Method for difference-range-finding location of receiver cartesian co-ordinates

FIELD: submarine, marine terrestrial and close-to-ground navigation, in particular type GPS and GLONASS systems.

SUBSTANCE: at a time instant, that is unknown for the receiver, a signal is synchronously radiated by several radiators with known co-ordinates. The radiated signals are received by the receiver, the signal speed square is measured in the current navigation session, the Cartesian co-ordinates of the receiver are computed according to the moments of reception of the radiated signal and the measured signal speed square.

EFFECT: enhanced precision of location of the signal receiver.

2 dwg

 

The invention relates to the field of underwater, marine, terrestrial, and terrestrial navigation, particularly, those using satellite navigation systems GPS and GLONASS.

There is a method of determining the coordinates of the receiver (see Anderson E. the Principles of navigation. - M.: Voenizdat, 1968, s), consisting in the measurement of two or more sequences, the time difference, which find directly on the map, which caused two or more collections of hyperbole in accordance with the difference of time.

The disadvantage of this method is that it applies only in the planar case and thus has low accuracy as graphical method.

The closest to the technical nature of the claimed invention is a method differential-ranging determining the spatial coordinates of the receiver (see Soloviev V.A. satellite navigation System. - M..: Eco-Trends, 2000, p.35-36), including simultaneous emission of a signal at an unknown point in time, multiple beacons-emitters with known coordinates and the subsequent calculation of the coordinates of the receiver on the moments of reception of the signal at a given speed signal. At the same time to improve the accuracy using an excessive number of emitters (e.g., five in the three-dimensional positioning) and iterative least squares Gow is sa-Newton.

The disadvantage of this method is the inevitable presence of systematic errors due to the a priori assignment of the speed signal. Signal in an inhomogeneous medium passes from each of the beacons its curved path, and the physical conditions in each of their own ways. Accordingly, any a priori assignment of the speed signal contains an implicit averaging, based on certain navigation conditions, does not necessarily coincide with the terms of this navigation session. This becomes the source of poorly controlled systematic errors of the method. To improve accuracy for satellite systems impose different atmospheric corrections, however, many researchers note that they sometimes even worsen the results (see Serapinas B.B. Global positioning system. - M.: the IPC Directory, 2002, p.45).

The present invention is to improve the accuracy of positioning of the receiver.

This is achieved in that in the method of determining the Cartesian coordinates of the receiver, which consists in the simultaneous emission of a signal at an unknown point in time, multiple emitters with known coordinates with the subsequent calculation of the coordinates of the receiver on the moments of the reception signal at the time of reception of the signal from the last emitter measure the square of the speed with which they persecuted the time of reception of the signal in the current navigation session.

Measuring the square of the speed signal at the time of reception of the signal in the current navigation session, in fact, define the effective speed of the signal. Possible as flat (typical for marine and land navigation), and three-dimensional (typical for submarine and satellite navigation) implement the method. Let n be the dimension of the space Rnin which positioning, n=2, 3. To implement the proposed method requires at least n+2 beacon emitter. Unknown column Cartesian coordinates x∈Rnreceiver, unknown time τ simultaneous radiation and unknown speed signal are related to the n+2 equations

where aj∈Rn- known location of the j-th emitter.

Without limiting the generality of the place

, t0=0,

where- zero column. Then the original system can be written in equivalent form as

where x2=xTx - scalar square (•)T- transpose operation.

Subtracting the first equation (2) from the remaining equations (3), we obtain the subsystem

In the new unknown variables

θ=c2τ, x κ=C2

systems is (2), (3), (4) is equivalent to the system

Let L be the matrix of coefficients of linear (n+1)×(n+1) system of equations (6) relative to column X=(θ,xt)tthat θ=X0column u consists of aj2and the column ν consists of (-tj2), j=1, ...,n+1. Then from (6) X=U+k·V, where U=L-1·u, V=L-1·ν. Denoting p=U0q=V0, Ri=Ui, Qi=Vi, i=1, ..., n, we get

After substituting (8), (9) in (5) we obtain a cubic with respect to the equation

Q2κ3+(2PTQ-q22+(R2-2q)κ-R2=0.

Let κ1that κ2that κ3his roots. From these roots is selected root κ*closest to par. In the end, the desired x is calculated by the formula

x=R+κ*·Q+a0.

Below is MathCAD procedure X(t) processing column t of the moments of the reception signal in the proposed method. Figure 1 shows the model configuration differential-ranging system with parameters close to the satellite radio navigation system. Figure 2 shows a graph of the relationship of the accuracy of the prototype method to the proposed method, depending on the relationship to the accuracy of the speed signal to the precision of the watch receiver.

Glazeware of the proposed method with the known method was used simulation model in MathCAD 11 (see the following procedure SS). In this model, for an arbitrary configuration 5 beacon emitters and receiver in three-dimensional space compared to the work of well-known methods with the proposed method with the same input data. For specific configuration parameters close to satellite radionavigation system, when five satellites - the vertices of the hexagon, two of them are in the Zenith, the receiver on the Earth's surface, the origin in the center of the Earth (see figure 1 and the original data, the result of the comparison methods were as follows. In real terms that the root mean square error (RMSE) measure the time the GPS receiver is σt=0.001 Ás and standard deviation of the speed of light there σc- 0.0001 m/Ás (see Berliawsky physics course. Volume 1. The H. Kittel, knight, U., Ruderman, M. Mechanics - M.: Nauka, 1975, s-342) the accuracy of the proposed method is superior to the accuracy of this method in the s=6 times according to the results of 100 simulation trials using the procedure SS.

The graph of s=s(γ), where

shown in figure 2. From this graph, it follows that the proposed method is more accurate known method, the more accurate the clock of the receiver with respect to the accuracy of a priori assignment of the speed signal.

To play the MathCAD calculation you want to perform the standard initial installation of the sensor the random number ka, it is necessary to enter in the window menu Tools/Worksheet options/Built-in Variables and activate the Restore Defaults option.

Five beacons in three-dimensional space, the proposed method leads to a simple finite algorithm, whereas the known method requires an iterative algorithm, the precision of which depends on the initial approximation. This quality of the proposed method gives, in addition, higher performance and reliability compared to the prototype.

The method of difference-ranging definition of the Cartesian coordinates of the receiver, which consists in the simultaneous emission of the signal is unknown to the receiver point multiple emitters with known coordinates and receiving radiated signals, the receiver with the subsequent calculation of the coordinates of the receiver, wherein the measure of the square of the velocity signal in the current navigation session, and the Cartesian coordinates of the receiver calculated by the moments of reception of the emitted signals and the measured square of the speed signal.



 

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SUBSTANCE: the legitimate signal in the digital correlator is detected by the hardware, which makes it possible to relieve the load of the processor and use its released resources for solution of additional problems. The digital correlator has a commutator of the SPNS signals, processor, digital mixers, digital controllable carrier-frequency oscillator, units of digital demodulators, accumulating units, programmed delay line, control register, digital controllable code generator, reference code generator and a signal detector. The signal detector is made in the form of a square-law detector realizing the algorithm of computation of five points of the Fourier sixteen point discrete transformation with additional zeroes in the interval of one period of the, c/a code with a subsequent computation of the modules of the transformation results and their incoherent summation and comparison with a variable threshold, whose value is set up depending on the noise power and the number of the incoherent readout. The signal detector has a controller, multiplexer, complex mixer, coherent summation unit, module computation unit, incoherent summation unit, noise power estimation unit, signal presence estimation unit and a unit for determination of the frequency-time coordinates of the global maximum.

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FIELD: submarine, marine terrestrial and close-to-ground navigation, in particular type GPS and GLONASS systems.

SUBSTANCE: at a time instant, that is unknown for the receiver, a signal is synchronously radiated by several radiators with known co-ordinates. The radiated signals are received by the receiver, the signal speed square is measured in the current navigation session, the Cartesian co-ordinates of the receiver are computed according to the moments of reception of the radiated signal and the measured signal speed square.

EFFECT: enhanced precision of location of the signal receiver.

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