# Method of locating mobile object in navigation measurements

FIELD: physics, navigation.

SUBSTANCE: invention relates to methods of determining and predicting the position of an object in space. Dynamic properties of an object are used to predict the region in space of possible location of the object during subsequent navigation measurements. The corrected position of the object in space during the next navigation measurements is the intersection of regions in space of the subsequent navigation measurements with predicted regions.

EFFECT: high accuracy of locating moving objects in space during navigation measurements based on use of dynamic properties of said objects.

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The invention relates to methods for determining and predicting the location of an object in space and can be used to improve the accuracy of the location of moving objects in the navigation measurements. The method may find application in navigation systems, in systems near field navigation and landing, in control systems and automatic control of moving objects, systems, air traffic control and collision avoidance, automated docking of moving objects, in radar systems, for example, in situations when the target is identified and is known for its potential to move in space, and the update rate of the radar information is low.

Currently, there are various ways to determine the location of the object.

So, from the description to the patent of Russian Federation №2202102 (published 10.04.2003) there is a method of determining the coordinates of the moving ground objects, light aircraft, boats, yachts. The method involves the measurement in the calibration cycle control values of the horizontal projections of the total intensity vector of the Earth magnetic field and the magnetic field of the object, the measurement for the operating cycle time averaged values of the projections of the acceleration of gravity and projections of the total vector napryajenno and the Earth's field and the magnetic field of the object. Taking into account correction factors determine the values of the horizontal projection of the vector field strength of the Earth. Determine the angle of direction of motion. Determine the increments of the coordinates during the operating cycle. Determine the relative coordinates of the summation of the increments of coordinates. Determine the coordinates of the object by summing the relative coordinates and the coordinates of the initial point. Measured by a satellite navigation system receiver coordinates of the object, based on which correction of the relative coordinates and the coordinates of the initial point. Determine correction factors, which in each duty cycle correction angle direction and the increment of the path. Improved the accuracy of the measurement direction and the coordinates of the object and the simplification of the calibration device.

Also from the patent of the Russian Federation No. 2399065 (published 10.09.2010) there is a method of determining the location of a moving object by means of a hybrid navigation system that integrates satellite navigation system receiver for receiving a navigation signal, which allows to determine the position of the satellites, speed, satellites, pseudoresistance to the object of observation and evaluation of the Doppler shift of the carrier frequency navigation signal, the measuring device inertial N. the navigation system and the computing device, located on the movable object, which receives the angular velocity for each of the orthogonal axes X, Y and Z linear acceleration along orthogonal axes, namely, that believe that the initial location of a moving object and the initial value of the vector of its velocity is known, the received data from the satellites that are within range, used for the formation via the computing device of the two rotation matrices, one of which is the rotation matrix for the coordinates of the satellites, the other is a rotation matrix for the velocities of the satellites, using the generated rotation matrix by a computing device, perform a coordinate transformation of the satellites and their velocities from geocentric fixed coordinate system the local coordinate system, taking data from the measuring device inertial navigation system of a moving object angular velocity and linear acceleration of a moving object using the received data about the angular velocity of a moving object, form the rotation matrix R from the coordinate system associated with a movable object in a local coordinate system using the generated rotation matrix R, convert the data about the linear acceleration of a moving object; form the transition matrix for the state vector, to relational matrix of the errors of the inertial measurement Q, characterizing measurement performed by the measuring device inertial navigation system, the correlation matrix of the measurement errors W characterizing the data coming from the satellite navigation system receiver using the received converted data about the linear acceleration of a moving object, and the values of position, velocity, generated rotation matrix, by the computing device calculates the location of a moving object and its speed; the converted satellite data, the transition matrix for the state vector, the correlation matrix of the errors of the inertial measurement Q, the correlation matrix of the measurement errors W, the calculated location of the mobile object and its speed of movement, are used to form matrix N describing linear connection all dimensions with components of the state vector, to calculate the predicted values of the state vector dx and to calculate the correlation matrix of the error estimates of the components of the state vector P using the calculated values, compute the state vector and the correlation matrix of the errors, the results of the calculated state vector determine the current location of the object, characterized in that the formed correlation matrix of the errors of the inertial measurement Q is the correlation matrix of the measurement errors W multiplied by corresponding weighting coefficients, using the computing device, when calculating the predicted values of the state vector dx and the correlation matrix of the errors performed by the computing device conversion matrix approximate formula:

(W+H·P·HT )-1≈ 1/W(1-H·P·HT/W),

where T is the transposition of a matrix, with weights chosen so that to satisfy the condition H·P·H^{T}/W<1, the elements of the correlation matrix of the error state vector is compared with the preset threshold value, if at least one of the elements exceeds a predefined threshold value, to calculate the state vector of the current stage we use the calculated values of the matrix of the error state vector of the previous stage, in case of exceeding the threshold is at least one element of the returned matrix is the variance calculated in the previous step.

The closest analogue to the invention is a method of determining the coordinates of moving objects based on the reception signals spacecraft global navigation satellite systems, the measurement of the pseudorange, the introduction of the amendments and the calculation of coordinates of moving objects, characterized in that they have n measurements of pseudorange and coordinates of a moving object at a known route, identify points x_{io}, y_{io}, z_{io}on a known route, soo is concerned, the shortest distance to points with measured coordinates x_{
i}*, y_{i}*, z_{i}*determine amended by solving a system of 3 n equations

x = a_{xxi}x_{i}+a_{XVI}y_{i}+a_{xzi}z_{i},

y = a_{yxi}x_{i}+a_{yyi}y_{i}+a_{yzi}z_{i},

z = a_{zxi}x_{i}+a_{zyi}y_{i}+a_{zzi}z_{i},

where i = 1, n;

and_{xxi}and_{XVI}and_{xzi}and_{yxi}, a_{yyi}, a_{yzi}, a_{zxi}, a_{zyi}, a_{zzi}- conversion factors coordinate of special topocentric coordinate system with the center at the point X_{io}, Y_{io}, Z_{io}, X_{ti}and Y_{ti}lying in the horizontal plane, and Z_{ti}directed vertically upwards, and the point x_{i}*, y_{i}*, z_{i}* lies in the plane X_{ti}, Z_{ti}and tangent to the well-known route lies in the plane Y_{ti}, Z_{ti}in the geocentric coordinate system;

x_{i}= b_{xxi}(x_{i}- x_{io}) + b_{XVI}(y_{i}- y_{io}) + b_{xzi}(z_{i}- z_{io}),

z_{i}= b_{zx}
(x_{i}- x_{io}) + b_{zyi}(y_{i}- y_{io}) + b_{zzi}(z_{i}- z_{io}),

b_{xxi}b_{XVI}b_{xzi}b_{zxi}b_{zyi}b_{zzi}- conversion factors coordinate of the geometric coordinate system in a special topocentric coordinate system with the specified characteristics;

y_{i}- n associated unknown;

xy,z - determined corrections (RF patent No. 2145423 published 10.02.2000).

However, the proposed technical solutions or require additional navigation measurements or reference points with known geodetic coordinates and the availability of the communication channel between the moving object and a reference point, or fully known and with a given accuracy of the predicted trajectory of the object.

The technical result of the invention is to improve the accuracy of the positioning of a moving object in space based on its dynamic characteristics.

The proposed method of determining the location (coordinates) of moving objects in the navigation measurement differs from the known fact that on the basis of the dynamic properties of the object projected area of the space of possible locations of the object at point p the following navigation measurements. Adjusted the location of the object in space during subsequent navigation dimensions is the intersection of the fields of space subsequent navigation measurements with the predicted fields.

The claimed technical result is achieved due to the implementation of the method of determining the location of a moving object in space, characterized in that exercise, at least three navigational measurements, which determine the coordinates of_{1}-t_{n}according to the navigation measurement determine the areathe space in which the object at time t_{1}-t_{n}:

...

when the navigation measurements to determine the following conditions:

- accuracy of each subsequent measurement and the actual measurement values do not depend on the results of previous measurements and their errors, they are statistically independent;

- the error of each measurement is not dependent on the location of the object in space, or such dependence in the framework of several consecutive and the measurements of the coordinates can be neglected and put, that hx; hy; hz = const when several successive navigational measurements,

next determine the projected area of the space occupied by the object over the time interval ∆ T the parameters of the traffic restrictions that are determined by on-Board meters, located on the movable object, at the same time as parameters restrictions take:

- directional velocity V_{K MAX}- maximum speed rate when the object is moving (at each stage of the movement);

- maximum directional acceleration and_{K MAX}- the maximum acceleration of the object on the course (at each stage of the movement);

- maximum vertical velocity V_{MAX};

- a_{MAX}- the maximum vertical acceleration (at each stage of the movement);

- the maximum change of the yaw angle Ψ_{MAX}during the time Δt between successive navigational measurements;

- the maximum change of the pitch angle Θ_{MAX}during the time Δt between successive navigational measurements and generalized conditions restrict the position of the object according to the navigation measurements and dynamic properties of the object expressed in the form of a system of inequalities:

The values of V_{K MAX}; a_{K MAX}; V_{B MAX}; a_{B MAX}; Θ_{MAX}; Ψ_{MAX}in systemproject generalized constraints the location of the object according to the navigation measurements with the influence of wind can be written as the readings of onboard datalogger as follows:

where

Λ_{PR1}- forecast at time t_{1}the area of the space, which may take the moving body at time t_{2}through Δt, lies within the cone formed by the tangent to the surfaces of the spheres Λ_{1}and Λ_{2};

next, the true, the extreme, the position of the rate increase at the maximum possible angle for the time Δt deviations of the object at the corners of the pitch and angle of the course, resulting in a gain projected space Λ_{AC2}a possible location of the object at time t_{2}in the form of a convex elliptical cone with the angle of aperture θ_{MAX}and Ψ_{MAX}and the height of the specified cone determine the maximum possible exchange rate movement speed of the object during the time Δt, and the true location of the object after the second navigational measurements over the interval Δt (space win) determine the intersection of the regions of space

this joint probability is p(0,95)×p(0,95)=0,9025, and the space win Λ_{AC2}∩Λ_{2}∩Λ_{PR1}should be increased in all three coordinates x; y; z within the space Λ_{2}as a percentage, equal percentages of cases what Inoi values p(0,95)/C(0,9025),
next, carry out the correction of the location of moving objects according to the results of the three navigation measurements as follows:

according to the results of the first and second navigational measurements by the above algorithm determines Λ_{2CO}- win in determining the location after the second navigational measurements, the correction is carried out on speed and maximum angles of deflection;

on the basis of the distribution law of a random variable - error navigation measurements - determine the area of the space Λ'_{2CO}(p(0,95)) with probability not less than 0.95, the true position of the object Λ'_{2CO}(p(0,95)) is inside the space Λ_{2};

when receiving data of the third navigation measurement region Λ_{3}- determine the region Λ_{CAR}- win in determining the location after the third navigation measurements, using as input data to the second reading and the third dimension, in this case, the correction is carried out on speed and the maximum inclination angles, and as a source for predicting take area-adjusted space location of the object when the second navigational measurements Λ'_{2CO}(p(0,95));

then, on the basis of the distribution law of a random variable - error navigation and the measurements -
determine the area of the space Λ'_{CAR}(p(0,95)) with probability not less than 0.95, while Λ'_{CAR}(p(0,95)) is inside the space Λ_{3},

on the basis of all three navigation measurements again define the region Λ_{CAR USK}- win in determining the location after the third navigation measurement, and the correction occurs for values of accelerations, and as a source for predicting accepted region Λ'_{2CO}(p(0,95)) - already adjusted the amount of space possible location of the object at the time of the second navigational measurements;

on the basis of the distribution law of a random variable - error navigation measurements - determine the area of the space Λ'_{3 USK}(p(0,95)) with probability not less than 0.95, while Λ'_{3 USK}(p(0,95)) is inside the space Λ_{3};

determine the intersection volume of space found adjusted amounts of space location of the object Λ'_{CAR}(p(0,95)) with Λ'_{CAR USK}(p(0,95)), the space of intersection of these volumes Λ_{COR THE END.}will be final adjusted position of the object at time t_{3};

next, on the basis of the distribution law of a random variable - error navigation measurements - determine the area of the space is Λ'_{
CAR WINDOWS}(p(0,95)) with probability not less than 0.95, while Λ'_{CAR WINDOWS}(p(0,95)) is inside the space Λ_{3}for the region of space of the third dimension gain values of the index range of the coordinates x; y; z (i...j; r...p; q...f)within the space finally adjusted position of the object at time t_{3}Λ'_{CAR WINDOWS}(p(0,95)):

m=i...j is the index range of the x coordinate included in the space Λ'_{CAR WINDOWS};

n=r...p - index range of y coordinates included in the space Λ'_{CAR WINDOWS};

k=q...f - range index (z) belonging to the space Λ'_{CAR WINDOWS};

as a end result of the location of an object in space with a probability of at least p(0,95) consider the geometric middle of the adjusted region of space Λ'_{CAR WINDOWS}with the corrected coordinates x_{(j-i)/2}; y_{(p-r)/2}; z_{(f-q)/2}.

The essence of the above method is as follows.

Let x,y,z,are the real coordinates of the object in the base coordinate system associated with the center of mass of the object, and_{X}; h_{Y}; h_{Z}known from tactical and technical characteristics of the navigation system.

For example, for a global satellite navigation systems GPS and GLONASS, with a probability of at least p(0,95) it can be argued that the true value will differ from the measured no more than 8-10 meters in the horizontal plane and 1.5÷2 times higher than the error in the vertical plane.

The results of any navigational measurements can be represented as a spatial region, where with probability p(0,95) the measurement error shall not exceed the values of h_{X}; h_{Y}; h_{Z}. For global satellite navigation systems such area of space can be interpreted as the vertical ellipsoid. Suppose that when the navigation measurements the following conditions are true:

the error of each subsequent themselves and dimension values do not depend on the results of previous measurements and their errors, they are statistically independent;

the error of each measurement is not dependent on the location of the object in space, or a dependence within the last few the consecutive measurements of the coordinates can be neglected and put,
that h_{X};h_{Y};h_{Z}=const when several successive navigational measurements.

Let according to the results of navigational measurements at time t is specified region of space Λ. It can be represented in discrete form as_{X}/Δx; n=0...N=2h_{Y}/Δy; k=0...K=2h_{Z}/Δz; m; n; k are integers (indices breakers coordinates). The values of h_{X}; h_{Y}; h_{Z}- the maximum error in measuring the coordinates of a moving body with a probability of at least p(0,95), i.e.,

Consider successive navigational measurements at time t_{1}-t_{n}determining areas of space Λ_{1}-Λ_{n}the location of the object at time t_{1}-t_{n}:

...

_{1}-t_{n}.

To predict the area of each successive navigational measurements of Λ_{CR}select options to limit the location of the object because of its dynamic properties, which can be: the maximum speed and acceleration (depending on the task can be vertical and horizontal, directional and reduction, and other linear and angular velocity and acceleration); the maximum change of the azimuth angle (or yaw)angle of months is a (or roll) or other parameters.

For example, as parameters of the traffic restrictions can be: directional velocity V_{K MAX}- maximum speed rate when the object is moving (at each stage of the movement); the maximum course acceleration and_{K MAX}- the maximum acceleration of the object on the course (at each stage of the movement); the maximum vertical speed of - V_{MAX};_{MAX}-the maximum vertical acceleration (at each stage of the movement); the maximum change of the yaw angle ψ_{MAX}during the time Δt between successive navigational measurements; the maximum change of the pitch angle θ_{MAX}during the time Δt between successive navigational measurements; if necessary, you can use the maximum change of the roll angle γ_{MAX}during the time Δt between successive navigational measurements.

Generalized conditions restrict the position of the object according to the navigation measurements and dynamic properties of the object can be written as:

(1)

when you do this :

(2)tabtabtabtab

t_{1}-t_{3}- times of three successive navigational measurements.

These inequalities should be interpreted as follows.

The first inequality is the speed of object paths for a time Δt between first is m and the second dimension may not exceed the maximum possible exchange rate.

The second inequality is similar, but between the second and third dimension.

The third inequality - directional acceleration of the object should not exceed the maximum.

The fourth to sixth inequality similarly 1-3 inequality for the vertical velocity and acceleration.

Seventh-eighth inequality determines the maximum possible angle of the object from the vertical (which actually determines the pitch) for the second and third dimension.

Ninth-tenth inequality determines the maximum possible angle of deviation from the course for the second and third dimension.

The maximum value of possible velocities, accelerations and angles deviations in expressions (1)-(2) should take into account the effect of wind and its effect on the moving object. For specific technical tasks and limiting conditions the location of the object because of its dynamic properties can have a slightly different view.

As the maximum possible velocities, accelerations and angles of deviation can be taken as physically impossible for a moving object (e.g. car), and not recommended at this stage of the movement (for example, the flight phase) for reasons of safety (for example, the critical angle of attack, glide path, the critical speed reduction etc). As a rule, for example, on Board an aircraft system has the volumes alerts for critical modes of motion (exceeding the maximum speed value, accelerations and angles of deviation. Therefore, with probability of at least p(0,95) it can be argued that the object does not exceed the critical values.

To improve the accuracy of location of an object in space may not use the limiting values of speed, acceleration and change of the angular positions of the object, and the current real data onboard datalogger (B) of object motion parameters (velocity, angles, accelerations). The maximum parameters V_{K MAX}; a_{K MAX}; V_{B MAX}; a_{B MAX}; Θ_{MAX}; Ψ_{MAX}defined by current readings of onboard datalogger, their errors, sensors wind and wind direction, as well as the increment of the measured parameters during navigation between the measurement and the next after receipt of the information from the onboard meter.

In this case (and with the influence of wind) the values of V_{K MAX}; a_{K MAX}; V_{B MAX}; a_{B MAX}; Θ_{MAX}; Ψ_{MAX}in the system of inequalities (1) generalized constraints the location of the object according to the navigation measurements can be written as the readings of onboard datalogger as follows:

(3)

where

In these expressions, the values of the errors in the readings of onboard measurement is of Italy and frequency of information update onboard datalogger is determined by the performance characteristics (TTD) specific instruments. Often, the value of the measurement errors on data expressed in percentage values of the measured parameters.

Thus, using restrictions on the ability of movement of the object (1)to(3) it is possible to predict the area of the space of possible locations of each subsequent after the initial navigation measurements.

Let there are two navigation measurement at time t_{1}:_{}_{2}:_{1}and Δ_{2}(see figure 1)._{}Λ_{PR1}- forecast at time t_{1}the area of the space, which may take the moving body at time t_{2}through Δt (the update interval of the navigation information) due to its dynamic properties of the movement. Λ_{1}∈Λ_{PR1}i.e. Λ_{PR1}absorbs the_{
1}. Because after the first measurement rate of the object is not obvious, then the space Λ_{PR1}determines the maximum possible speed of movement of the object during the time Δt.

The direction determined by the line connecting the point of navigation measurements_{1}and Λ_{2},_{}as presented in figure 1. For ease of graphical representation, we will assume that h_{X}=h_{Y}=h_{Z}. and Λ_{1}; Λ_{2}; Λ_{3}are the spheres (although for global navigation satellite systems would be correct to assume that h_{X}=h_{Y}and h_{Z}≈1,5÷2 h_{X}).

True, the end position of course, it is necessary to increase the angle of the maximum possible (for the time Δt) deviations of the object at the corners of the pitch is the angle of the course.
Consider the cross section of the spheres Λ_{1}and Λ_{2}with respect to an axis of pseudosource in horizontal and vertical plane. As a result, will receive the projected space Λ_{AC2}a possible location of the object at time t_{2}in the form of convex elliptic cone (the corners of the aperture are determined by θ_{MAX}and ψ_{MAX})_{.}The height of the specified cone is determined by the maximum possible exchange rate movement speed of the object during the time Δt. The true location of the object after the second navigational measurements over the interval Δt will be determined not by region Λ_{2}and the intersection of the areas of the spaces Λ_{AC2}∩Λ_{2}∩Λ_{PR1}.

The following are possible prediction of the position of the object, they are schematically shown in figures 1-3.

In the first case (figure 1) Λ_{2}fully belongs to the region Λ_{AC2}and win in determining the location of a moving object no.

In the second case (figure 2) Λ_{AC2}∩Λ_{2}∩Λ_{PR1}<Λ_{2}and a win in determining the location of a moving object.

In the third case (figure 3) the intersection of Λ_{AC2}and Λ_{2}is the empty set. In this case, the result of the second navigational measurements are not consistent with the data predicted by the dynamic characteristics of the location of the object.
This means that any great error of this navigation measurements (falls out of the confidence interval in p(0,95))or wrong (or with a large error) estimated dynamic properties of a moving object. The probability that both navigation measurements at the moments t_{1}and t_{2}lie in the interval p(0,95) is slightly lower. Since the initial conditions it is assumed that the navigation measurements at different time points are statistically independent, the joint probability is p(0,95)x p(0,95)=0,9025. If you know the distribution law of the random variable errors of navigation measurements, the space win Λ_{AC2}∩Λ_{2}∩Λ_{PR1}should be increased (in all three coordinates x;y;z, but so that they entered the space Λ_{2}) a percentage equal to the percentage ratio of the random variable p(0,95)/p(0,9025). It reduces the gain in determining the location of the object, but at the same time adjusted the amount of space possible location of a moving object to be determined with a probability of at least p(0,95). The resulting amount of space is shown in figure 4.

Denote the winning location as Λ_{2CO}= Λ_{AC2}∩Λ_{2}∩Λ_{PR1}and Λ'_{2CO}(p(0,95)) - winning in positioning with probability not less than 0.95.

For practical implementation it is proposed to use the following algorithm to correct the location of moving objects according to the results of the three navigation measurements:

1. According to the results of the first and second navigational measurements by the above algorithm, we define Λ_{2CO}- win in determining the location after the second navigational measurements. Thus to predict the location of use the readings of onboard datalogger based on the inequalities (1)-(3). The correction is for speed and the maximum inclination angles.

2. On the basis of the distribution law of a random variable - error navigation measurement determine the area of the space Λ'_{2CO}(p(0,95)) with probability not less than 0.95. Thus Λ'_{2CO}(p(0,95)) is inside the space Λ_{2}.

3. When receiving data of the third navigation measurements (region Λ_{3}), similar to item 1, we define the region Λ_{CAR}- win in determining the location after the third navigation measurements, using as source data readings of the second and third dimension. The correction is on speed and maximum angles of deflection. The contrast of paragraph 1 is that as the source for the prediction area is not Λ_{2}and Λ'_{2CO}(p(0,95)) - already adjusted the amount of space possible location of the object at the time of the second navigational measurements.

4. On the basis of the distribution law of random variables is -
the error in the navigation measurement determine the area of the space Λ'_{CAR}(p(0,95)) with probability not less than 0.95. Thus Λ'_{CAR}(p(0,95)) is inside the space Λ_{3}.

5. On the basis of all three navigation measurements again define the region Λ_{CAR USK}- win in determining the location after the third navigation measurements. When this correction occurs for values of accelerations. As the source for the prediction area is not Λ_{2}and Λ'_{2CO}(p(0,95)) - already adjusted the amount of space possible location of the object at the time of the second navigational measurements.

6. On the basis of the distribution law of a random variable - error navigation measurement determine the area of the space Λ'_{CAR USK}(p(0,95)) with probability not less than 0.95. Thus Λ'_{CAR USK}(p(0,95)) is inside the space Λ_{3}.

7. We define the intersection of the volumes of space that are found in paragraphs 4 and 6, i.e. Λ'_{CAR}(p(0,95)) ∩ Λ'_{CAR USK}(p(0,95)) = Λ_{COR THE END.}-final (proposed algorithm) the adjusted position of the object at time t_{3}.

8. On the basis of the distribution law of a random variable - error navigation measurement determine the area of the space Λ'_{CAR WINDOWS}(p(0,95)) is the probability of not less than 0.95.
Thus Λ'_{CAR}_{WINDOWS}(p(0,95)) is inside the space Λ_{3}.

The proposed algorithm is a variant of the correction of the location of the object based on the data of the navigation measurements and restrictions associated with the dynamic properties of a moving object. This method of determining the location of an object in space, updating navigation data due to restrictions related to the dynamic properties of a moving object can be called using dynamic recurrent correction.

To increase the accuracy of determining the location of a moving object, using not only the first three dimensions, but the results of subsequent fourth and fifth dimensions. In this case, the first correction is delayed in 5 steps (5Δt), and each subsequent measurements will come with delay in step 2 (2Δt), where Δt is the update frequency of navigational information.

The use of a positioning method of an object in space, updating navigation data due to restrictions related to the dynamic properties of a moving object depends on the accuracy of the navigation system, the accuracy of the onboard sensors of the motion parameters and the speed and force of the wind.

The conditions of the possibility of using the ü dynamic recurrent correction can be considered as exceeding the accuracy of estimating the motion parameters compared to the accuracy of the positioning navigation system (figure 5):

Thus, a withdrawal from the use of dynamic recurrent correction is possible for different velocities and lateral displacements of the object, if it is possible to provide an accurate prediction (accurate measurements of its motion parameters).

Possible situation depicted in figure 3, when the data subsequent navigation measurements are not consistent with the data predicted by the dynamic characteristics of the location of the object. In this case, with probability P(95%) it can be argued that such a measurement should not be. However, such cases are possible due to failure of navigational AIDS, and with the passage of aircraft through the "infected zone", where due to reflections or other destabilizing factors, the measurement error increases dramatically. Separate such cases you can put the misses, but when they are repeated in the sample accumulated values of navigational measurements over a critical value, the navigation system is considered failed. For these purposes you can use any statistical criterion, with known statistical distribution law of probability of error in the navigation measurement.

Comparing and statistically analyzing the spatial domain, consistent navigation is the R measurements the location of the object and the projected area of the space of possible location of the object (based on its dynamic properties of the movement in space) at the time of the next measurement, it is possible to draw conclusions about the credibility of the testimony of navigational AIDS.

Similarly, it is possible to identify errors readings of onboard measuring motion parameters of the object (for example, DISS, bravestar, radio and others). For practical implementation we propose the following procedure for finding the area of space of the possible location of a moving object using dynamic constraints (smfg).

We define a three-dimensional matrix A={a_{m};_{n};_{k}}; B={b_{m};b_{n};b_{k}}; C={c_{m};c_{n};c_{k}}, corresponding to areas of Λ_{1}; Λ_{2}; Λ_{3}; elements which take the values 0 or 1. Each element of the matrix A;B;C means the point in space when partitioning the regions Λ_{1}; Λ_{2}; Λ increments in Δ;Δy;Δz. The values of the matrices A; B; C "0" or "1" (1 - an object can be at this point; 0-does not). At the initial step of the calculation (the raw data), all matrix elements are equal to 1 (the unadjusted values of the navigation measurement).

In the basic procedure is to simply try all possible values of the matrices a,b,C (dots spaces Λ_{1}; Λ_{2}; Λ_{3})satisfying the conditions of dynamic constraints (1)-(3). The result of the calculation is the matrix b or C (depending on steps 1-8 above algorithm to the recchi),
such that its elements B={b_{m};b_{n};b_{k}} or C={c_{m};c_{n};c_{k}} define the ability to stay in space

In the example implementation of the algorithm (smpeg) correction of basic computational procedure for the second and subsequent cycles of the calculation must be modified. The meaning of the modification is that the checks are not all terms of the equations of dynamic correction or not for the whole area of space of the previous navigation measurements for the region of space the previous measurement, already limited by the previous cycle of calculation. This reduces the number of calculations.

Win in determining the location of the object can be estimated as the ratio of the number of elements of the matrix are not equal to zero, to the total number of elements of the matrix.

The proposed algorithm and the baseline in the computation procedure is only one possible implementation of dynamic recurrent correction. The actual algorithm for a particular object may only deduct the portion of the proposed conditions of correction (1)-(3), or to consider its terms.

The proposed algorithm involves modification of the basic computational procedures (enumeration of points of the space) at the initial and subsequent measurement cycles. During subsequent cycles of calculations as the source region for prediction is area of the space of possible locations already adjusted the previous measurements. The algorithm implementing dynamic recurrent correction allows to process the data with BI, wind sensors and the navigation system in real-time as they are received.

In practice it should be possible to stop the flow of data from the navigation system. Upon termination of the receipt of the navigation data for the period more time updating the navigation information, the calculation has to be repeated, with the primary cycle calculations.

With the implementation of the basic algorithm in real time, you must perform the entire computation time less than the minimum update time information of the source data calculations. To reduce the computational complexity of the basic algorithm, reducing the number of calculations and implement it in real in the time, you can optimize it as follows:

consistently decrease the interval partitioning the space of possible location of the object Δx; Δy;Δz. Initially, you can do the calculation with a large split, then on the border region of space specified location to do the calculation with a smaller break;

to use (or not use) conditions limits the location of the object associated with acceleration. If a priori it is known that a moving object has a positive acceleration (linear or angular), the equations associated with the acceleration can not be used. Then in the main computational procedure the basic algorithm will not nine, and six cycles of calculation.

Incoming data from on-Board gauges, wind sensors and navigation system can be discrete with a specific refresh rate, then to carry out the calculations necessary intervals minimum update frequency information onboard datalogger. If the data flows from the on-Board gauges are analog, the changes to such data and allocations can be performed at a given threshold changes such data (if the data format conversion is to install either the threshold or differential constraints). If the data flows are discrete and random (variable time is otopleniya information) changes to such data and allocations should be undertaken as soon as they come (in real time).

As an example, a suggested block diagram of the device with which it is possible to carry out the method of dynamic recurrent correction (Fig).

Data onboard gauges, wind sensors and navigation systems come in separate channels in the corresponding blocks of data format conversion 1, 2, and 3, respectively. Blocks 1-3 performs conversion of data from on-Board gauges, wind sensors and navigation systems for the processing of numerical data in the block of the on-Board computer 6. Next on separate channels of converted data in the unit of meter interval data 5, which is the formation of information about the time intervals of the data, and all data is synchronized in time with the help of the synchronization unit time calculations 4. From block 5 meter data in the block of the on-Board computer 6 (solver algorithm dynamic correction), which implements the algorithm of dynamic correction of the location of a moving object. From block 6 of the processed data are output, and written into the buffer memory in which is stored data of the previous change in the response.

For data format conversion (on the level and format) depending on the type of trip meter can be used ADC (analog output signals from the meters) or, if necessary, interface converters (for example, RS485/RS232 or similar). As a measure of time intervals you can use counters with a clock generators and holders of temporary provisions of the pulse. As the on-Board computer is used on-Board computer or a separate mini-computer.

In the process of calculation (at the above algorithm is correct the location of moving objects according to the results of the three navigation measurements), we obtain the area of the space Λ'_{CAR}_{WINDOWS}(p(0,95)), which is located within the volume of space Λ_{3}in the field of space, the third dimension is obtained values:

m=i...j is the index range of the x coordinate included in the space Λ'_{CAR}_{WINDOWS};

n=r...p - index range of y coordinates included in the space Λ'_{CAR}_{WINDOWS};

k=q...f - range index (z) belonging to the space Λ'_{CAR}_{WINDOWS}.

In this case, as a end result of increasing the processing accuracy of the navigation measurements with a probability of at least p(0,95) can be considered as geometricas the th middle of the adjusted region of space Λ'_{
CAR}_{WINDOWS}i.e. instead of the values of the third dimension

Block diagram (Fig) can be viewed as a pattern for the integration of the onboard measuring motion parameters of the object with the navigation system of the object.

Thus, the method of determining the location of an object in space according to the invention, updating the navigation data due to restrictions related to the dynamic properties of a moving object, allows you to:

to improve the accuracy of positioning the volume of the KTA in space;

- does not require additional navigation measurements or reference points with known geodetic coordinates, or a priori known trajectory of the object;

- can be used for different values of the velocities and angular displacements of the object;

is algorithmical and does not require complex computational procedures;

- allows you to kompleksirovat equipment onboard measuring motion parameters and navigation equipment. Allows to increase the reliability of detection of failures of onboard sensors of the motion parameters and navigation equipment.

The method of determining the location of a moving object in space, characterized in that exercise, at least three navigational measurements, which determine the coordinates of_{1}-t_{n}according to the navigation measurements determine the region Λ_{1}-Λ_{n}the space in which the object at time t_{1}-t_{n}:

where m=0...M=2h_{X}/Δx; n=0...N=2h_{Y}/Δ_{y}; k=0...K=2h_{Z}/Δz; m; n; k are integers (indices breakers coordinates),

h_{X}; h_{Y}; h_{Z}- the maximum error in measuring the coordinates of a moving body with a probability of at least p(0,95), i.e.,

Δx; Δy; ∆ - interval partitioning to achieve the required accuracy of the sampling space,_{1}-t_{n},

x_{1}...x_{n}, y_{1}...y_{n}, z_{1}...z_{n}data true position of the object at time t_{1}-t_{n},

when the navigation measurements to determine the following conditions:

- accuracy of each subsequent measurement and the actual measurement values do not depend on the results of previous measurements and their errors, they are statistically independent;

- the error of each measurement is not dependent on the location of the object in space, or such dependence in the framework of several consecutive measurements of the coordinates can be neglected and assume that h_{X}; h_{Y}; h_{Z}=const when several successive navigational measurements,

next determine the projected area of the space occupied by the object over the time interval ∆ T the parameters of the traffic restrictions that are determined by on-Board meters, located on the movable object, at the same time as parameters restrictions take:

- directional velocity V_{To}_{MAX}- maximum speed rate when the object is moving (at each stage of the movement);

- maximum directional acceleration*and*_{To}_{
- the maximum acceleration of the object on the course (at each stage of the movement);- maximum vertical velocity VBMAX;-aBMAX- the maximum vertical acceleration (at each stage of the movement);- the maximum change of the yaw angle ψMAXduring the time Δt between successive navigational measurements;- the maximum change of the pitch angle θMAXduring the time Δt between successive navigational measurements,and generalized conditions restrict the position of the object according to the navigation measurements and dynamic properties of the object expressed in the form of a system of inequalities:when you do this:the values of VMAX;aMAX; VB MAX;aB MAX; ΘMAX; ψMAXin the system of inequalities of generalized constraints the location of the object according to the navigation measurements with the influence of wind can be written as the readings of onboard datalogger as follows:where$${V}_{K}{}_{\text{}B\mathrm{And}}|{{}_{t=t}}_{{}_{K}{\text{}}_{B\mathrm{And}}\ge {t}_{2}}$$;$${V}_{K}{}_{\text{}B\mathrm{And}}|{{}_{t=t}}_{{}_{K}{\text{}}_{B\mathrm{And}}\ge {t}_{3}}$$- the value of the exchange rate on the testimony of an onboard meter at time of receipt of the information from the onboard meter immediately after the navigation measurements at the moments t2and t3;$${V}_{K}{}_{\text{}\mathrm{In}ET}|{{}_{t=t}}_{{}_{K}{\text{}}_{\mathrm{In}ET}\ge {t}_{2}}$$$${V}_{K}{}_{\text{}\mathrm{In}ET}|{{}_{t=t}}_{{}_{K}{\text{}}_{\mathrm{In}ET}\ge {t}_{3}}$$- component of the exchange rate due to the effects of wind (according to the sensors of the wind) immediatly after the navigation measurements at the moments t
2and t3;ΔVTo B- accuracy on-Board meter vehicle speed;$${V}_{\mathrm{In}}{}_{\text{}B\mathrm{And}}|{{}_{t=t}}_{{}_{K}{\text{}}_{B\mathrm{And}}\ge {t}_{2}}$$;$${V}_{\mathrm{In}}{\text{}}_{B\mathrm{And}}\text{}|{{}_{t=t}}_{{}_{K}{\text{}}_{B\mathrm{And}}\ge {t}_{3}}$$;$${V}_{\mathrm{In}}{}_{\text{}\mathrm{In}ET}|{{}_{t=t}}_{{}_{K}{\text{}}_{\mathrm{In}ET}\ge {t}_{2}}$$;$${V}_{\mathrm{In}}{}_{\text{}\mathrm{In}ET}|{{}_{t=t}}_{{}_{K}{\text{}}_{\mathrm{In}ET}\ge {}_{3}}$$; ΔVIn Bvalues of the vertical velocity on the testimony of an onboard meter, sensor data of the wind and the accuracy of the onboard meter vertical speed, all values are similar to values above values;$$\Delta {t}_{K\text{}B\mathrm{And}}=\left({t}_{K\text{}B\mathrm{And}}|{{}_{t=t}}_{{}_{K}{\text{}}_{B\mathrm{And}}\ge {t}_{3}}-{t}_{K\text{}B\mathrm{And}}|{{}_{t=t}}_{{}_{K}{\text{}}_{B\mathrm{And}}}{}_{\ge {t}_{2}}\right)$$- frequency update rate onboard meter vehicle speed;ΔtInBAnd=(tInBAnd|t=tIn
BAnd≥t3-tInBAnd|t=tInBAnd≥t2)- frequency update rate onboard meter vertical speed;$${\Theta}_{B\mathrm{And}}{}_{|t={t}_{\Theta}{\text{}}_{B\mathrm{And}}\ge {t}_{2}}$$;$${\Theta}_{B\mathrm{And}}|{{}_{t=t}}_{{}_{\Theta}{\text{}}_{B\mathrm{And}}}{{}_{\ge t}}_{{}_{3}}$$- the value of the angle of the object from the vertical (which actually determines the pitch angle) according to the indications of the on-Board meter immediately after the navigation measurements at the moments t2and t3;$${\Theta}_{\mathrm{In}ET}{}_{|t={t}_{\Theta}{\text{}}_{B\mathrm{And}}\ge {t}_{2}}$$;$${\Theta}_{\mathrm{In}ET}|{{}_{t=t}}_{{}_{\Theta}{\text{}}_{B\mathrm{And}}}{}_{\ge {t}_{3}}$$- component of the angle of inclination of the object from the vertical due to the influence of wind (according to the sensors of the wind) immediately after the navigation measurements at the moments t2and t3;ΔΘBthe accuracy of the onboard measuring the tilt angle of the object from the vertical;$${\Theta}_{B\mathrm{And}}{}_{|t={t}_{\Theta}{\text{}}_{B\mathrm{And}}\ge {t}_{2}}$$;$${\Theta}_{B\mathrm{And}}|{{}_{t=t}}_{{}_{\Theta}{\text{}}_{B\mathrm{And}}}{}_{\ge {t}_{3}}$$;$${\Psi}_{{}_{\mathrm{In}ET}}{}_{|t={t}_{\psi}{\text{}}_{B\mathrm{And}}\ge {t}_{2}}$$;$${\Psi}_{\mathrm{In}ET}|{{}_{t=t}}_{{}_{\psi}{\text{}}_{B\mathrm{And}}}{}_{\ge {t}_{3}}$$; ΔψBthe value of the deflection angle of the course readings, trip meter, sensor data of the wind and the accuracy of the onboard meter deflection angle of the course;ΛPR1- forecast at time t1the area of the space, which may take the moving body at time t2through Δt, lies within the cone formed by the tangent to the surfaces of the spheres Λ1and Λ2;next, the true, the extreme, the position of the rate increase at the maximum possible angle for the time Δt deviations of the object at the corners of the pitch and angle of the course, resulting in a gain projected space ΛAC2a possible location about the project at time t
2in the form of a convex elliptical cone with the angle of aperture θMAXand ψMAXand the height of the specified cone determine the maximum possible exchange rate movement speed of the object during the time Δt, and the true location of the object after the second navigational measurements over the interval Δt (space win) determine the intersection of the regions of spaceΛ2CO=ΛAC2∩Λ2∩ΛPR1,this joint probability is p(0,95)×p(0,95)=0,9025, and the space win ΛAC2∩Λ2∩ΛPR1should be increased in all three coordinates x; y; z within the space Λ2as a percentage equal to the percentage ratio of the random variable p(0,95)/p(0,9025), then carry out the correction of the location of moving objects according to the results of the three navigation measurements as follows:according to the results of the first and second navigational measurements by the above algorithm determines Λ2CO- win in determining the location after the second navigational measurements, the correction is carried out on speed and maximum angles of deflection;on the basis of the distribution law of a random variable - error navigation measurements - determine the area of the space Λ'2CO(p(0,95)) with probability not less than 0.95, the true position of the of the target Λ'
2CO(p(0,95)) is inside the space Λ2; when receiving data of the third navigation measurement region Λ3- determine the region ΛCAR- win in determining the location after the third navigation measurements, using as source data readings of the second and third measurements, the correction is carried out on speed and the maximum inclination angles, and as a source for predicting take area-adjusted space location of the object when the second navigational measurements Λ'2CO(p(0,95));then, on the basis of the distribution law of a random variable - error navigation measurements - determine the area of the space Λ'CAR(p(0,95)) with probability not less than 0.95, while Λ'CAR(p(0,95)) is inside the space Λ3,on the basis of all three navigation measurements again define the region ΛCAR USK- win in determining the location after the third navigation measurement, and the correction occurs for values of accelerations, and as a source for predicting accepted region Λ'2CO(p(0,95)) - already adjusted the amount of space possible location of the object at the time of the second navigational measurements;on the basis of the law is raspredeleniya random variables -
error navigation measurements - determine the area of the space Λ'CAR USK(p(0,95)) with probability not less than 0.95, while Λ'CAR USK(p(0,95)) is inside the space Λ3;determine the intersection volume of space found adjusted amounts of space location of the object Λ'CAR(p(0,95)) with Λ'CAR USK(p(0,95)), the space of intersection of these volumes ΛCAR WINDOWSwill be final adjusted position of the object at time t3;next, on the basis of the distribution law of a random variable - error navigation measurements - determine the area of the space Λ'CAR WINDOWS(p(0,95)) with probability not less than 0.95, while Λ'CAR WINDOWS(p(0,95)) is inside the space Λ3and for the space of the third dimension gain values of the index range of the coordinates x; y; z (i...j; r...p; q...f)within the space finally adjusted position of the object at time t3Λ'CAR WINDOWS(p(0,95)):m=i...j is the index range of the x coordinate included in the space Λ'CAR WINDOWS;n=r...p - index range of y coordinates included in the space Λ'CAR WINDOWS;k=q...f - range index (z) belonging to the space Λ'3 the PRS WINDOWS
,as a end result of the location of an object in space with a probability of at least p(0,95) consider the geometric middle of the adjusted region of space Λ'CAR WINDOWSwith the corrected coordinates x(j-i)/2; y(p-r)/2; z(f-q)/2.
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Device for determining coordinates based on satellite radionavigation systems gps/glonass // 2419103FIELD: physics.SUBSTANCE: device includes a GPS/GLONASS receiver, an antenna, a user interface (keyboard, display, sound), a communication interface, nonvolatile memory, a microcontroller, consisting of a unit for calculating the coordinate vector from code measurements, a unit for calculating the increment of the coordinate vector from phase measurements, a filter unit based on a least-square method, a unit for calculating a specified coordinate vector from the filtration results, a unit for working with interfaces, where the microcontroller includes a unit for analysing stability of the phase solution, a unit for evaluating duration of measurements and geometrical factor of the constellation of satellites, as well as a correcting unit consisting of a counter for counting stable solutions and a decision unit for deciding on continuing measurements, interfaces for time marking external events and outputting the second mark.EFFECT: highly accurate determination of coordinates of a receiver based on differential processing of phase measurements with complete elimination of phase ambiguity.1 dwg
Device for determining coordinates based on satellite radionavigation systems gps/glonass // 2419103FIELD: physics.SUBSTANCE: device includes a GPS/GLONASS receiver, an antenna, a user interface (keyboard, display, sound), a communication interface, nonvolatile memory, a microcontroller, consisting of a unit for calculating the coordinate vector from code measurements, a unit for calculating the increment of the coordinate vector from phase measurements, a filter unit based on a least-square method, a unit for calculating a specified coordinate vector from the filtration results, a unit for working with interfaces, where the microcontroller includes a unit for analysing stability of the phase solution, a unit for evaluating duration of measurements and geometrical factor of the constellation of satellites, as well as a correcting unit consisting of a counter for counting stable solutions and a decision unit for deciding on continuing measurements, interfaces for time marking external events and outputting the second mark.EFFECT: highly accurate determination of coordinates of a receiver based on differential processing of phase measurements with complete elimination of phase ambiguity.1 dwg
Universal high-performance navigation system // 2428714FIELD: physics.SUBSTANCE: navigation is performed using low earth orbit (LEO) satellite signals, as well as signals from two sources of ranging signals for determining associated calibration information, where a position is calculated using a navigation signal, a first and a second ranging signal and calibration information. Also possible is providing a plurality of transmission channels on a plurality of transmission time intervals using pseudorandom noise (PRN) and merging communication channels and navigation channels into a LEO signal. The method also involves broadcasting a LEO signal from a LEO satellite. Also disclosed is a LEO satellite data uplink. The invention also discloses various approaches to localised jamming of navigation signals.EFFECT: high efficiency and ensuring navigation with high level of integration and security.14 cl, 34 dwg
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