CN105718736A - Novel generalized integrated positioning principle, mathematical model and solving method - Google Patents

Abstract

The invention discloses a novel generalized integrated positioning principle, a mathematical model and a solving method. According to the novel generalized integrated positioning principle, the mathematical model and the solving method, the conventional navigation positioning determination solving concept is broken through; on the basis of a fuzzy and statistical uncertain concept, parameter combination, equation solving, error correction and data fusion are carried out; a method for successively performing cross fusion and integration on an absolute measured value and a relative measured value and successively checking correction errors is provided. A generalized integrated positioning mathematical model and a solving algorithm are constructed according to the generalized integrated positioning principle, so that soft acting force of the mathematical and the algorithm is fully exerted, and the performance of a navigation positioning parameter and a state solution and the navigation positioning quality are greatly improved.

Description

Novel generalized integrated positioning principle, mathematical model and solving method

Technical Field

The invention relates to a novel generalized integrated positioning principle, a mathematical model and a solving method, belonging to the technical field of satellite navigation positioning.

Background

Currently, all satellite navigation positioning systems realize positioning by adopting a spherical surface intersection triangular positioning principle which takes the length of a measured pseudo range from a satellite to a terminal user as a radius in a geocentric geostationary coordinate system. In this positioning mode, the positioning accuracy depends directly on the accuracy of the pseudorange measurements, and in fact there are other measurements, but the positioning principle does not play a role of all measurements in the positioning result. In addition, in the dead reckoning positioning process, measurement values such as speed or step distance plus angle are applied, and the measurement accuracy of the measurement values of the speed or step distance is still relatively accurate, but the error of the positioning principle is accumulated and increased along with time, which is called as an accumulated error, and finally influences the positioning track accuracy. The accumulated error can be corrected by using the absolute measurement value, and the method for correcting the accumulated error aims to exert the advantages and the advantages of the absolute measurement value and the relative measurement value respectively to make up for the short swing of the absolute measurement value and the relative measurement value, but because the accuracy of the absolute positioning measurement value is not high enough generally, the correction effect is achieved only after the accumulated error of the relative positioning is large to a certain degree, and therefore the accuracy of the traditional combined positioning method is not high.

For example, in month 6 of 2015, the United States Patent and Trademark Office (USPTO) granted apple corporation a patent that automatically switches from one positioning subsystem to another using positioning, communication, and other sensors to gather information. This patent is entitled "location switching management" with patent number 9066207. Apple filed this patent at 12 months 2012, patented by lukasm.

The iPhone can seamlessly navigate the automobile, and navigate the user outdoors and indoors through the GPS and the indoor wireless gateway. In actual use, the first sensor subsystem is used by the user device. For example, an iPhone can collect outdoor location information via GPS satellite signals. This is not much different from the navigation and instant location information provided by most current map services. When the user enters a building and the device cannot acquire the GPS signal, the device can automatically detect indoor wireless access hotspots, and the RF signals of the hotspots can measure position data. In addition, when the iPhone detects the change of the air pressure, the navigation mode can be automatically changed. Information from the device gyroscope, hygrometer, microphone, acceleration sensor, and light sensor can also be used to determine the position of the iPhone. More importantly, the second subsystem of the location subsystem call can provide more accurate location. Although not mentioned in the patent, apple iBeacons micropositioning technology can also be integrated into the system. Bluetooth-based iBeacons can replace wireless hotspots in patents, providing more accurate location data, such as hallways, rooms, walls, offices, and other locations.

After a plurality of positioning devices are arranged in a building to form an indoor positioning system, the mobile phone can receive signals sent by the system to determine the position of the mobile phone. This suite of positioning systems is called the HAIP. It adopts the principle of triangulation location and its location method. Because it uses the same 2.4GHz frequency as Bluetooth and WiFi, the existing mobile phone does not need to add extra antenna and other devices, and the user can realize indoor positioning navigation by only installing a newly developed positioning software on the mobile phone. Such a short-range positioning signal can control power consumption to a very low level, which requires only one-thirtieth of the power consumption required for receiving a normal GPS signal. The indoor positioning uses a Bluetooth module of a mobile phone, but needs to deploy a Bluetooth base station, and can reach the sub-meter positioning precision to the maximum. However, because bluetooth base stations are not popular, it is necessary to invest in base station construction, and the cost for forming indoor positioning is also high.

From the two application examples, it can be seen that the indoor positioning has not broken through the traditional GPS triangulation positioning principle and the traditional positioning method.

Disclosure of Invention

In order to solve the technical problems, the invention provides a novel generalized integrated positioning principle, a mathematical model and a solving method. The invention breaks through the concept of traditional navigation positioning determination solution, and carries out parameter combination, equation solution, error correction and data fusion on the basis of fuzzy and statistical uncertain concepts; the invention also breaks through the traditional method that the absolute positioning solution and the relative positioning solution exist independently and operate independently, and provides the method that the absolute measurement value and the relative measurement value are successively hybridized and integrated in a coordinate system, and the errors are successively corrected and corrected mutually, so that the indoor and outdoor seamless navigation positioning precision is greatly improved.

The invention provides a state value obtained by directly solving an absolute positioning state equation, or an absolute measurement value (hereinafter, simply referred to as an absolute measurement value) obtained directly and a low-order state value obtained by solving the low-order state equation, or a measurement value (hereinafter, simply referred to as a relative measurement value) obtained by relative measurement, and converts the state values and the measurement value into the same coordinate system, and realizes navigation positioning and obtaining an optimized solution by successive hybridization integration and successive mutual error correction on the corresponding state variable level. The invention establishes the mathematical model and the solving algorithm of the generalized integrated positioning according to the generalized integrated navigation positioning principle, and fully exerts the soft acting force of the mathematical model and the algorithm, thereby greatly improving the performance of navigation positioning parameters and state solutions and the quality of navigation positioning.

The novel principle of generalized integrated positioning, the mathematical model and the solving method comprise the following steps:

s100, establishing a mathematical model fusing an optimization integration positioning navigation principle;

step S101, resolving coordinates are unified in the same coordinate system;

step S102, performing fine pre-processing treatment on the measured value;

step S103, establishing a plurality of groups of state quantity solving relational expressions by using various types of finely processed measured values;

step S104, fusing a plurality of groups of state quantity solving relational expressions and integrating the state quantity solving relational expressions into a generalized state quantity solving equation set;

step S105, solving a solving equation set of the generalized state quantity by using a generalized fusion optimization algorithm;

step S106, fine post-processing treatment of the state quantity solution value.

In the step S100, a generalized fusion optimization integrated positioning and navigation principle and a mathematical model are established, and then the mathematical model is solved. Now set x_sj,y_sj,z_sjFor satellite position, the solution set of acquired generalized navigational fixes is (x)_i,y_i,z_i) And i is 1,2,3 Λ n, the trajectory solution must satisfy the following condition:

$\{\begin{array}{c}{f}_1(x_i,y_i,z_i,x_{sj},y_{sj},z_{sj})={\mathrm{\ρ}}_j+{\mathrm{c\Δt}}_{ui}(j=1,\mathrm{2.......}m)\\ s.t.g_1(x_i,y_i,z_i)={\mathrm{\η}}_l(l=1,2,\mathrm{.....}k)\\ x_i=f_2\left({\mathrm{\Δx}}_i\right)\\ y_i=f_3\left({\mathrm{\Δy}}_i\right)\\ z_i=f_4\left({\mathrm{\Δz}}_i\right)\\ s.t.g_2({\mathrm{\Δx}}_i,{\mathrm{\Δy}}_i,{\mathrm{\Δz}}_i)={\mathrm{\α}}_i\\ i=1,2,\mathrm{......}n\end{array}---\left(1\right)$

the generalized positioning mathematical model (1) consists of two parts, wherein the upper part of the mathematical model (1) is an absolute positioning solving part, and n is an epoch number; f. of₁(x_i,y_i,z_i,x_sj,y_sj,z_sj) Is a relation of a measuring function; g₁(x_i,y_i,z_i) As a relation of a constraint function, p_j，η_lAre all absolute measurements; c is the speed of light; Δ t_uiThe deviation of the time of the receiver terminal and the reference time is shown, and m is the number of signal sources; k is the number of constraint equations.

The lower part of the mathematical model (1) is the recursion solving part of the relative positioning measurements, where f₂(Δx_i),f₃(Δy_i),f₄(Δz_i) Are recursion relational expressions respectively; g₂(Δx_i,Δy_i,Δz_i) As a function of a relation between relative measured quantitiesNumerical expression, Δ x_i,Δy_i,Δz_iFor the relative measurement, the relative measurement can be a relative change of the state variable, or can be a derivative or derivative of the state variable α_iFor navigation of the heading angle, it is characterized by the absolute deviation angle of the heading from true or magnetic north, where the subscript i represents the time series (epoch) variables, the subscript j represents the satellite series variables, k is the number of constraint equations and also the number of constraint variables, t represents time, and Λ represents the number of erasures.

In step S101, coordinate systems when the fusion equation group is solved are unified in the same coordinate system, and the method includes: the generalized fusion optimization integrated positioning navigation principle mathematical model is established in a geocentric geostationary coordinate system and can also be established in a station center coordinate system or a building coordinate system; but one coordinate system must be selected finally, and combined modeling and solving are carried out in a unified coordinate system.

In step S102, in order to make the measured value more accurate, a fine preprocessing process of the measured value is performed, characterized in that: after the measured value is subjected to fine processing, the precision of the measured value can be improved, a processing tool adopts a data processing method of a generalized fusion calculation method, and the adopted data processing technology comprises the following steps: grinding process, fusion process, filtering process and smoothing process.

In step S103, a plurality of sets of state quantity solving relations are established by using various types of measured values after fine processing, for example; listing a relation between speed and acceleration and a position quantity by utilizing a kinematics principle; the relationship between the two velocity components and the heading angle can also be listed in the x-y plane:

$\frac{{\mathrm{\Δx}}_i}{{\mathrm{\Δy}}_i}={\mathrm{tan\α}}_i---\left(2\right)$

in step S104, the state quantity solution relational expression is fused and integrated into a generalized state quantity solution equation set, i.e. a trajectory solution set (x) of positioning navigation is solved_i,y_i,z_i) I is 1,2,3 Λ n so as to satisfy equation (1).

In the formula (1), in step S105, a system of solution equations of the generalized state quantities is solved by a generalized fusion optimization algorithm; the successive integration fusion mutual calibration solving method is characterized by comprising the following steps: the absolute measurements in the state variables are successively combined with state estimates, obtained by recursion of the relative measurements, in each epoch to obtain the optimal estimate.

In step S106, a fine post-processing process is performed on the obtained optimum estimated value, characterized in that: and performing fine post-processing treatment on the optimal estimated value obtained by solving by adopting a generalized filtering method and the like, namely smoothing, filtering, predicting and forecasting.

The novel generalized integrated positioning principle, the mathematical model and the solving method have the following advantages:

(1) the internal relation of various measurement quantities can be exerted, and the positioning precision is improved;

(2) in the successive mixed interaction calibration and fusion process, not only the high-precision relative measurement value is successively fully utilized, but also the absolute measurement value is successively utilized for calibration. The method of long-time accumulation and re-correction in the original dead reckoning algorithm is divided into every epoch for implementation, so that the correction is uniform and successive, and the improvement of the data sequence precision of the optimal estimation value is guaranteed;

(3) the new positioning solving method formed by the invention can be widely applied to the existing navigation positioning system, can solve the technical problems existing in the field of navigation positioning at present, and can solve the problem of difficulty in indoor and outdoor seamless navigation, so that the method has higher application value and practical value.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. Embodiments of the present invention employ extrapolation only at ground level, which also corresponds to vehicle driving conditions. Although embodiments of the present invention provide examples of parameters that include particular values, the parameters need not be exactly equal to the corresponding values, but can be approximated to the corresponding values within acceptable error tolerances or design constraints. The invention discloses a novel generalized integrated positioning principle, a mathematical model and a solving method, which comprise the following steps:

step S100, establishing a generalized integrated positioning principle mathematical model, and solving a track solution (x) of navigation positioning_i,y_i,z_i) 1,2,3 Λ n, x_sj,y_sj,z_sjFor the satellite position, it is made to satisfy:

$\left\{\begin{array}{c}\sqrt{{(x_i-x_{sj})}^2+{(y_i-y_{sj})}^2+{(z_i-z_{sj})}^2}={\mathrm{\ρ}}_j+{\mathrm{c\Δt}}_{ui},j=1,\mathrm{2.......}m\\ \left\{\begin{array}{c}{x}_i=x_{(i-1)}+{\mathrm{\Δx}}_i\\ y_i=y_{(i-1)}+{\mathrm{\Δy}}_i\\ \frac{{\mathrm{\Δx}}_i}{{\mathrm{\Δy}}_i}={\mathrm{tan\α}}_i|x_0=x_{bg},y_0=y_{bg},h_0=f\left(z_{bg}\right)\end{array}\right.\end{array}\right.---\left(3\right)$

wherein x is₀＝x_bg,y₀＝y_bg,h₀＝f(z_bg) Indicating the initial conditions, the subscript bg is shown as the initial value and the subscript 0 indicates the initial point of x, y, z.

The mathematical model (1) consists of two parts; the upper part of the mathematical model (1) is an absolute positioning solving part, wherein n is an epoch number;is a relation of a measuring function; rho_jIs an absolute measurement; c is the speed of light; Δ t_uiM is the time of the receiver terminal offset from the base time, and m is the number of signal sources. The lower part of the mathematical model (1) is the relative positioning recursion solving part, where Δ x_i,Δy_iCan be the relative change of the state variable for relative measurement α_iRepresenting the navigation advancing direction angle by using the absolute deviation angle between the advancing direction and the positive north or the magnetic north direction; | x₀＝x_bg,y₀＝y_bg,h₀＝f(z_bg) The initial values of the plane coordinate position and the elevation coordinate position are obtained. In the above formula, h is represented as an elevation variable, h₀Expressed as the starting variable of the elevation variable.

And step S101, the mathematical model (3) can be established in a geocentric coordinate system, a station center coordinate system or a building coordinate system. If the upper part and the lower part of the mathematical model (3) are respectively established in different coordinate systems, coordinate conversion is carried out, and the two parts are unified to the same coordinate system for resolving; or after the solution is completed in different coordinate systems, the data is converted into one coordinate system for fusion integration during combination.

Step S102, in order to make the measured value more accurate, carry on the fine pre-processing treatment of the measured value, characterized by that: when the measured values are subjected to fine processing. The processing tool adopts a generalized fusion resolving method, and the process comprises the following steps: grinding process, fusion process, filtering process and smoothing process. For example: integrated fusion of pseudoranges and carrier phase differences, instead of carrier phase-smoothed pseudoranges, i.e.

Solving the following steps: ${\widehat{\mathrm{\ρ}}}_i,i=1,2,\mathrm{......},n$ make it

Wherein,the optimal combined pseudo range is obtained; rho_iThe pseudo range is an absolute measurement value;integrating the mutually calibrated pseudorange pre-optimum recursions for hybridization with the carrier phase difference, ank_iλ is the carrier wavelength for the combining weight coefficient. WhereinIs the value of the change in carrier phase between epochs. In step S103, a plurality of sets of state quantity solving relations are established by using various types of measured values after fine processing, for example; listing the speed v in x and y directions of a time sequence i by using the kinematics principle_xi,v_yiAcceleration of a_xi,a_yiAmount of positionPosition values, a, in time series i or i-1, respectively_xi,a_yiThe middle subscript x, y represents the direction, i represents the time epoch sequence variable:

wherein Δ t is a time interval; two step components Δ x can also be listed in the x-y plane_i，Δy_iAngle of travel α_iThe relation between:

$\frac{{\mathrm{\Δx}}_i}{{\mathrm{\Δy}}_i}={\mathrm{tan\α}}_i---\left(6\right)$

step S104, integrating the state quantity solving relational expression into a generalized state quantity solving equation set, establishing a generalized integrated positioning principle mathematical model, and solving a track solution (x) of navigation positioning_i,y_i,z_i) I is 1,2,3 Λ n, such that it satisfies:

$\left\{\begin{array}{c}\sqrt{{(x_i-x_{sj})}^2+{(y_i-y_{sj})}^2+{(z_i-z_{sj})}^2}={\mathrm{\ρ}}_j+{\mathrm{c\Δt}}_{ui},j=1,\mathrm{2.......}m\\ \left\{\begin{array}{c}{x}_i=x_{(i-1)}+{\mathrm{\Δx}}_i\\ y_i=y_{(i-1)}+{\mathrm{\Δy}}_i\\ \frac{{\mathrm{\Δx}}_i}{{\mathrm{\Δy}}_i}={\mathrm{tan\α}}_i|x_0=x_{bg},y_0=y_{bg},h_0=f\left(z_{bg}\right)\end{array}\right.\end{array}\right.---\left(7\right)$

in the formula (7), the above absolute positioning solving part can add constraint conditions, so that the equation can be solved under an underdetermined condition, the underdetermined condition is changed into a positive or over-determined condition, an accurate relevant solution is obtained, and the solution is changed into a real vector solution. One constraint that may be added is a high-range constraint. The elevation constraint solving method is characterized by comprising the following steps: the elevation constraint solution utilizes elevation constraint conditions. Firstly, on an x-y plane after an elevation constraint, utilizing relative measurement values to carry out position calculation on the x-y plane to obtain x when an i epoch is obtained_i,y_iThe position coordinate value of (2). And then, carrying out state recursion estimation on a position value obtained by recursion of the relative measurement value, establishing a minimized mathematical model of the position residual error, and carrying out optimization solution by using a generalized fusion solution algorithm to obtain an optimal three-dimensional position solution. The specific method for solving by using the elevation constraint is as follows:

in particular, when navigating to locate the start position, i is equal to 1. If the number m of the ranging signal sources is more than 4, firstly directly solving to obtain x_i-1,y_i-1,z_i-1A value, and calculating to obtain h_i-1. If m < 4, then x₀,y₀,z₀Must be assigned an initial value x_bg,y_bg,z_bg. Wherein, because Z is related to h, the initial elevation h can be assigned₀；

In step S1041, when i is equal to 1, that is, at the start position, it is assumed that the start elevation value is h₀＝h_bgAnd in the starting elevation plane h₀Initial plane position x of₀＝x_bg，y₀＝y_bgIf so, then the step S1042 is carried out;

step S1042, constraining the plane h in elevation_i-1Above, the recursion formula using relative measurements is listed in the x-y plane:

in the formula (8), the reaction mixture is,representing the estimated values in x, y directions for the i epoch,represents the optimal position value, Δ x, in the x, y direction at i-1 epoch_i，Δy_iThe amount of change in the x, y position coordinates in the i epoch is expressed, and the amounts of change are listedThe purpose of (2) is to change the amount of change Deltax in the x direction_iAmount of change Δ y from the y direction_iAngle of direction α_iClosely related, making its solution a true vector solution.

Step S1043, theSubstituting the following formula (9):

$\frac{x_i^2+y_i^2}{{(a+h_i)}^2}+\frac{z_i^2}{{(b+h_i)}^2}=1---\left(9\right)$

can obtainIn formula (9), h_iThe elevation value of the i epoch is shown, and a and b are respectively a long half shaft and a short half shaft of the earth reference ellipsoid.

Step S1044, obtaining the relative measurement value and the recurrence equation Represents the optimal position value at time epoch i,represents the extrapolated value of the state at time epoch i; later, the method can be integrated with an absolute positioning equation of distance measurement to establish a residual minimization mathematical model, namely (x) is solved_i,y_i,z_i) 1,2,3 Λ n optimum position valueMake it

In the formula (10), I is an objective function; omega₁，ω₂，ω₃，ω₄Is a weight coefficient; rho_jMeasuring pseudo range values; t is t_uiIs as follows; x is the number of_sj,y_sj,z_sjSatellite position at j epoch;representing the estimated value of x and y directions of i epoch, and n is the number of epoch; c is the speed of light；Δt_uiM is the number of signal sources, which is the deviation of the time of the receiver terminal from the reference time.

Step S1045, getFormula (9):

$\frac{x_i^2+y_i^2}{{(a+h_i)}^2}+\frac{z_i^2}{{(b+h_i)}^2}=1---\left(9\right)$

can obtain new elevation valueThereby selecting good elevation constraint values for continued solution for the next epoch. When the instruction i is equal to i +1, go to step S1042, and continue to solve the solution until i is equal to n, the solution is ended;

step S105, the generalized integrated mutual correction solving method of successive fusion adopts successive combination of the state variable absolute measurement value and the state estimated value obtained by recursion of the relative measurement value in each epoch to obtain the optimal estimated value. When the optimal estimated value is obtained by successive fusion, the estimated state value obtained by recursion of the relative measured value is corrected by adopting the absolute state measured value and other nominal values, and the estimated state value obtained by recursion of the relative measured value is hybridized, integrated and fused with the absolute measured value of the state to realize parameter hybridization, performance fusion, error mutual correction and equation solution, and finally the optimal state estimated value is obtained. The cross-integration and fusion mutual calibration process is a combined optimization solving process of mutual fusion, mutual integration, mutual calibration and mutual error correction between two measurement values. The relative measurement value has higher measurement precision in a short period, so the estimated value obtained by recursion of the relative measurement value is combined, and the precision of the state measurement value obtained by solving the absolute measurement value can be improved; after a period of time, the successive mutual correction does not generate larger accumulated error and have low precision like a dead reckoning method.

The specific steps of solving the mathematical model by the successive fusion optimization integration mutual correction solving method are as follows:

to findMake it

$\min E=\underset{j=m}{\overset{n}{\&Sigma;}}{(a_1{t}_j^2+a_2{t}_j+a_3-{\hat{X}}_j)}^2$

In the formula (10), X_nIn the form of a state value, the state value,the optimal estimated state value is the quantity to be solved; is a state change amount, respectively X_nThe first derivative and the second derivative of the state variable are relative measured values;a predicted value of the state quantity obtained after recursion of the relative measurement quantity; rho_n，ζ_nIs an observed value;to approximate a polynomialWherein a is₁，a₂，a₃Approximating polynomial coefficients, and optimizing variables; f (·), g (·) is a functional relation; e₁,E₂For an optimized objective function, K_nAs the weight coefficient,the optimal value of X in the j sequence.

Step S1051, solving the measurement equation of the state quantity, directly solving to obtain the absolute state quantity value x_i,y_i,z_i；

Step S1052, solving a recursion equation of the relative measurement value to obtain a state quantity recursion estimated valueThe method is characterized in that:

on the basis of the optimal estimated value of the previous epoch, the relative measurement value with higher precision is utilizedAndrecursion is carried out to obtain the estimated value of the state quantityAt each epoch, K is weighted once by the recursive estimate and the state measurement_nAnd (4) fusing. That is to say that the first and second electrodes,corrections are made once in each iteration, using absolute measurements.

In the above formula, X_nIn the form of a state value, the state value,the optimal estimated state value is the quantity to be solved;is a state change amount, respectively X_nThe first derivative and the second derivative of the state variable are relative measured values; Δ t is a time variable;a predicted value of the state quantity obtained after recursion of the relative measurement quantity; zeta_nIs an observed value; g (-) is a functional relation; e₂Is an optimized objective function.

The successive mixed interaction calibration and fusion process of the invention not only successively makes full use of the high-precision relative measurement value, but also successively makes use of the absolute measurement value for calibration. The method of long-time accumulation and re-correction in the dead reckoning algorithm is divided into every epoch for implementation, so that the correction is uniform and successive, and the accuracy of the optimal estimated value data sequence is improved.

Step S1053, the two obtained state values are fused, optimized and generalized integrated and solved, namely, the optimized position value is solvedMake it

In the formula (12), the reaction mixture is,to optimize the position value;for obtaining by using the incremental of speed value and acceleration valueA position pre-estimate of (d);pre-estimating the initial position; k is a radical of_xi，k_yi，k_ziRespectively, x-direction, y-direction, z-direction and direction are combined.

K in formula (12)_xi,k_yi,k_ziAre weight coefficients. The mathematical model (12) can be solved by a generalized fusion solving method to obtain an optimal estimation value

And step S1054, assigning i +1 to i, turning to steps S1041 to S1043, and performing iterative solution until i is equal to n.

Step S106, in order to make the solution value more accurate and more in line with the motion trail requirement, the measured value can be finely processed:

(x_i,y_i) Combined with Doppler velocity and acceleration values $({\hat{x}}_i,{\hat{y}}_i),$ $i=1,2,......,n,$ Make it

In the formulae (13) and (14),to optimize the position value; v. of_xi，v_yiAnd a_xi，a_yiRespectively obtaining the speed and acceleration values of the terminal in the directions of an x coordinate and a y coordinate through Doppler velocity measurement; Δ t is a time variable;the position pre-estimated value is obtained after the speed value and the acceleration value are deducted; k is a radical of_xi，k_yiThe weight coefficients when x-direction and y-direction are combined respectively.

At height h_i-1On the constraint plane, the recursion formula is built using relative measurements listed in the x-y plane:

a position state estimate obtained by recursion using a position state value obtained by direct solution and a velocity relative measurement value, or a position solution obtained using a measurement equation for absolute positioning, the recursion formula characterized by: the coupling matching degree between different relative measurement values can be enhanced after the addition of correlation constraint between the relative measurement values.

HandleSubstituting the following formula:

$\frac{x_i^2+y_i^2}{{(a+h_i)}^2}+\frac{z_i^2}{{(b+h_i)}^2}=1---\left(16\right)$

can obtain

In the formula (16), h_iThe elevation value of the i epoch is shown, and a and b are respectively a long half shaft and a short half shaft of the earth reference ellipsoid.

The elevation constraint solving method is characterized by comprising the following steps: the elevation constraint solution utilizes elevation constraint conditions. Firstly, on an x-y plane after an elevation constraint, utilizing relative measurement values to carry out position calculation on the x-y plane to obtain x when an i epoch is obtained_i,y_iThe position coordinate value of (2). And then, a state recursion estimated position value obtained by recursion of the relative measurement value is used for establishing a minimization mathematical model of the position residual error, and a generalized fusion solving algorithm is used for carrying out optimization solving, so that an optimal three-dimensional position solution can be obtained.

In step S1041, when i is equal to 1, that is, at the start position, it is assumed that the start elevation value is h₀＝h_bgAnd in the starting elevation plane h₀Initial plane position x of₀＝x_bg，y₀＝y_bgThen, the process proceeds to step S1032;

step S1042, constraining the plane h in elevation_i-1Above, the recursion formula using relative measurements is listed in the x-y plane:

making its solution a true vector solution.

Step S1043, theSubstituting the following formula:

$\frac{x_i^2+y_i^2}{{(a+h_i)}^2}+\frac{z_i^2}{{(b+h_i)}^2}=1---\left(18\right)$

can obtain

Step S1044, obtaining the relative measurement value and the recurrence equationLater, the method can be integrated with an absolute positioning equation of distance measurement to establish a residual minimization mathematical model, namely solvingMake it

Step S1045, getSubstituting the following formula:

$\frac{x_i^2+y_i^2}{{(a+h_i)}^2}+\frac{z_i^2}{{(b+h_i)}^2}=1---\left(20\right)$

can obtain new elevation valueThereby selecting good elevation constraint values for continued solution for the next epoch. If i is equal to i +1, the process goes to step S1032, and the solution is continued until i is equal to n, and the solution is ended.

Position accuracy, satellite navigation plane position measurement (x) using velocity values_i,y_i) Combined with Doppler velocity and acceleration valuesMake it

The coupling matching degree between different relative measurement values can be enhanced after the addition correlation constraint between the relative measurement values,

firstly, on an x-y plane after an elevation constraint, utilizing relative measurement values to carry out position calculation on the x-y plane to obtain x when an i epoch is obtained_i,y_iThe position coordinate value of (2). And then, by directly solving the obtained position state value and the position state estimated value obtained by recursion of the speed relative measurement value or the position solution obtained by the measurement equation of absolute positioning and the state recursion estimated position value obtained by recursion of the relative measurement value, establishing a minimized mathematical model of the position residual error, performing optimized solution by using a generalized fusion solution algorithm, and processing random errors by using a generalized filtering method, thus obtaining the optimal three-dimensional position solution. The following is a specific step flow of solving the elevation constraint, and the specific implementation manner is as follows:

step S1030, listing specific integration fusesSynthetic positioning mathematical models, i.e. finding the solution (x) to the trajectory of the navigational positioning_i,y_i,z_i) I is 1,2,3 Λ n, so as to satisfy

$\left\{\begin{array}{c}\sqrt{{(x_i-x_{sj})}^2+{(y_i-y_{sj})}^2+{(z_i-z_{sj})}^2}={\mathrm{\&rho;}}_j+{\mathrm{c\&Delta;t}}_{ni}(j=1,\mathrm{2.......}m)\\ \left\{\begin{array}{c}{x}_i=x_{(i-1)}+{\mathrm{\&Delta;x}}_i\\ y_i=y_{(i-1)}+{\mathrm{\&Delta;y}}_i\\ \frac{{\mathrm{\&Delta;x}}_i}{{\mathrm{\&Delta;y}}_i}={\mathrm{tan\&alpha;}}_i|x_0=x_{bg},y_0=y_{bg},h_0=f\left(z_{bg}\right)\end{array}\right.\end{array}\right.---\left(23\right)$

Wherein, Δ x_i,Δy_iRespectively, the relative change value x of the terminal position coordinate when the terminal evolves from i-1 epoch to i epoch_i,y_i,z_iThe coordinate value of the three-dimensional position of the terminal user in the earth-centered earth-fixed coordinate system at the i epoch; x is the number of_i-1,y_i-1,z_i-1Respectively is a three-dimensional position coordinate value of the terminal user in the geocentric coordinate system when the terminal user is in the i-1 epoch; x is the number of_si,y_si,z_siThree-dimensional position coordinate values of a navigation signal source (satellite) in a geocentric geostationary coordinate system are respectively set; rho_jThe pseudo range length from the j signal source to the terminal user is obtained; c is the speed of light; Δ t_uiα clock skew for termination_iIs the deviation angle of the terminal travel direction from true north.

The above-mentioned embodiments are only examples of the present invention, and are not intended to limit the present invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A novel generalized integrated positioning principle, a mathematical model and a solving method are characterized by comprising the following steps:

s100, establishing a fusion optimization integrated positioning navigation principle mathematical model;

step S101, unifying the resolving coordinates in a coordinate system;

step S102, performing fine pre-processing treatment on the measured value;

step S103, establishing a plurality of groups of state quantity solving relational expressions by using various types of finely processed measured values;

step S104, fusing a plurality of groups of state quantity solving relational expressions and integrating the state quantity solving relational expressions into a generalized state quantity solving equation set;

step S105, solving a solving equation set of the generalized state quantity by using a generalized fusion optimization algorithm;

step S106, fine post-processing treatment of the state quantity solution value.

2. The novel generalized integrated positioning principle, mathematical model and solving method according to claim 1, characterized in that:

in the step S100, a generalized fusion optimization integrated positioning and navigation principle and a mathematical model are established, the mathematical model is solved, and x is now set_sj,y_sj,z_sjFor satellite position, the solution set of acquired generalized navigational fixes is (x)_i,y_i,z_i) And i is 1,2,3 Λ n, the trajectory solution must satisfy the following condition:

$\left\{\begin{array}{c}{f}_1(x_i,y_i,z_i,x_{sj},y_{sj},z_{sj})={\mathrm{\&rho;}}_j+{\mathrm{c\&Delta;t}}_{ui},(j=1,\mathrm{2.......}m)\\ s.t.g_1\left(x_i,y_i,z_i\right)={\mathrm{\&eta;}}_l,\left(l=1,2,\mathrm{.....}k\right)\\ x_i=f_2\left({\mathrm{\&Delta;x}}_i\right)\\ y_i=f_3\left({\mathrm{\&Delta;y}}_i\right)\\ z_i=f_4\left({\mathrm{\&Delta;z}}_i\right)\\ s.t.g_2\left({\mathrm{\&Delta;x}}_i,{\mathrm{\&Delta;y}}_i,{\mathrm{\&Delta;z}}_i\right)={\mathrm{\&alpha;}}_i\\ i=1,2,\mathrm{......}n\end{array}\right.---\left(1\right)$

the generalized positioning mathematical model (1) consists of two parts, wherein the upper part of the mathematical model (1) is an absolute positioning solving part, and n is an epoch number; f. of₁(x_i,y_i,z_i,x_sj,y_sj,z_sj) Is a relation of a measuring function; g₁(x_i,y_i,z_i) As a relation of a constraint function, p_j，Λ_lAre all absolute measurements; c is the speed of light; Δ t_uiThe deviation of the time of the receiver terminal and the reference time is shown, and m is the number of signal sources; k is the number of constraint equations;

the lower part of the mathematical model (1) is the relative positioning measurement recursion solving part, where f₂(Δx_i),f₃(Δy_i),f₄(Δz_i) Are recursion relational expressions respectively; g₂(Δx_i,Δy_i,Δz_i) Δ x being a function of a constraint relating between the relative measured quantities_i,Δy_i,Δz_iFor relative measurement, the relative measurement can be a relative change of the state variable, or can be a derivative or derivative of the state variable α_iFor navigation traveling direction angle, the navigation traveling direction angle is characterized by an absolute deviation angle between the traveling direction and the true north or the magnetic north, wherein the subscripts i and j respectively represent sequence variables, the subscript j represents a satellite sequence variable, k represents the number of constraint equations and also represents the number of constraint variables, t represents time, and Λ represents a truncation number.

3. The novel generalized integrated positioning principle, mathematical model and solving method according to claim 1, characterized in that:

in step S101, the coordinate system when the fusion equation group is solved is unified in one coordinate system, and the method includes: the generalized fusion optimization integrated positioning navigation principle mathematical model is established in a geocentric geostationary coordinate system and can also be established in a station-center coordinate system or a building coordinate system; but one coordinate system must be selected finally, and combined modeling and solving are carried out in a unified coordinate system.

4. The novel generalized integrated positioning principle, mathematical model and solving method according to claim 1, characterized in that:

in step S102, in order to make the measured value more accurate, a fine preprocessing process of the measured value is performed, characterized in that: after the measured value is subjected to fine processing, the precision of the measured value can be improved, a processing tool of the method adopts a data processing method of a generalized fusion calculation method, and the adopted data processing technology comprises the following steps: grinding process, fusion process, filtering process and smoothing process.

5. The novel generalized integrated positioning principle, mathematical model and solving method according to claim 1, characterized in that:

in step S103, a plurality of sets of state quantity solving relations are established by using various types of measured values after fine processing, for example; listing a relation between speed and acceleration and a position quantity by utilizing a kinematics principle; the relationship between the two velocity components and the heading angle can also be listed in the x-y plane, as shown in equation (2) below:

$\frac{{\mathrm{\&Delta;x}}_i}{{\mathrm{\&Delta;y}}_i}={\mathrm{tan\&alpha;}}_i---\left(2\right)$

in step S104, the state quantity solution relational expression is fused and integrated into a generalized state quantity solution equation set, i.e. a trajectory solution set (x) of positioning navigation is solved_i,y_i,z_i) I is 1,2,3 Λ n so as to satisfy formula (1);

in the formula (1), in step S105, a system of solution equations of the generalized state quantities is solved by a generalized fusion optimization algorithm; the successive integration fusion mutual calibration solving method is characterized by comprising the following steps: the absolute measurement of the state variable is combined successively in each epoch with the state estimate obtained by recursion of the relative measurements to obtain the optimum estimate.

6. The novel generalized integrated positioning principle, mathematical model and solving method according to claim 1, characterized in that:

in step S106, a fine post-processing process is performed on the obtained optimum estimated value, characterized in that: and performing fine post-processing such as smoothing, filtering, prediction and prediction on the optimal estimated value obtained by solving by adopting methods such as generalized filtering.