellite positioning after adding the horizontal and vertical error equations of the motion trajectory is: Among them, P is the weight matrix corresponding to the first error equation group of pseudo-satellite positioning, P ′ is the weight matrix corresponding to the horizontal error equation of the motion trajectory; P″ is the weight matrix corresponding to the vertical error equation of the motion trajectory; in, is the unit weight variance, Horizontal variance of pseudolite receiver, is the elevation variance of the pseudo-satellite receiver.

9. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 1 or 2, characterized in that: First, pseudo-satellite base stations are arranged at the inflection points of the motion trajectory polyline, and then pseudo-satellite base stations are evenly arranged on the polyline segment according to the length of the polyline segment, so that the shape of the entire trajectory polyline can be fitted with fewer base stations; When the number of broken line segments is M, use M+1 pseudo-satellite base stations located at the starting point, turning point and end point of the entire broken line, and name these pseudo-satellite base stations at the turning points of the trajectory broken line as STA in sequence. m , where m = 0, 1, 2···M, and the distance between two adjacent inflection point pseudo-satellite base stations is calculated and recorded as DD mm , where mm=1,2···M.

10. The pseudo-satellite navigation and positioning method under weak geometry configuration according to claim 9, characterized in that: According to the pseudo-satellite base station set at the inflection point, it is determined whether the pseudo-satellite receiver moves from the current broken line segment to the next broken line segment; To update the trajectory constraint equations; including: 1) When the pseudo-satellite receiver moves on the jth broken line segment, the trajectory constraint equation is determined by the inflection point pseudo-satellite base station STA j-1 Pseudo-satellite base station STA j The coordinates of are fitted; 2) According to the positioning results of each epoch, the distance between the pseudo-satellite receiver and the two pseudo-satellite base stations STA at both ends of the broken line segment are calculated respectively. j-1 , STA j The plane distance between 3) Determine the pseudo-satellite receiver and the pseudo-satellite base station STA at the head end of the broken line segment j-1 The distance between the two pseudo-satellite base stations at both ends of the broken line segment is greater than the plane distance between the two pseudo-satellite base stations at both ends of the broken line segment, and the shortest plane distance D between the pseudo-satellite receiver at the current epoch and the current broken line segment is MIN The pseudo-satellite receiver and the pseudo-satellite base station STA at the end of the broken line segment j When the plane distances between the two segments are consistent, it is determined that the pseudo-satellite receiver moves to the next broken line segment; 4) Update the trajectory constraint equation, by the inflection point pseudo-satellite base station STA j Pseudo-satellite base station STA j+1 The coordinates of are fitted.

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