Integrity monitoring of primary parameters and derived parameters

Abstract

The present invention is entitled "Integrity Monitoring of Primary and Derived Parameters." Systems and methods for integrity monitoring of primary and derived parameters are described herein. In certain embodiments, a method includes converting an estimated error state covariance matrix of at least one primary integrity monitoring parameter of a navigation system to an error state covariance matrix of one or more derived integrity monitoring parameters, wherein the one or more derived integrity monitoring parameters are dependent on the at least one primary integrity monitoring parameter. The method also includes converting an integrity threshold of the at least one primary integrity monitoring parameter to a separation parameter of the one or more derived integrity monitoring parameters. The method also includes calculating a protection limit for the one or more derived integrity monitoring parameters.

Description

Background Art

[0001] The Global Navigation Satellite System (GNSS) is a space-based system of satellites that provide autonomous geospatial positioning with global coverage. Generally speaking, a GNSS allows a receiver to determine its position using time signals sent from satellites along a line of sight. The Global Positioning System (GPS) is a GNSS maintained by the US government and can be used by anyone with a GPS receiver. Similarly, GLONASS is a navigation satellite system maintained by Russia. The Galileo system is another GNSS developed by the European Union (EU) and the European Space Agency (ESA). COMPASS (Beidou) is a navigation satellite system developed by China.

[0002] GNSS provides position information anywhere on or near Earth where there is an unobstructed line of sight to four or more GNSS satellites. A processor coupled to a GNSS receiver uses at least four of the distances from the receiver to the satellites, called pseudoranges, to accurately approximate the receiver's position. The accuracy of the approximated position, or position solution, varies due to changing atmospheric conditions that affect the signal-to-noise ratio and signal transmission time. Accuracy also varies due to the fact that orbiting satellites occasionally experience extended outages during which they continue to operate while providing erroneous or excessively noisy signals. These and other factors manifest as random noise in the transmitted signals, random errors in the calculated pseudoranges, and ultimately, random errors in the position solution itself.

[0003] GNSS-based aircraft navigation systems typically include a subsystem for integrity monitoring. Integrity is a measure of the confidence that can be placed in the correctness of the information supplied by the navigation system. Integrity includes the system's ability to provide effective warnings to the user in a timely manner (within limits specified in the warning time) when the system cannot be used for the intended operation (or flight phase). As part of these warnings, the system can calculate one or more protection limits. In order for the integrity to be considered usable for a specific flight phase, the protection level should be less than the warning limit specified for this flight phase. If the protection level exceeds the allowed warning limit, this means that the navigation system does not provide the required integrity and cannot be used further. Summary of the Invention

[0004] Systems and methods for integrity monitoring of primary and derived parameters are described herein. In certain embodiments, a method includes converting an estimated error state covariance matrix for at least one primary integrity monitoring parameter of a navigation system into an error state covariance matrix for one or more derived integrity monitoring parameters, wherein the one or more derived integrity monitoring parameters are dependent on the at least one primary integrity monitoring parameter. The method also includes converting an integrity threshold for the at least one primary integrity monitoring parameter into separate parameters for the one or more derived integrity monitoring parameters. The method also includes calculating protection limits for the one or more derived integrity monitoring parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Understanding that the drawings depict only some embodiments and are therefore not to be considered limiting in scope, exemplary embodiments will be described with additional specificity and detail using the accompanying drawings, in which:

[0006] Figure 1 is a block diagram illustrating an exemplary system for integrity monitoring of primary and derived parameters according to an aspect of the present disclosure;

[0007] Figure 2 is a flow chart illustrating an exemplary method for integrity monitoring of primary and derived parameters according to an aspect of the present disclosure;

[0008] Figure 3 is a flow chart illustrating another exemplary method for integrity monitoring of primary and derived parameters according to an aspect of the present disclosure; and

[0009] Figure 4 is a flow chart illustrating an additional exemplary method for integrity monitoring of primary and derived parameters according to an aspect of the present disclosure.

[0010] According to common practice, the various features described are not necessarily drawn to scale, the emphasis instead being placed on specific features relevant to the example embodiments. DETAILED DESCRIPTION

[0011] In the following detailed description, reference is made to the accompanying drawings which form a part hereof, and in which are shown by way of illustration specific illustrative embodiments. However, it is to be understood that other embodiments may be utilized and that logical, mechanical, and electrical changes may be made.

[0012] As described above and used herein, integrity is a measure of the level of confidence that can be placed in the correctness of information supplied by a navigation system. A system performing integrity monitoring can monitor the integrity of various measurements during operation of the navigation system. To perform integrity monitoring, the system can implement an integrity monitoring algorithm.

[0013] In certain embodiments, the integrity monitoring algorithm is based on a solution separation approach. In the solution separation approach, the system determines a full solution and one or more sub-solutions, where the full solution is calculated based on information obtained from a set of information sources, and the sub-solutions are calculated based on information obtained from a subset of the set of information sources. Using the full solution and the sub-solutions, the system can determine the integrity of the full solution.

[0014] The solution separation method described above can be used to determine the integrity of a position solution calculated based on information acquired from navigation satellites. For example, a master position solution can incorporate a set of pseudoranges from available satellites integrated with inertial sensor measurements, while a sub-solution can be based on a subset of pseudoranges from available satellites. The system can then determine a protection limit for the master position solution based on the difference, or separation, between the master and sub-solutions.

[0015] In certain embodiments, the system can perform integrity monitoring using a solution separation approach for a defined set of primary parameters. Primary parameters can be parameters for which the system directly performs fault detection and troubleshooting. When the system calculates navigation parameters, the system can calculate protection limits for the primary navigation parameters. Examples of primary navigation parameters can include horizontal position, vertical position, horizontal velocity, vertical velocity, roll angle, pitch angle, and true heading angle.

[0016] In some embodiments, it may be desirable to determine parameters in addition to the primary parameters. For example, a system that calculates navigation parameters may attempt to determine additional navigation parameters, which may include body longitudinal velocity, body lateral velocity, body normal velocity, magnetic track angle, yaw angle, (hybrid) flight path angle, along-course velocity, true track angle, and cross-course velocity. However, calculating additional parameters may increase the amount of fault detection and troubleshooting performed by a particular system. Therefore, the systems and methods described herein derive integrity monitoring parameters for the additional parameters from the primary integrity monitoring parameters for which the system has performed fault detection and troubleshooting.

[0017] Figure 1 A navigation system 110 is shown according to one embodiment, which can implement the method for deriving integrity monitoring parameters from primary integrity monitoring parameters described herein. The navigation system 110 can be mounted on a vehicle, such as an aircraft, spacecraft, automobile, or other mobile vehicle. Additionally, the navigation system 110 can obtain navigation information from one or more different sources. To process the obtained navigation information, the navigation system 110 can include at least one processor 116 and at least one memory unit 118.

[0018] In some embodiments, the navigation system 110 can acquire navigation information including inertial motion information and GNSS measurements. To obtain inertial motion information, the navigation system 110 can include an inertial sensor 120 that measures and senses the inertial motion of a vehicle containing the navigation system 110. To obtain GNSS measurements, the navigation system 110 can include a satellite receiver 112 having at least one antenna 114 that receives satellite signals from GNSS satellites. Additionally, the navigation system 110 can include one or more other sensors 122 that can provide additional sensor data to the processor 116. Examples of other sensors 122 can include an altitude sensor, an electro-optical sensor, or a magnetometer, among others.

[0019] During operation, the satellite receiver 112 can receive satellite signals (such as GNSS signals), extract position and time data from the signals, and provide pseudorange measurements to the processor 116. From the pseudorange measurements and inertial measurements, the processor 116 derives position, velocity, and attitude solutions. The processor 116 can also use the pseudorange measurements to detect satellite transmitter failures and determine worst-case error or protection limits. The processor 116 can then provide the protection limits along with the position solution to the vehicle management system 130. The vehicle management system 130 can compare the protection limits with warning limits for the specific vehicle that includes the navigation system 110.

[0020] The processor 116 or other computing devices used in the present systems and methods may be implemented using software, firmware, hardware, or any suitable combination thereof. The processor 116 and other computing devices may be supplemented by or incorporated into a specially designed application-specific integrated circuit (ASIC) or field-programmable gate array (FPGA). In some implementations, the processor 116 and / or other computing devices may communicate with other computing devices external to the navigation system 110 via an additional transceiver. The processor 116 and other computing devices may also include or operate with software programs, firmware, or other computer-readable instructions to perform the various processing tasks, calculations, and control functions used in the present methods and systems.

[0021] The present method can be implemented by computer-executable instructions (such as program modules or components) executed by at least one processor. Typically, program modules include routines, programs, objects, data components, data structures, algorithms, etc. that perform specific tasks or implement specific abstract data types.

[0022] The instructions for performing the various process tasks, calculations, and generation of other data used in the operation of the methods described herein can be implemented in software, firmware, or other computer-readable instructions. These instructions are typically stored on any suitable computer program product that includes a computer-readable medium for storing computer-readable instructions or data structures. Such a computer-readable medium can be any available medium that can be accessed by a general-purpose or special-purpose computer or processor or any programmable logic device.

[0023] Suitable computer-readable storage media may include, for example, nonvolatile memory devices, including semiconductor memory devices, such as random access memory (RAM), read-only memory (ROM), electrically erasable programmable ROM (EEPROM), or flash memory devices; magnetic disks, such as internal hard disks and removable magnetic disks; optical disk storage devices, such as compact disks (CDs), digital versatile disks (DVDs), Blu-ray disks; or any other medium that can be used to carry or store desired program code in the form of computer-executable instructions or data structures.

[0024] In certain embodiments, the processor 116 may use a solution separation method to receive GNSS signals and monitor integrity monitoring parameters. As described above, in the solution separation method, a set of test statistics can be formed by the difference between the calculated full solution position and each calculated sub-solution position. The processor 116 can calculate a set of decision thresholds based on the statistics of the separation between the full solution position and the sub-solution position. The full solution provides a position estimate calculated using all available satellite measurements (pseudoranges). In contrast, the set of sub-solutions provides an estimate using a subset of available satellite measurements defined according to a specified fault state. For example, under the assumption that only one satellite can be in failure at any given time and N satellite measurements are available, there will be N statistics to test and N sub-solutions, where each sub-solution position is calculated by removing a different measurement. Therefore, the solution separation method is an integrity method that works in the position domain and can be used by the processor 116 in the navigation system 110 to determine the integrity of the measured parameters calculated by the pseudoranges.

[0025] Using the decoupling method, the processor 116 can perform integrity monitoring on primary integrity monitoring parameters. As used herein, a primary integrity monitoring parameter (also referred to as a primary parameter) can be a parameter for which the processor 116 directly performs fault detection and troubleshooting independently of other primary integrity monitoring parameters. For example, the processor 116 can perform integrity monitoring on the following primary integrity monitoring parameters: horizontal position, vertical position, horizontal velocity, vertical velocity, roll angle, pitch angle, and true heading angle.

[0026] In certain embodiments, the processor 116 may monitor the integrity of parameters other than the primary integrity monitoring parameters described above. For example, the processor 116 may monitor parameters that may include body longitudinal velocity, body lateral velocity, body normal velocity, magnetic track angle, yaw angle, (hybrid) flight path angle, along-course velocity, true track angle, and cross-course velocity. Further, the processor 116 may monitor these additional parameters based on monitoring the primary integrity monitoring parameters. Therefore, as used herein, integrity monitoring parameters that are fully algebraically derived from the primary integrity monitoring parameters may be referred to as derived integrity monitoring parameters. Because fault detection and troubleshooting are performed on the primary integrity monitoring parameters and the derived integrity monitoring parameters are derived from the primary integrity monitoring parameters, fault detection and troubleshooting need not be performed on the derived integrity monitoring parameters. In some embodiments, protection limits may be calculated for the derived integrity monitoring parameters. In some embodiments, a set of primary integrity monitoring parameters may be expanded to ensure full algebraic dependence of the derived integrity monitoring parameters on the primary integrity monitoring parameters.

[0027] In some embodiments, the processor 116 may determine the protection limits of the derived integrity monitoring parameters by converting the estimated error state covariance matrix of one or more primary integrity monitoring parameters into the error state covariance matrix of the desired derived integrity monitoring parameters. For example, when converting the primary integrity monitoring parameters into the derived integrity monitoring parameters, the processor 116 may calculate the Jacobian, where the Jacobian is the matrix of first-order partial derivatives of the function that converts the primary integrity monitoring parameters into the derived integrity monitoring parameters. Using the calculated Jacobians, the processor 116 may then convert the covariance matrix of the primary integrity monitoring parameters into a covariance matrix for the derived integrity monitoring parameters. Additionally, the processor 116 may convert the integrity thresholds of the primary integrity monitoring parameters into separation parameters for the derived integrity monitoring parameters. Further, the processor 116 may also calculate the protection limits for the derived integrity monitoring parameters. Figure 2 and Figure 3 The calculation of the protection limits of the derived integrity monitoring parameters is described in more detail.

[0028] Figure 2Flowchart of an exemplary method 200 for calculating protection limits for derived integrity monitoring parameters. As described herein, method 200 may be performed by processor 116. However, method 200 may be performed by a different processor on navigation system 110 or another processor as part of a system in communication with navigation system 110. In certain embodiments, method 200 continues at 202 where primary integrity monitoring parameters are acquired. As described above, the integrity monitoring parameters are calculated based on the measurements. For example, the primary integrity monitoring parameters may include horizontal position, vertical position, horizontal velocity, vertical velocity, roll, pitch angle, and true heading angle.

[0029] When calculating the primary integrity monitoring parameter, the processor 116 on the navigation system 110 may obtain pseudorange measurements from the receiver 112. The processor 116 may determine the number of satellite transmitters in communication with the navigation system 110, where the number of satellites changes as satellites move in and out of view of the receiver 112 and as satellites fail or otherwise become unavailable. Furthermore, the processor 116 may obscure certain satellites. In some embodiments, after determining the number of satellite transmitters, the processor 116 may integrate the pseudorange measurements using a Kalman filter to obtain a position solution for the navigation system 110.

[0030] In another embodiment, processor 116 may use pseudorange Kalman filter innovations derived from different signals from associated satellites to determine a full solution position. Processor 116 may use any known technique for determining a full solution position for navigation system 110. Once processor 116 determines the full solution position, processor 116 may then calculate a sub-solution based on one or more corresponding subsets of pseudorange measurements. For example, when there are N satellites each providing a corresponding pseudorange measurement, a subset may be based on N-1 pseudorange measurements. Each different sub-solution excludes pseudorange measurements received from different satellites.

[0031] In additional embodiments, processor 116 may calculate a discriminator for each sub-solution. The discriminator may be any mathematical quantity based on a mathematical distance or separation between the sub-solution and the full solution. Additionally, processor 116 may calculate a set of solution separation parameters based on the discriminator. Further, processor 116 may then compare the actual separation to the solution separation parameters, where the solution separation parameters serve as a fault detection threshold for separating the sub-solutions. For example, if the actual separation between the sub-solution and the full solution exceeds the corresponding separation parameter or threshold, processor 116 may set a fault flag indicating that a satellite transmitter fault has been detected.

[0032] In another embodiment, the processor 116 may determine an error parameter or auxiliary term based on noise-induced errors in the corresponding sub-solutions, wherein the noise-induced errors force the sub-solutions to deviate from the actual position of the navigation system 110. Furthermore, the processor 116 may use the solution separation parameter and the sub-solution auxiliary term to determine a protection limit or error bound. For example, the processor 116 may determine the protection limit based on a sub-solution threshold or a maximum of the separation parameter and the auxiliary terms for different sub-solutions.

[0033] In some embodiments, the processor 116 may calculate auxiliary terms for the sub-solution n of the primary parameter. In some implementations, the covariance of the sub-solution may be expressed in terms of velocity vector, roll, pitch, and heading uncertainties according to the following equations:

[0034]

[0035] In some implementations, the error state covariance matrix of the full solution can be expressed in terms of velocity vector, roll, pitch, and heading uncertainties according to the following equation:

[0036]

[0037] In certain embodiments, once the primary integrity monitoring parameters are obtained, method 200 may continue at 204 by determining separate parameters for derived integrity monitoring parameters based on the primary integrity monitoring parameter thresholds. For example, processor 116 may convert the thresholds for one or more of the primary integrity monitoring parameters into separate parameters for one or more derived integrity monitoring parameters.

[0038] The processor 116 may calculate a threshold value for the primary integrity monitoring parameter The separation parameter for each derived integrity monitoring parameter is calculated as follows:

[0039]

[0040] Accordingly, the separation parameter for a particular derived integrity monitoring parameter may be set equal to the Jacobian for the derived integrity monitoring parameter. The vector magnitude of is multiplied by the threshold value for the main integrity monitoring parameter 的向量。

[0041] As described above, the derived integrity monitoring parameters may include the subject longitudinal velocity and the subject lateral velocity. As described herein, different derived integrity monitoring parameters may be derived from the primary integrity monitoring parameters. For example, a separate parameter for the subject longitudinal velocity may be set equal to the vector magnitude of the Jacobian for the subject longitudinal velocity multiplied by the threshold vector for the primary integrity monitoring, as shown below:

[0042]

[0043] Further, the separation parameter for the subject lateral velocity may be equal to the vector magnitude of the Jacobian for the subject lateral velocity multiplied by the threshold vector for primary integrity monitoring, as shown below:

[0044]

[0045] Additionally, the separation parameter for the body normal velocity may be equal to the vector magnitude of the Jacobian for the body normal velocity multiplied by the threshold vector for primary integrity monitoring, as shown below:

[0046]

[0047] In additional embodiments, the derived integrity monitoring parameters may include yaw angle, flight path angle, along-course velocity, cross-course velocity, and magnetic track angle. In a manner similar to the primary velocity described above, a separate parameter for yaw angle may be set equal to the vector magnitude of the Jacobian for yaw angle multiplied by the threshold vector for primary integrity monitoring, as shown below:

[0048]

[0049] Furthermore, the separation parameter for the flight path angle may be equal to the vector magnitude of the Jacobian for the flight path angle multiplied by the threshold vector for primary integrity monitoring, as shown below:

[0050]

[0051] Further, the separation parameter for along-course velocity may be equal to the vector magnitude of the Jacobian for along-course velocity multiplied by the threshold vector for primary integrity monitoring, as shown below:

[0052]

[0053] Additionally, the separation parameter for lateral heading velocity may be equal to the vector magnitude of the Jacobian for lateral heading velocity multiplied by the threshold vector for primary integrity monitoring, as shown below:

[0054]

[0055] In some embodiments, the method 200 can continue at 206, where fault-free and aiding terms for the derived integrity monitoring parameters can be computed. To compute the fault-free and aiding terms, the processor 116 can convert the estimated state covariance for one or more primary integrity monitoring parameters of the navigation system 110 into a covariance for one or more derived integrity monitoring parameters. In certain implementations, the processor 116 can convert the estimated state covariance for one or more error estimates of the primary integrity monitoring parameters for both the full solution and the different sub-solutions. For example, when determining the covariance for the derived integrity monitoring parameters for the full solution, the processor 116 can compute the covariance for the derived integrity monitoring parameters for the full solution as follows:

[0056]

[0057] Also, the processor 116 can compute the covariance for the sub-solution of the derived integrity monitoring parameters as follows:

[0058]

[0059] As shown, the processor 116 can compute the covariance for the full solution and the sub-solution of the derived integrity monitoring parameters by multiplying the Jacobian for the derived integrity monitoring parameters by the covariance of the full solution error estimate and the sub-solution error estimate, respectively, and then multiplying the result by the transpose of the Jacobian for the derived integrity monitoring parameters.

[0060] In additional embodiments, the processor 116 can use the computed covariance matrix for the derived integrity monitoring parameters to compute the aiding term for a particular derived integrity monitoring parameter. For example, the processor 116 can compute the aiding term for the derived integrity monitoring parameters as follows:

[0061]

[0062] As shown, the processor 116 computes the aiding term for a particular sub-solution by multiplying the leak detection sigma multiplier by the square root of the covariance of the sub-solution error estimate for the particular derived integrity monitoring parameter.

[0063] Similar to the computation of the separate parameters, the aiding term for the derived integrity monitoring parameters can be computed for the subject longitudinal velocity, the subject lateral velocity, and the subject normal velocity. For example, the aiding term for the subject longitudinal velocity can be set equal to the leak detection sigma multiplier multiplied by the square root of the covariance of the sub-solution error estimate for the subject longitudinal velocity, as follows:

[0064]

[0065] Furthermore, the auxiliary term for the subject's lateral velocity may be equal to the missed detection sigma multiplier multiplied by the square root of the covariance of the sub-solution error estimates for the subject's lateral velocity, as follows:

[0066]

[0067] Additionally, the auxiliary term for the body normal velocity may be equal to the missed detection sigma multiplier times the square root of the covariance of the sub-solution error estimates for the body normal velocity, as follows:

[0068]

[0069] In additional embodiments, the derived integrity monitoring parameters may include yaw angle, flight path angle, along-course velocity, cross-course velocity, and magnetic track angle. In a manner similar to the body velocity described above, the auxiliary term for yaw angle may be equal to the missed detection sigma multiplier multiplied by the square root of the covariance of the sub-solution error estimates for yaw angle, as shown below:

[0070]

[0071] Furthermore, the auxiliary term for the flight path angle may be equal to the missed detection sigma multiplier times the square root of the covariance of the sub-solution error estimates for the flight path angle as follows:

[0072]

[0073] Furthermore, the auxiliary term for along-course velocity may be equal to the missed detection sigma multiplier multiplied by the square root of the covariance of the sub-solution error estimates for along-course velocity, as shown below:

[0074]

[0075] Additionally, an auxiliary term for lateral heading velocity may be equal to the missed detection sigma multiplier times the square root of the covariance of the sub-solution error estimates for lateral heading velocity as follows:

[0076]

[0077] In some embodiments, method 200 may continue at 208 where a protection limit may be calculated for the derived integrity monitoring parameter. To calculate the protection limit, processor 116 may first calculate a no-fault protection limit for the particular derived integrity monitoring parameter. For example, when determining the no-fault protection limit for the particular derived integrity monitoring parameter, processor 116 may multiply the no-fault sigma multiplier by the square root of the covariance of the full solution error estimate or the full solution error state covariance for the particular derived integrity monitoring parameter, as shown below:

[0078]

[0079] When calculating the no-fault protection limit, the processor 116 may calculate the protection of the derived integrity monitoring parameters as follows:

[0080]

[0081] As shown, the processor 116 may calculate the protection limit as the maximum of the no-fault protection limit and the maximum separation parameter and auxiliary term combination for each sub-solution.

[0082] Similar to the calculation of the separation parameters, the processor 116 can calculate the no-fault protection limit and the protection limit for the derived integrity monitoring parameters of the body longitudinal velocity, the body lateral velocity, and the body normal velocity. For example, the no-fault protection limit for the body longitudinal velocity can be equal to the no-fault sigma multiplier multiplied by the square root of the covariance of the full solution error estimate for the body longitudinal velocity, as shown below:

[0083]

[0084] Furthermore, the protection limit for the longitudinal velocity of the main body may be equal to the maximum value of the no-fault protection limit and the combination of the maximum separation parameter and the auxiliary term of each sub-solution for the longitudinal velocity of the main body, as shown below:

[0085]

[0086] Further, the no-fault protection limit for the subject's lateral velocity may be equal to the no-fault sigma multiplier times the square root of the covariance of the full solution error estimate for the subject's lateral velocity as follows:

[0087]

[0088] Furthermore, the protection limit for the subject lateral velocity may be equal to the maximum value of the no-fault protection limit and the combination of the maximum separation parameter and the auxiliary term of each sub-solution for the subject lateral velocity, as shown below:

[0089]

[0090] Additionally, the fault-free protection limit for the body normal velocity can be equal to a fault-free sigma multiplier multiplied by the square root of the covariance of the full solution error estimate for the body normal velocity, as follows:

[0091]

[0092] Also, the protection limit for the body normal velocity can be equal to the maximum of the fault-free protection limits for the individual sub-solutions of the body normal velocity and the maximum separation parameter combined with the auxiliary term, as follows:

[0093]

[0094] In additional embodiments, the derived integrity monitoring parameters can include a yaw angle, a flight path angle, a downtrack velocity, a cross-track velocity, and a magnetic track angle. In a similar manner as the body velocities described above, the fault-free protection limit for the yaw angle can be equal to a fault-free sigma multiplier multiplied by the square root of the covariance of the full solution error estimate for the yaw angle, as follows:

[0095]

[0096] Also, the protection limit for the yaw angle can be equal to the maximum of the fault-free protection limits for the individual sub-solutions of the yaw angle and the maximum separation parameter combined with the auxiliary term, as follows:

[0097]

[0098] Further, the fault-free protection limit for the flight path angle can be equal to a fault-free sigma multiplier multiplied by the square root of the covariance of the full solution error estimate for the flight path angle, as follows:

[0099]

[0100] Also, the protection limit for the flight path angle can be equal to the maximum of the fault-free protection limits for the individual sub-solutions of the flight path angle and the maximum separation parameter combined with the auxiliary term, as follows:

[0101]

[0102] Further, the fault-free protection limit for the downtrack velocity can be equal to a fault-free sigma multiplier multiplied by the square root of the covariance of the full solution error estimate for the downtrack velocity, as follows:

[0103]

[0104] Further, the protection limit for the lateral velocity can be equal to the maximum of the fault-free protection limit for each of the sub-solutions for the lateral velocity and the maximum separation parameter combined with the auxiliary term, as follows:

[0105]

[0106] Further, the fault-free protection limit for the lateral velocity can be equal to the fault-free sigma multiplier multiplied by the square root of the covariance of the full solution error estimate for the lateral velocity, as follows:

[0107]

[0108] Further, the protection limit for the lateral velocity can be equal to the maximum of the fault-free protection limit for each of the sub-solutions for the lateral velocity and the maximum separation parameter combined with the auxiliary term, as follows:

[0109]

[0110] As described above, the processor 116 can derive a derived integrity monitoring parameter from the primary integrity monitoring parameter.

[0111] Figure 3 is a flowchart of an exemplary method 300 for computing a derived integrity monitoring parameter. Similar to the method 200, the method 300 can be performed by the processor 116, a different processor on the navigation system 110, or other processor that is part of a system in communication with the navigation system 110. In certain embodiments, the method 300 continues at 302, where the primary integrity monitoring parameter is obtained. The method 300 obtains the primary integrity monitoring parameter in a manner similar to that described above with respect to the method 200. Figure 2

[0112] In certain embodiments, the method 300 continues at 304, where one or more derived integrity monitoring parameters are computed. Further, the method 300 continues at 306, where the one or more derived integrity monitoring parameters are employed to be the primary integrity monitoring parameter. For example, the processor 116 can compute one or more derived integrity monitoring parameters, and then employ the derived integrity monitoring parameter as the primary integrity monitoring parameter, and then base the computation of subsequent derived integrity monitoring parameters on a new set of primary integrity monitoring parameters.

[0113] In some embodiments, the processor 116 can compute the true track angle based on previously computed navigation parameters. In some implementations, the computation of the true track angle and the ground speed is based on the horizontal component of the velocity. For example, the processor 116 can compute the true track angle and the ground speed according to the following:

[0114] TA​t =atan2(v Ny , v Wx )as well as

[0115]

[0116] The processor 116 may then employ the true track angle and ground speed as primary integrity monitoring parameters by converting the horizontal velocity component into the true track angle and ground speed domain.

[0117] In another embodiment, the processor 116 may calculate the covariance in the true track angle and ground speed domain by converting the covariance of the horizontal component of the velocity estimate error into the (full and sub) covariance (variance) of the true track angle and ground speed estimate errors. For example, the processor 116 may calculate the discriminator for the true track angle and ground speed as the absolute value of the sub-solution true track angle / ground speed minus the full solution true track angle / ground speed:

[0118] as well as

[0119]

[0120] Regarding the covariance of the true track angle estimation error, the processor 116 may calculate the following terms for the sub-solution and the full solution respectively:

[0121] as well as

[0122]

[0123] in To convert the horizontal velocity into the Jacobian of the true track angle, the processor 116 can calculate the following terms for the sub-solution and the full solution respectively regarding the covariance of the ground velocity estimation error:

[0124] as well as

[0125]

[0126] in is the Jacobian that converts horizontal velocity to ground velocity.

[0127] In additional embodiments, processor 116 may calculate thresholds and auxiliary terms for the true track angle and ground speed. For example, processor 116 may calculate thresholds for the true track angle and ground speed as follows:

[0128] as well as

[0129]

[0130] If the magnitude of the discriminator exceeds the magnitude of the threshold, the processor 116 may issue an alert. Additionally, the processor 116 may calculate auxiliary terms for the true track angle and ground speed as follows:

[0131] as well as

[0132]

[0133] When calculating the covariance, thresholds, and auxiliary terms for the true track angle and ground speed, the processor 116 may calculate the protection limits for the true track angle and ground speed. For example, to first calculate the no-fault protection limit for the true track angle / ground speed, the processor 116 may multiply the no-fault sigma multiplier by the square root of the covariance of the full solution error estimate for the true track angle / ground speed as follows:

[0134] as well as

[0135]

[0136] Furthermore, processor 116 may calculate protection limits for the true track angle and ground speed by identifying the no-failure protection limits for the various sub-solutions for the true track angle / ground speed and the maximum value of the maximum threshold and auxiliary term combination, as follows:

[0137] as well as

[0138]

[0139] In some embodiments, the processor 116 may convert the covariance matrix for the navigation parameters into the domain of the primary integrity monitoring parameters including the true track angle and ground speed. For example, the processor 116 may convert the covariance matrix for each sub-solution of the navigation parameters into the domain including the true track angle and ground speed according to the following equation:

[0140]

[0141] in is the Jacobian that converts horizontal velocity to true track angle, and Convert horizontal velocity to ground velocity Jacobian.

[0142] Further, the processor 116 may convert the covariance matrix of the full solution for the navigation parameters into a domain including the true track angle and ground speed according to the following equation:

[0143]

[0144] Converting the navigation parameters into the primary integrity monitoring parameter domain, including true track angle and ground speed, may facilitate subsequent calculation of derived integrity monitoring parameters.

[0145] In some embodiments, the method 300 may continue at 308 where separate parameters for the derived integrity monitoring parameters may be determined based on the transformed primary integrity monitoring parameter thresholds. In particular, the processor 116 may calculate a covariance matrix for the derived integrity monitoring parameters based on the transformed covariance matrix for the primary integrity monitoring parameters. For example, the covariance matrix for the sub-solutions of the derived integrity monitoring parameters (including body velocity, yaw angle, flight path heading, along-course velocity, and lateral course velocity) may be calculated by multiplying the Jacobian matrix for the derived integrity monitoring parameters by the covariance matrix of the primary integrity monitoring parameter error estimates, and then multiplying the result by the transpose of the Jacobian of the derived integrity monitoring parameters, as shown below:

[0146]

[0147] In a similar manner, the processor 116 may calculate the covariance matrix of the full solution for the derived integrity monitoring parameters as follows:

[0148]

[0149] Further, the method 300 may continue at 310 where the fault-free and auxiliary terms for the derived integrity monitoring parameters may be calculated. In some implementations, the processor 116 may calculate the fault-free and auxiliary terms for the derived integrity monitoring parameters as described above in Figure 2 As described in.

[0150] In some embodiments, the processor 116 may calculate the true track angle based on previously calculated navigation parameters. In some implementations, the calculation of the true track angle is based on the horizontal component of the velocity that is independent of the ground velocity. For example, the processor 116 may calculate the true track angle according to the following formula:

[0151] TA t =atan2(v Ny ,v Nx ).

[0152] The processor 116 may then employ the true track angle as the primary integrity monitoring parameter by converting the horizontal velocity component into the true track angle domain.

[0153] In further embodiments, the processor 116 can compute the covariance in the true track angle domain by converting the covariance of the horizontal components of the velocity estimate error into (full and sub) covariances (variances) of the true track angle estimate error. For example, the processor 116 can compute a discriminator for the true track angle as the absolute value of the sub-solution true track angle minus the full-solution true track angle:

[0154]

[0155] With respect to the covariance of the true track angle estimate error, the processor 116 can compute the following for the sub-solution and the full-solution, respectively:

[0156] and

[0157]

[0158] where is the Jacobian that converts the horizontal velocity to the true track angle.

[0159] In additional embodiments, the processor 116 can compute a threshold and a helper for the true track angle. For example, the processor 116 can compute a threshold for the true track angle as follows:

[0160]

[0161] The processor 116 can issue an alert if the magnitude of the discriminator exceeds the magnitude of the threshold. Additionally, the processor 116 can compute a helper for the true track angle as follows:

[0162]

[0163] When computing the covariance, threshold, and helper for the true track angle, the processor 116 can compute a protection limit for the true track angle. For example, to first compute a faultless protection limit for the true track angle, the processor 116 can multiply the faultless sigma multiplier by the covariance square root of the full-solution error estimate for the true track angle, as follows:

[0164]

[0165] Also, the processor 116 can compute a protection limit for the true track angle by identifying the maximum of the faultless protection limits for the various sub-solutions of the true track angle and the maximum threshold and helper combination, as follows:

[0166]

[0167] In certain embodiments, the processor 116 can convert the covariance matrix for the navigation parameters into the primary integrity monitoring parameter domain including the true track angle. For example, the processor 116 can convert the covariance matrix for the individual sub-solutions of the primary integrity monitoring parameters into the domain including the true track angle according to:

[0168]

[0169] where is the Jacobian for converting the horizontal velocity to the true track angle, and is the largest eigen vector of the horizontal velocity covariance, representing the uncertainty of the ground speed in the worst-case direction.

[0170] Further, the processor 116 can convert the covariance matrix for the full solution of the primary integrity monitoring parameters into the domain including the true track angle according to:

[0171]

[0172] Converting the navigation parameters into the primary integrity monitoring parameter domain including the true track angle can facilitate subsequent computation of the derived integrity monitoring parameters.

[0173] In some embodiments, the method 300 can continue at 308, where a separation parameter for the derived integrity monitoring parameters can be determined based on the converted primary integrity monitoring parameter threshold. In particular, the processor 116 can compute the covariance matrix for the derived integrity monitoring parameters based on the converted covariance matrix for the primary integrity monitoring parameters. For example, the covariance matrix for the sub-solutions of the derived integrity monitoring parameters (including the body velocity, yaw angle, flight path heading, along- heading velocity, and cross- heading velocity) can be computed by multiplying the Jacobian matrix for the derived integrity monitoring parameters by the covariance matrix of the primary integrity monitoring parameter error estimate, and then multiplying the result by the transpose of the Jacobian of the derived integrity monitoring parameters, as follows:

[0174]

[0175] In a similar manner, the processor 116 can compute the covariance matrix for the full solution of the derived integrity monitoring parameters as follows:

[0176]

[0177] Further, the method 300 can continue at 310, where the fault-free and assistance terms for the derived integrity monitoring parameters can be computed. In some implementations, the processor 116 can compute the fault-free and assistance terms for the derived integrity monitoring parameters as described above in Figure 2 As described in.

[0178] The derived integrity monitoring parameters may be completely derived from the primary integrity monitoring parameters by promoting certain derived integrity monitoring parameters, such as the true track angle, to primary integrity monitoring parameters.

[0179] Figure 4 4 is a flow chart of an exemplary method 400 for calculating derived integrity monitoring parameters. In certain embodiments, method 400 continues at 402 by converting an estimated state covariance matrix of at least one primary integrity monitoring parameter into a covariance matrix of at least one derived integrity monitoring parameter. Additionally, method 400 continues at 404 by converting a threshold value of at least one primary integrity monitoring parameter into a separate parameter of at least one derived integrity monitoring parameter. Further, method 400 continues at 406 by calculating a protection limit for at least one derived integrity monitoring parameter.

[0180] Exemplary embodiments

[0181] Embodiment 1 includes a method comprising: converting an error state covariance matrix of an estimate of at least one primary integrity monitoring parameter of a navigation system into an error state covariance matrix of one or more derived integrity monitoring parameters, wherein the one or more derived integrity monitoring parameters depend on the at least one primary integrity monitoring parameter; converting integrity thresholds of the at least one primary integrity monitoring parameter into separation parameters of the one or more derived integrity monitoring parameters; and calculating protection limits for the one or more derived integrity monitoring parameters.

[0182] Embodiment 2 includes the method of embodiment 1, wherein the at least one primary integrity monitoring parameter comprises at least one of: horizontal position; vertical position; horizontal velocity; vertical velocity; roll angle; pitch angle; and true heading angle.

[0183] Embodiment 3 includes a method according to any one of embodiments 1 to 2, wherein the one or more derived integrity monitoring parameters include: body longitudinal velocity; body lateral velocity; body normal velocity; yaw angle; flight path angle; along-course velocity; and cross-course velocity.

[0184] Embodiment 4 includes the method of any one of embodiments 1 to 3, further comprising employing at least one derived integrity monitoring parameter as a primary integrity monitoring parameter among the one or more derived integrity monitoring parameters.

[0185] Embodiment 5 includes the method of embodiment 4, wherein employing the at least one derived integrity monitoring parameter as a primary integrity monitoring parameter comprises converting the navigation parameter to a primary integrity parameter domain including the employed primary integrity monitoring parameter.

[0186] Embodiment 6 includes the method according to any one of embodiments 4 to 5, wherein the primary integrity monitoring parameters employed are true track angle and ground speed integrity monitoring parameters.

[0187] Embodiment 7 includes the method of embodiment 6, wherein the uncertainty associated with the ground speed integrity monitoring parameter is transformed by the largest eigenvector of the horizontal speed covariance, wherein the largest eigenvector of the horizontal speed covariance is the uncertainty of the ground speed in the worst case direction.

[0188] Embodiment 8 includes a system comprising: a receiver configured to receive a plurality of signals transmitted from a plurality of transmitters; and a processor operably coupled to the receiver, the processor configured to perform a method of integrity monitoring, wherein the integrity monitoring performed by the processor comprises: calculating one or more primary integrity monitoring parameters based on the plurality of signals; and deriving one or more derived integrity monitoring parameters from the one or more primary integrity monitoring parameters; converting an estimated error state covariance of the one or more primary integrity monitoring parameters of a navigation system into an error state covariance of one or more derived integrity monitoring parameters; converting integrity thresholds of the one or more primary integrity monitoring parameters into separation parameters of the one or more derived integrity monitoring parameters; and calculating protection limits for the one or more derived integrity monitoring parameters.

[0189] Embodiment 9 includes the system of embodiment 8, wherein the one or more primary integrity monitoring parameters include at least one of: horizontal position; vertical position; horizontal velocity; vertical velocity; roll angle; pitch angle; and true heading angle.

[0190] Embodiment 10 includes a system according to any one of embodiments 8 to 9, wherein the one or more derived integrity monitoring parameters include: body longitudinal velocity; body lateral velocity; body normal velocity; yaw angle; flight path angle; along-heading velocity; and cross-heading velocity.

[0191] Embodiment 11 includes the system of any one of embodiments 8 to 10, further comprising employing at least one derived integrity monitoring parameter as a primary integrity monitoring parameter among the one or more derived integrity monitoring parameters.

[0192] Embodiment 12 includes the system of embodiment 11, wherein employing the at least one derived integrity monitoring parameter as a primary integrity monitoring parameter comprises converting the navigation parameter to a primary integrity monitoring parameter domain including the employed primary integrity monitoring parameter.

[0193] Embodiment 13 includes the system of any one of embodiments 11-12, wherein the primary integrity monitoring parameters employed are true track angle and ground speed integrity monitoring parameters.

[0194] Embodiment 14 includes the system of embodiment 13, wherein the uncertainty associated with the ground speed integrity monitoring parameter is transformed by a maximum eigenvector of the horizontal speed covariance, wherein the maximum eigenvector of the horizontal speed covariance is the uncertainty of the ground speed in the worst case direction.

[0195] Embodiment 15 includes a method comprising: receiving a plurality of pseudorange measurements from a plurality of satellites; calculating one or more primary integrity monitoring parameters based on the plurality of signals; and deriving one or more derived integrity monitoring parameters from the one or more primary integrity monitoring parameters by: converting an estimated error state covariance of the one or more primary integrity monitoring parameters of a navigation system into an error state covariance of one or more derived integrity monitoring parameters, wherein the one or more derived integrity monitoring parameters depend on the one or more primary integrity monitoring parameters; converting integrity thresholds of the one or more primary integrity monitoring parameters into separation parameters of the one or more derived integrity monitoring parameters; and calculating protection limits for the one or more derived integrity monitoring parameters.

[0196] Embodiment 16 includes the method of embodiment 15, further comprising employing at least one derived integrity monitoring parameter as a primary integrity monitoring parameter among the one or more derived integrity monitoring parameters.

[0197] Embodiment 17 includes the method of embodiment 16, wherein adopting the derived integrity monitoring parameters as primary integrity monitoring parameters comprises converting the navigation parameters to a primary integrity monitoring parameter domain including the adopted primary integrity monitoring parameters.

[0198] Embodiment 18 includes the method according to any one of embodiments 16 to 17, wherein the primary integrity monitoring parameters employed are true track angle and ground speed integrity monitoring parameters.

[0199] Embodiment 19 includes the method of any one of embodiments 15 to 18, wherein the one or more primary integrity monitoring parameters include at least one of: horizontal position; vertical position; horizontal velocity; vertical velocity; roll angle; pitch angle; and true heading angle.

[0200] Embodiment 20 includes the method of any one of embodiments 15 to 19, wherein the one or more derived integrity monitoring parameters include: body longitudinal velocity; body lateral velocity; body normal velocity; yaw angle; flight path angle; along-course velocity; and cross-course velocity.

[0201] Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement calculated to achieve the same purpose may be substituted for the specific embodiments shown. It is manifestly intended that the present invention be limited only by the claims and the equivalents thereof.

Claims

1. A method for integrity monitoring, comprising: receiving a plurality of signals sent from a plurality of transmitters; calculating one or more primary integrity monitoring parameters based on the plurality of signals; as well as Deriving one or more derived integrity monitoring parameters from the one or more primary integrity monitoring parameters, wherein deriving the one or more derived integrity monitoring parameters comprises: converting an estimated error state covariance matrix of at least one primary integrity monitoring parameter of the navigation system into an error state covariance matrix of the one or more derived integrity monitoring parameters by multiplying the estimated error state covariance matrix of the at least one primary integrity monitoring parameter by the Jacobian of the one or more derived integrity monitoring parameters, wherein the one or more derived integrity monitoring parameters are dependent on the at least one primary integrity monitoring parameter; converting the integrity threshold of the at least one primary integrity monitoring parameter into a separate parameter of the one or more derived integrity monitoring parameters by multiplying the integrity threshold of the at least one primary integrity monitoring parameter; and A protection limit for the one or more derived integrity monitoring parameters is calculated by identifying a larger value of a no-fault protection limit for a sub-solution of the one or more derived integrity monitoring parameters and a maximum combination of the separation parameter and the auxiliary term. 2 . The method of claim 1 , further comprising employing the at least one derived integrity monitoring parameter as a primary integrity monitoring parameter among the one or more derived integrity monitoring parameters.

3. A system for integrity monitoring, comprising: a receiver configured to receive a plurality of signals transmitted from a plurality of transmitters; as well as a processor operatively coupled to the receiver, the processor configured to perform a method of integrity monitoring, wherein the integrity monitoring performed by the processor comprises: calculating one or more primary integrity monitoring parameters based on the plurality of signals; and Deriving one or more derived integrity monitoring parameters from the one or more primary integrity monitoring parameters, wherein deriving the one or more integrity monitoring parameters comprises: converting an estimated error state covariance matrix of the at least one primary integrity monitoring parameter into an error state covariance of the one or more derived integrity monitoring parameters by multiplying the estimated error state covariance of the one or more primary integrity monitoring parameters of the navigation system by the Jacobian of the one or more derived integrity monitoring parameters; converting the integrity thresholds of the one or more primary integrity monitoring parameters into separate parameters of the one or more derived integrity monitoring parameters by multiplying the integrity thresholds of the at least one primary integrity monitoring parameter by the Jacobian of the one or more derived integrity monitoring parameters; and A protection limit for the one or more derived integrity monitoring parameters is calculated by identifying a larger value of a no-fault protection limit for a sub-solution of the one or more derived integrity monitoring parameters and a maximum combination of the separation parameter and the auxiliary term.

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