JP5566599B2 - Navigation system having a device for detecting inaccuracy - Google Patents

Description

The present invention relates to a navigation system provided with a device for detecting an inaccuracy.
[Cross-reference of related applications]
This application claims priority from US Provisional Patent Application No. 61 / 012,303, filed December 7, 2007, entitled “RAIM WITH SPATIALLY CORRELATED IONOSPHERIC ERRORS”. In the specification, it is incorporated by reference as if set forth in its entirety.

  The conventional RAIM algorithm can be based on either a weighted least squares solution or an unweighted least squares solution, in which case the error of each satellite's pseudo-range measurement is another There is no correlation with the error of the satellite pseudorange measurement.

  However, the ionospheric error within the pseudorange of each satellite (which is likely to be the dominant error source) is actually highly correlated with the respective ionospheric errors of other satellites. By ignoring this correlation, the calculated value of the horizontal protection limit (HPL) that limits the horizontal position error is much larger than the required value. As a result, there arises a problem that the GPS cannot be used in the method of Low Navigation Performance Requirements (RNP).

US Pat. No. 5,760,737 US Pat. No. 6,639,549

  The present invention aims to solve the above-mentioned problems.

  In one embodiment of the present invention, a navigation system for a vehicle having a receiver that is operable to receive a plurality of signals from a plurality of transmitters comprises a processor and a memory device. The memory device stores machine-readable instructions that, when executed by a processor, cause the processor to generate a set of error estimates corresponding to pseudorange measurements derived from a plurality of signals. Determining an error covariance matrix for the main navigation solution using ionospheric delay data and determining at least one protection level value based on the error covariance matrix using a parity space technique. to enable.

  Preferred and alternative embodiments of the present invention are described in detail below with reference to the following drawings.

1 is a diagram illustrating a navigation system incorporating an embodiment of the present invention. FIG. 6 is a diagram illustrating a process according to an exemplary embodiment of the present invention. The satellite for the most difficult satellite to detect in the presence of expected noise. It is a figure which shows the noise scattering which will arise when there is an alias. Maximum conversion-free fault parity error and horizontal position error at the time of fault of satellite k It is a figure which shows cloth.

  FIG. 1 illustrates a wireless navigation system incorporating the teachings of one embodiment of the present invention. This system includes several transmitters 1 -N and a user set 12. In the preferred embodiment, transmitters 1 -N are a subset of the satellite transmitter's NAVSTAR GPS constellation, with each transmitter visible from the antenna of user set 12. The transmitters 1 to N broadcast N individual signals indicating the individual transmitter positions and signal transmission times to the user set 12.

  User set 12 is attached to an aircraft (not shown) and includes a receiver 14, a processor 16, and a memory device such as processor memory 18. The receiver 14 is preferably NAVSTAR GPS compatible, receives signals, extracts position and time data, and provides pseudorange measurements to the processor 16. From the pseudorange measurements, the processor 16 derives a position solution for the user set 12. The satellite transmits its position in the 1984 World Geodetic System (WGS-84) coordinates, Cartesian Earth Centered Earth fixed coordinate system, but the preferred embodiment is horizontal to the northeast coordinate plane and to the Earth A position solution is obtained in the local reference system L that is in contact with each other. However, this coordinate system selection is not important because the method of converting coordinates between coordinate systems is well understood.

  The processor 16 also uses the pseudorange measurements to detect satellite transmitter failures and to determine the worst error, i.e., protection limit. Both are output by the processor 16 to the flight management system 20 along with the position solution. Flight management system 20 compares the protection limits with the alarm limits corresponding to a particular aircraft flight stage. For example, during the pre-landing flight phase, such as non-precise approach, the warning limit (or tolerance radius error) is 0.3 nautical miles, but during the less severe ocean flight phase, the warning limit is 2 nautical miles to 10 nautical miles. (For further details regarding these limitations, see RT-CA issued DO-208, incorporated herein by reference). If the protection limit exceeds the warning limit, the flight management system, or equivalent, will notify or notify the navigation display in the aircraft cockpit of the integrity failure. The processor also informs whether any satellite transmitter failure has been detected.

  One embodiment of the present invention models the correlation of ionospheric errors between each satellite pair as a function of the distance between their ionospheric pierce points. The closer the Pierce point, the greater the correlation. The root mean square (RMS) uncertainty (or σ) of each satellite's pseudorange measurements is calculated using the ionospheric dispersion model defined in DO-229D, Appendix J. An ionospheric measurement error covariance matrix is formed using the correlation coefficient and σ calculated for each satellite. The remaining errors (satellite clock and ephemeris, troposphere, multipath and receiver noise) are assumed to be uncorrelated. Therefore, the combined measurement error covariance matrix for these error sources is a diagonal matrix. These two matrices are added to form the total measurement error covariance matrix. This matrix is then inverted to form a weight matrix for finding the least squares solution. Fault detection and exclusion can then be performed and the horizontal protection level (HPL) based on the solution separation model already described in US Pat. Nos. 5,760,737 and 6,639,549. Various protection levels can be calculated, such as vertical protection level (VPL), horizontal exclusion level (HEL) and vertical exclusion level (VEL), which are described herein in their entirety. As if incorporated by reference.

  FIG. 2 shows a process 200 according to an embodiment of the invention that can be implemented in the wireless navigation system shown in FIG. The process 200 is shown as a set of operations or steps shown as individual blocks. The process 200 can be implemented in any suitable hardware, software, firmware, or combination thereof. Thus, process 200 can be implemented in computer-executable instructions that can be transferred from one electronic device to a second electronic device via a communication medium. The order in which the operations are described should not necessarily be construed as a limitation.

Referring to FIG. 2, in step 210, the processor 16 calculates σ (error) values for pseudoranges and measured values.
In step 220, the processor 16 determines a measurement matrix. The true vector of the pseudorange residual Δρ is related to the incremental position / time solution vector Δx (distance from the position linearization point) as follows:

In the equation, H is a measurement value matrix and is given by the following equation.

However, the following vectors are line-of-sight vectors pointing from the user to satellite i.

Also, the following equation is equal to true position / clock bias-linearization point.

  In step 230, the processor 16 calculates an error covariance matrix. Vector of measured pseudorange residuals

Is the true pseudorange residual vector + residual error vector δρ, and therefore:

  The processor 16 calculates the updated estimated value of Δx.

Is specified. In this case, the processor 16 can define the updated measurement residual vector as follows.

  Each updated measurement residual is the measured pseudorange residual and the updated estimate

Is the difference between the pseudorange residual predicted based on
"Weighted least squares solution" minimizes the weighted sum of the squared residuals

Can be determined by the processor 16 by finding the value of. Thus, the processor 16 can minimize the following equation:

Where W is an appropriate weight matrix. The generally selected weight matrix is a matrix that normalizes the residual based on the uncertainty of each pseudorange measurement. Therefore, processor 16 assumes the uncorrelated measurements and generates the following matrix:

This represents the inverse of the pseudorange measurement error covariance matrix, assuming that each pseudorange error is uncorrelated with the others.
However, the vertical ionospheric delay component of each pseudorange error is highly correlated with others. If this correlation is known, the processor 16 can use that knowledge by using the true pseudorange measurement error covariance matrix R. At that time, the weight matrix is as follows.

  Minimize (4)

The value of takes a derivative and it is equal to 0,

It is calculated by solving. As a result, the following expression is generated.

However, the processor 16 defines the weighted least square solution matrix S as follows.

To augment the altitude assisted GPS pseudorange measurement, the processor 16 can use the barometric altitude. When barometric altitude is used, the measurement matrix is expanded as follows.

  This measurement matrix assumes that the incremental position vector (first three elements) in Δx is given in local level coordinates (down on the z axis). In so doing, line-of-sight (LOS) elements must also be represented in local level coordinates. The weight matrix is also expanded as follows.

Compute the Measurement Covariance Matrix Many methods can be used to determine the measurement error covariance matrix. When applying the Kalman filter, the temporal behavior (time correlation) of the ionospheric delay can be modeled. The spatially correlated ionospheric error for satellite i is scaled by the nominal iono σ value for that satellite as follows: = 1.0) can be modeled as a weighted sum of Gaussian random errors.

_Where x _ref is a 3 × 1 vector of independent Gaussian random errors with an average of 0 and a variance of 1. Weight vector

Is defined by the processor 16 by first defining three grid points on the ionospheric thin shell model (at a height of 350 km) that are equally spaced azimuthally at a great circle distance of 1500 km from the user. Desired. The processor 16 can then define a 3 × 1 vector x _grid of normalized delays at these points. The delays at grid points i and j can be spatially correlated with each other based on the great circle distance between them according to the following equation:

Where
d _{grid_i, grid_j} = _Greater circle distance between grid point i and grid point j d _iono = correlation distance of ionospheric delay = 4000 km (13)
It is.

Using that relationship, the processor 16 can form a 3 × 3 covariance matrix P _grid describing the correlation between each grid point.

If the delay processes present at these grid points are some linear combination of reference independent Gaussian random errors, they have the desired spatial and temporal correlation. The processor 16 can assume that the desired linear combination is obtained by using the 3 × 3 upper triangular mapping matrix U _grid as follows.

  At that time, the grid covariance matrix is as follows.

Therefore, the mapping matrix U _grid can be formed by the processor 16 simply by factoring the covariance matrix P _grid . Since the geometry of the three grid points is fixed, the covariance matrix _Pgrid is constant and can therefore be precalculated by the processor 16. Here, the processor 16 can select a linear combination of three grid point delays, which produces a normalized delay at the Pierce point of satellite i, and thus three grid points (and therefore probably Appropriate spatial correlation with each of the other satellites) will be achieved as follows.

Where
k _sat — i — _grid = 3 vector of weighting factors δρ _norm — ion — _i = normalized delay at the satellite Pierce point.

  The satellite pseudorange delay can be correlated with the delay at the kth lattice point according to the following equation:

Where
d _{sat — i, grid} — _k = _greater circle distance between satellite pierce points and grid points d _iono = correlation distance of nominal ionospheric delay (18)
It is.

The 1 × 3 covariance matrix P _{sat_i_grid} defines the correlation between the satellite i and each lattice point, and is as follows.

Therefore, the weight vector k _{sat_grid} can be found by the processor 16 as follows.

  Combining (14) and (16), the processor 16 can obtain the normalized vertical delay directly from the three independent reference delays as follows.

  Therefore, the weight vector is:

  The processor 16 can form a vector of N normalized pseudorange iono delays from (21) as follows.

  By scaling the normalized delay by the σ value for that satellite based on the geomagnetic latitude of the Pierce point and the slope factor as defined in DO-229, the processor 16 follows the line of sight. The actual (unnormalized) delay can be obtained. In vector form, the processor 16 generates the following equation:

  The ionospheric delay error covariance matrix can be defined as follows:

The remainder of the pseudorange measurement error is assumed to be uncorrelated with the combined 1σ value represented by _{σother_i} for satellite i. For simplicity, the processor 16 can assume that the 1σ value per satellite is a constant 6 meters. At that time, the total measurement error covariance matrix is as follows.

  In the snapshot RAIM approach, the correlation between satellites is calculated directly without using a grid. Directly calculating the correlation between satellites is simpler than using a grid and may be slightly more accurate.

  Specifically, the ionospheric error covariance can be modeled as a function of the great circle distance between Pierce points along the ionospheric shell (above 350 km above the ground).

Where
d _ij = _Greater circle distance between Pierce points for satellites i and j d _iono = uncorrelated distance = 4000 km
It is.

  Ionospheric errors are highly correlated. Therefore, the following equation holds.

However, the following two expressions hold.

Error Covariance for Weighted Least Squares Solution At step 240, processor 16 calculates a weighted least squares solution. The error in the post-update solution is as follows.

  Substituting (2) into (27) generates the following expression.

  Thus, the solution matrix S maps the pseudorange error to the updated solution error vector. The solution error covariance matrix can be defined as follows:

  The x and y horizontal position errors are statistically described by the upper 2 × 2 portion of P. The major and minor axes of the horizontal position error ellipse are equal to the square root of the maximum and minimum eigenvalues of this 2 × 2 matrix and represent 1σ error in the corresponding direction. Thus, the 1σ error in the worst direction is given by:

  The 1σ error at the vertical position is given by:

  The horizontal figure of merit is a conservative 95% fault free error limit and can be calculated by the processor 16 as a 2D RMS error from the error covariance matrix.

  Similarly, the vertical figure of merit can be calculated by the processor 16 as a 2σ vertical error from the error covariance matrix.

Parity space RAIM
In step 250, the processor 16 calculates at least one protection level value. In doing so, the processor 16 can utilize parity space techniques. Recall that the weighted least squares solution can be expressed as:

  A correlated measurement set can be converted by processor 16 into an uncorrelated set by factoring weight matrix W using matrix factorization methods known in the art.

  Where L is the lower triangular square root of W. As a result, the following expression is generated.

Where

  The covariance of the converted measurement error is as follows:

  Thus, it is clear that the converted measurements are uncorrelated and each have unit variance. By multiplying the measurement equation of the present invention by L, the processor 16 obtains the following equation:

  The processor 16 can find an N × N orthogonal matrix Q such that the following relationship holds:

  Thus, when the processor 16 multiplies the measured value expression by Q, the following expression is obtained as a result.

  Where A is the 4 × N portion above Q and B is the lower (N−4) × N portion. As a result, the following two expressions hold.

  By using the first equation and setting the pseudorange error to 0, the estimated least squares solution can be determined.

This equation is more efficient than the equation given earlier because it only requires reversing the upper triangular matrix.
The second equation gives a parity vector p that is a non-zero value only when there is a pseudorange error. In the absence of a failure, the parity covariance is

Thus, the parity element is also an uncorrelated cello-mean Gaussian random variable with unit variance.
In one embodiment, processor 16 utilizes a chi-square method using the p-bias concept. In such an embodiment, the processor 16 uses the square of the parity amount as the discriminator (statistical test amount) d as follows.

  In this case, the discriminator has a central chi-square distribution having N-4 degrees of freedom. The processor 16 sets a threshold for this discriminator and a failure is declared if it is higher than that threshold. This threshold D is calculated by the processor 16 from a chi-square probability density function to generate an acceptable error warning probability.

  Once the threshold is set, the matter to consider is generated as a result, satisfying the probability of missing detection if the discriminator has just reached the threshold as a result of a single satellite failure. This is how large the position error may be. As a result of the bias fault ε in the k-th satellite, the following solution error and parity error occur.

  Thus, the parity bias is related to the horizontal position error through the following gradient function:

The satellite with the largest gradient is the most difficult to detect. This gradient is called Slope _max . FIG. 3 represents noise scatter that would only occur if there was a bias for the most difficult satellite to detect in the presence of expected noise. The particular bias that results in a portion of the data to occur to the left of the detection threshold D equal to the probability of missing detection is of particular consideration. The amount of parity associated with this bias is called “p-bias”.

  When there is a bias, the discriminator (parity squared) has a non-central chi-square distribution with N-4 degrees of freedom. It can be shown that the non-centrality parameter λ of the chi-square distribution is:

Therefore, using the non-central chi-square probability density function, the processor 16 can determine a value for the p bias that satisfies the required value of the probability of missing detection.
At that time, the horizontal protection level (HPL) is as follows.

Gaussian Method with Parity Space Rotation Referring to FIG. 4, through further orthogonal transformations, one embodiment ensures that the parity error due to the bias failure of satellite k is completely along axis 1 of the parity space. The parity space can be rotated.

  Since the bias only appears on axis 1, the result is a scalar and the discriminator can generally be determined by the processor 16 using the following equation:

  In the absence of a fault, there is only a correlated random error w.

  If there is a correlated random error w at each satellite in addition to a bias fault at satellite k, the discriminator can be determined by processor 16 using the following equation:

  In addition to failure, the effect of noise on the horizontal position is as follows.

Where ^Sh and

Are S and

The first two lines of

Is the column k of ^{S h.}
Using a Gaussian probability density function, a threshold D that satisfies the error warning probability can be determined by the processor 16. Upon detection, the discriminator amount is equal to the threshold value.

  Assuming the fault is positive and much larger than the noise, the following equation holds:

  The resulting horizontal position error can be determined by processor 16 using the following equation:

  The positional error amount in the direction of the failure is as follows.

  Since the random pseudorange error has no correlation with the unit variance, the variance of the noise term for the mean can be determined by the processor 16 using the following equation:

  The horizontal protection level for satellite k can be determined by processor 16 using the following equation:

In the equation, K _md and K _fa are σ multipliers set to satisfy the probability of error warning and the probability of missing detection.
This process is repeated for all N satellites and the processor 16 can determine the total HPL using the following equation:

Ionospheric Error Model Calculation Determination of Ionospheric Lattice Point and Pierce Point Coordinates In the case of the Kalman filter method and in order to use (17), processor 16 first determines the coordinates of each lattice point and the coordinates of the ionospheric pierce point of the satellite. can do. Then, using these two sets of coordinates, the processor 16 can calculate the great circle distance between the Pierce point and the grid point. For either Kalman filter or snapshot RAIM approaches, the coordinates of point i (eg, the system shown in FIG. 1, or “user”), and the distance from point i to point j (eg, a grid point) and When the azimuth is known, the processor 16 can determine the coordinates of the point j as follows.

Where
λ _i = Geodetic latitude of point i λ _j = Geodetic latitude of point j Λ _i = Geodetic longitude of point i Λ _j = Geodetic longitude of point j A _ij = Azimuth angle from point i to point j (azimuth)
ψ _ij = angle from point i to point j (center angle of the earth)
= D _ij / (R _e + h _I )
d _ij = Greater circle distance from point i to point j R _e = Earth radius = 6378 km
h _I = height of ionosphere thin shell model = 350 km
It is.

The coordinates of the ionosphere pierce point of the satellite can also be calculated using (A.1) and (A.2). In this case, ψ _ij represents the central angle from the user position to the Pierce point, and can be calculated by the processor 16 as follows.

Where E is the elevation angle of the satellite from the user position relative to the local tangent plane.
Calculate the elevation angle and azimuth angle of the satellite The elevation angle E of the satellite is defined as the angle that the line-of-sight vector forms with the local tangent plane (horizontal plane) of the user. The satellite azimuth A is the angle of the line-of-sight vector relative to true north, as measured in the horizontal plane. Therefore, the following relationship holds.

Where

The prospect vector

X component, y component, and z component, and α is a wonder angle (azimuth from north to x local level coordinate axis).
Note that the azimuth is adjusted by ± 2π so that the result is between −π and + π.
Determination of great circle distance The great circle distance along the ionosphere shell model from point i (eg, satellite pierce point) to another point j (eg, lattice point) is calculated by processor 16 as follows: be able to.

Where

It is.
Ionosphere Dispersion Model Algorithms that can be executed by processor 16 to calculate ionosphere model error variance are described in ICD-GPS-200C and DO-229D J. Org. It may be derived from 2.3. Note that the symbols in this section are unique to this section.

Using the elevation angle E of the satellite, the center angle ψ _pp of the earth between the user position and the ground projection position of the ionosphere pierce point is formed by using the equation (A.3).
Next, using the equations (A.1) and (A.2) using the satellite elevation angle E, azimuth angle A, earth center angle ψ _{pp and} user geodetic latitude λ _u and longitude Λ _u , Pierce Point geodetic latitude φ _pp and longitude λ _pp are obtained.

  Form the absolute value of the geomagnetic latitude of the ionosphere Pierce point.

  An estimate of the vertical delay error is formed based on the geomagnetic latitude.

  The square of the slope coefficient is calculated using the elevation angle E.

  Form a modeled estimated variance of ionospheric delay.

  Use the compensation value applied when available from the receiver to form the estimated variance (assuming 0 if not available).

  Form an estimated variance of the ionospheric delay.

  While the preferred embodiment of the invention has been illustrated and described, as noted above, many changes can be made without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is not limited by the disclosure of the preferred embodiment. Instead, the invention should be determined by reference to the following claims in their entirety.

Claims (10)

A vehicle navigation system (12) having a receiver (14) operable to receive a plurality of signals from a plurality of transmitters, the navigation system (12) comprising:
A processor (16);
A memory device (18) storing machine-readable instructions;
When the instructions are executed by the processor (16), the processor (16)
Measuring a pseudorange residual derived from the plurality of signals to determine a set of error estimates corresponding to the measured pseudorange residual ;
Calculate a weighted least squares solution that minimizes the weighted sum of the squared residuals using a measurement error covariance matrix that includes off-diagonal elements that represent ionospheric delay spatial correlation data and the corresponding solution error Rukoto to calculate the covariance matrix, and using the parity space technique, based on the measurement error covariance matrix, enabling the determination of the at least one protection level values, navigation system. The Rukoto to compute the solution error covariance matrix is associated with each of said transmitters comprises determining the ionospheric error is spatially correlated, according to claim 1 system. The Rukoto to compute the solution error covariance matrix includes defining a plurality of grid points on the thin shell model of the ionosphere, according to claim 2 system.   The system according to claim 3, wherein the defined grid points are equally spaced in the azimuth direction at great circle distances from the system (12).   The system of claim 4, wherein the great circle distance is 1500 km. Rukoto to calculate the solution error covariance matrix includes defining a vector of normalized ionospheric delay in the lattice points, the system of claim 3.   The system of claim 1, wherein the at least one protection level value comprises a horizontal protection level value.   The system of claim 1, wherein the at least one protection level value comprises a vertical protection level value.   The system of claim 1, wherein the at least one protection level value comprises a horizontal exclusion level value. A computer readable medium (18), the computer readable medium comprising:
Measuring a pseudorange residual derived from a plurality of signals to determine a set of error estimates corresponding to the measured pseudorange residual ;
Modeling spatially correlated ionospheric errors for multiple signals from each of multiple satellites;
Calculate a weighted least squares solution that minimizes the weighted sum of the squared residuals using a measurement error covariance matrix that includes off-diagonal elements representing ionospheric delay spatial correlation data and the corresponding solution error Rukoto to calculate the covariance matrix,
Computer-executable for performing steps including determining at least one protection level value based on the solution error covariance matrix using a parity space technique and displaying the at least one protection level value A computer readable medium having instructions.

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