System and method for estimating pose and heading based on gnss carrier phase measurements with assured integrity

Abstract

The invention provides systems and methods for estimating attitude and heading. The systems and methods utilize carrier phase single-difference (CSD) measurements or carrier phase double-difference (CDD) measurements and validation testing of CSD or CDD measurement residuals. The systems and methods include applying a wrapping function having a limit of plus or minus one-half of the wavelength of the GNSS carrier signal to the CSD or CDD measurement residuals to generate refined CSD or CDD measurement residuals, and validating the variance of the refined CSD or CDD measurement residuals to determine valid CSD or CDD measurements. By using validated CSD and CDD measurements, the systems and methods enable low-level hybrid inertial navigation systems to estimate attitude and heading with integrity and without a magnetometer or need for integer ambiguity resolution even during static or steady phases of flight / operation.

Description

[0001] Cross-reference to related applications

[0002] This application claims the benefit of U.S. Provisional Application Serial No. 63 / 076,649, filed on September 10, 2020, entitled “SYSTEM AND METHODS FORESTIMATING ATTITUDE AND HEADING BASED ON GNSS CARRIER PHASE MEASUREMENTS WITHASSURED INTEGRITY”, which is incorporated herein by reference.

[0003] Statement regarding non-U.S. sponsored research or development

[0004] The project that generated this application was funded by the Clean Sky 2 Consortium under the EU Horizon 2020 research and innovation program, pursuant to grant agreement No. 807097. Background Technology

[0005] Low-level hybrid inertial navigation systems (e.g., Global Navigation Satellite System (GNSS) Auxiliary Attitude and Heading Reference Systems (GPARRS)) rely on external measurements to assist heading during the static or stable phases of flight / operation. These systems cannot use gyroscope compass orientation to estimate heading, and therefore typically use magnetometers to provide heading estimates. However, using magnetometers is problematic because they are susceptible to environmental conditions and have limited performance that depends on location (they cannot be used near magnetic poles). Summary of the Invention

[0006] In one example, a method for estimating the attitude and heading of a system includes obtaining inertial measurements from one or more inertial sensors and raw carrier phase measurements from two or more Global Navigation Satellite System (GNSS) receivers communicatively coupled to corresponding GNSS antennas. The method further includes determining carrier phase double-difference (CDD) measurements from the raw carrier phase measurements and determining predicted CDD values ​​based on statistical filter prediction states. The method further includes determining CDD measurement residuals and corresponding variances based on the CDD measurements and predicted CDD values, and applying a wrapper function with limits of ± half the wavelength of the GNSS carrier signal to the CDD measurement residuals to generate refined CDD measurement residuals. The method further includes validating the variance of the refined CDD measurement residuals to determine effective CDD measurements, and using the effective CDD measurements and inertial measurements to estimate the attitude and heading of the system.

[0007] In another example, a system includes one or more inertial sensors configured to capture inertial measurement results. The system further includes a first Global Navigation Satellite System (GNSS) receiver communicatively coupled to a first GNSS antenna, wherein the first GNSS receiver is configured to receive signals from a plurality of GNSS satellites. The system further includes a second Global Navigation Satellite System (GNSS) receiver communicatively coupled to a second GNSS antenna, wherein the second GNSS receiver is configured to receive signals from a plurality of GNSS satellites. The system further includes at least one processor communicatively coupled to a memory, the one or more inertial sensors, the first GNSS receiver, and the second GNSS receiver. The at least one processor is configured to obtain inertial measurement results from the one or more inertial sensors and to obtain raw carrier phase measurement results from the first GNSS receiver and the second GNSS receiver. The at least one processor is further configured to determine carrier phase double difference (CDD) measurement results from the raw carrier phase measurement results and to determine predicted CDD values ​​based on statistical filter prediction states. The at least one processor is further configured to determine the CDD measurement residuals and corresponding variances based on the CDD measurement results and predicted CDD values, and to apply a wrap-around function with limits of ± half the wavelength of the GNSS carrier signal to the CDD measurement residuals to generate refined CDD measurement residuals. The at least one processor is further configured to verify the refined CDD measurement residuals to determine valid CDD measurement results, and to use the valid CDD measurement results and inertial measurement results to estimate the system's attitude and heading.

[0008] In another example, a system includes one or more inertial sensors configured to capture inertial measurement results. The system further includes a first Global Navigation Satellite System (GNSS) receiver communicatively coupled to a first GNSS antenna, wherein the first GNSS receiver is configured to receive signals from a plurality of GNSS satellites. The system further includes a second Global Navigation Satellite System (GNSS) receiver communicatively coupled to a second GNSS antenna, wherein the second GNSS receiver is configured to receive signals from a plurality of GNSS satellites. The system further includes at least one processor communicatively coupled to a memory, the one or more inertial sensors, the first GNSS receiver, and the second GNSS receiver. The at least one processor is configured to obtain inertial measurement results from the one or more inertial sensors and to obtain raw carrier phase measurements from the first and second GNSS receivers. The at least one processor is further configured to determine a carrier phase single difference (CSD) measurement from the raw carrier phase measurements and to determine an estimate of the clock offset between the first and second GNSS receivers based on the CSD measurements. The at least one processor is further configured to determine a predicted CSD value based on a statistical filter prediction state and to determine a CSD measurement residual and a corresponding variance based on the CSD measurements and the predicted CSD value. The at least one processor is further configured to apply a wrap-around function with limits of ± half the wavelength of the GNSS carrier signal to the CSD measurement residuals to generate refined CSD measurement residuals. The at least one processor is further configured to verify the refined CSD measurement residuals to determine valid CSD measurements, and to use the valid CSD measurements and inertial measurements to estimate the attitude and heading of the system. Attached Figure Description

[0009] It should be understood that the accompanying drawings only illustrate some embodiments and should not be considered as limiting the scope. Exemplary embodiments will be described with additional features and details in the drawings, in which:

[0010] Figure 1 This is a block diagram of an exemplary navigation system;

[0011] Figure 2 This is a flowchart of an exemplary method for estimating attitude and heading; and

[0012] Figure 3 This is a flowchart of an exemplary method for estimating attitude and heading.

[0013] By convention, the various features described are not necessarily drawn to scale, but are used to emphasize specific features relevant to the example implementation. Detailed Implementation

[0014] In the following detailed description, reference is made to the accompanying drawings, which form a part of the description, and specific exemplary embodiments are shown therein by way of illustration. However, it should be understood that other embodiments may be utilized, and logical, mechanical, and electrical changes may be made. Furthermore, the methods presented in the drawings and specification should not be construed as limiting the order in which the various steps can be performed. Therefore, the following detailed description should not be considered limiting.

[0015] Many navigation systems include GNSS antennas and mix / integrate / hybridize GNSS-assisted information with navigation information from inertial sensors. However, the heading of a navigation system cannot typically be directly observed using measurements from a single GNSS antenna. Even navigation systems that integrate measurements from a single GNSS antenna and low-level inertial sensors rely on measurements from external sensors (e.g., from a magnetometer) to assist heading during the static or steady phase of flight / operation. Since aircraft typically include more than one GNSS antenna and onboard receiver, dual-antenna GNSS heading estimation algorithms can be used instead of magnetometers. However, dual-antenna GNSS heading algorithms operate using carrier phase measurements, which require estimating integer ambiguities, a task that has proven difficult. Furthermore, ensuring the integrity of dual-antenna GNSS heading solutions is also highly challenging.

[0016] Some exemplary systems and methods described herein utilize carrier phase double-difference (CDD) measurements to assist hybrid (e.g., INS / GNSS) navigation systems, and perform validity tests on the CDD measurements to ensure the integrity of each CDD measurement used to assist the hybrid navigation system. Validity testing includes determining whether the variance of the CDD measurement residuals is below a threshold. In some examples, validity testing is applied with each measurement update. In other examples, validity testing is applied in the first iteration, and carrier phase range integer ambiguities are determined, with accumulated carrier phases, typically expressed as Δ ranges, used to propagate them during subsequent iterations. In some examples, CDD measurements are also decorrelated to enable sequential measurement processing, which reduces computational load.

[0017] Some exemplary systems and methods described herein utilize carrier phase single difference (CSD) measurements to assist hybrid (e.g., INS / GNSS) navigation systems. A first CSD measurement is provided to a global statistical estimator, which uses the first CSD measurement to estimate the clock offset between GNSS receivers. The global statistical estimator provides a globally valid state estimate and is independent of local (in terms of estimated and true state) validity constraints. In some examples, the global statistical estimator may be a particle filter or a point quality filter. In other implementations, the actual clock offset between GNSS receivers may first be identified based on all CSD measurements (e.g., using a trigonometric averaging algorithm), and then a local statistical estimator (such as an extended Kalman filter) may be deployed to hybridize all available sensor measurements and potentially fine-tune the actual clock offset. After estimating or identifying the clock offset between GNSS receivers, the systems and methods perform validity tests on the CSD measurements to ensure the integrity of each CSD measurement used to assist the hybrid navigation system. Validity tests include determining whether the variance of the CSD measurement residuals is below a threshold. In some examples, validity tests are applied with each measurement update. In other examples, after estimating the clock skew between GNSS receivers, an effectiveness test is applied in the first iteration to determine the integer ambiguity of the carrier phase range, and the accumulated carrier phase, typically expressed in the form of a Δ range, is used to propagate them during subsequent iterations.

[0018] Exemplary systems and methods enable low-level hybrid inertial navigation systems to estimate attitude and heading with integrity, even during the static or stable phases of flight / operation, without the need for magnetometers or integer ambiguity resolution.

[0019] Figure 1 A block diagram of an exemplary navigation system 100 is shown. Figure 1 In the example shown, navigation system 100 includes navigation computer 102, management system 108, GNSS antennas 110 and 112, GNSS receivers 114 and 116, inertial sensor 118, and other sensors 120.

[0020] In some examples, navigation system 100 is mounted on or incorporated into a vehicle (e.g., an aircraft, ship, spacecraft, automobile, or other type of vehicle). In other examples, navigation system 100 is located on or part of a movable object (e.g., a telephone, personal electronic device, land surveying equipment, or other object capable of being moved from one location to another). Navigation system 100 is configured to acquire navigation information from multiple sources. To process the acquired navigation information, navigation system 100 may include navigation computer 102, which may include at least one processor 104 and at least one memory 106.

[0021] In some examples, navigation system 100 acquires inertial measurement results that include inertial motion information. Figure 1 In the example shown, navigation system 100 includes inertial sensors 118 that measure and sense the inertial motion of navigation system 100. For example, navigation system 100 may be an inertial navigation system (INS) that receives raw inertial measurement data from a combination of inertial sensors 118, such as gyroscopes and accelerometers. Alternatively, inertial sensors 118 may be INS that provides processed inertial navigation data obtained from inertial measurement results to navigation computer 102.

[0022] In some examples, navigation system 100 may include one or more other sensors 120 to provide additional navigation information. One or more other sensors 120 may include vertical position sensors (e.g., altimeters), electro-optic sensors, magnetometers, barometers, speedometers, and / or other types of sensors.

[0023] exist Figure 1 In the example shown, navigation system 100 includes a first GNSS antenna 110, which is communicatively coupled to a first GNSS receiver 114 and configured to provide received GNSS signals to the first GNSS receiver 114. Figure 1 In the example shown, the navigation system 100 also includes a second GNSS antenna 112, which is communicatively coupled to a second GNSS receiver 116 and configured to provide received GNSS signals to the second GNSS receiver 116. The first GNSS antenna 110 and the second GNSS antenna 112 are separated by a specific distance, referred to as the baseline. In some examples, the first GNSS antenna 110 and the second GNSS antenna 112 are coupled together via a rigid body to reduce baseline flexibility during operation.

[0024] Navigation system 100 optionally includes a third GNSS antenna 113 communicatively coupled to an optional third GNSS receiver 117. The third GNSS antenna 113, the first GNSS antenna 110, and the second GNSS antenna 112 are separated by a specific distance, referred to as the baseline. In some examples, the third GNSS antenna 113, the first GNSS antenna 110, and the second GNSS antenna 112 are coupled together via a rigid body to reduce baseline flexibility during operation.

[0025] In some examples, navigation system 100 receives satellite signals from multiple GNSS satellites observable for a first GNSS antenna 110, a second GNSS antenna 112, and an optional third GNSS antenna 113. For example, during operation, GNSS receivers 114, 116, and an optional GNSS receiver receive GNSS satellite signals from currently observable GNSS satellites. As used herein, GNSS satellites can be any combination of satellites providing navigation signals. For example, GNSS satellites can be part of a Global Positioning System (GPS), a Global Navigation Satellite System (GLONASS), a Galileo system, a compass (BeiDou), or another satellite system forming part of GNSS. GNSS satellites can provide information that can be used for navigation purposes. Navigation computer 102 and GNSS receivers 114, 116, and an optional GNSS receiver 117 can receive satellite signals and extract position, velocity, and time data from the signals to obtain pseudorange and / or raw carrier phase measurements.

[0026] The processor 104 and / or other computing devices used in the navigation system 100, management system 108, or other systems and methods described herein can be implemented using software, firmware, hardware, or suitable combinations thereof. The processor 104 and other computing devices may be supplemented or incorporated therein by specially designed application-specific integrated circuits (ASICs) or field-programmable gate arrays (FPGAs). In some examples, the processor 104 and / or other computing devices may communicate with other computing devices external to the navigation system 100 via an attached transceiver, such as computing devices associated with the management system 108 or with other subsystems controlled by the management system 108. The processor 104 and other computing devices may also include or run with software programs, firmware, or other computer-readable instructions to perform various processing tasks, computational, and control functions used in the methods and systems described herein.

[0027] The methods described herein (such as method 200) may be implemented by computer-executable instructions (e.g., attitude and heading determination instructions 122) such as program modules or components, which are executed by at least one processor such as processor 104. Typically, program modules include routines, programs, objects, data components, data structures, algorithms, etc., that perform specific tasks or implement specific abstract data types.

[0028] Various procedural tasks, calculations, and generation instructions used in performing the operations of the methods described herein may be implemented in software, firmware, or other computer-readable instructions. These instructions are typically stored on a suitable computer program product, which includes a computer-readable medium for storing computer-readable instructions or data structures. Such a computer-readable medium may be a usable medium accessible by a general-purpose or special-purpose computer or processor or any programmable logic device. For example, memory 106 may be an example of a computer-readable medium capable of storing computer-readable instructions and / or data structures. Additionally, memory 106 may store navigation information such as maps, terrain databases, magnetic field information, path data, and other navigation information.

[0029] Suitable computer-readable storage media (such as memory 106) may include, for example, non-volatile 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; disks, such as internal hard disks and removable disks; optical disk storage devices, such as optical discs (CD), digital versatile optical discs (DVD), Blu-ray discs; or any other medium that may be used to carry or store desired program code in the form of computer-executable instructions or data structures.

[0030] In some examples, navigation computer 102 may use statistical filtering (e.g., using a local statistical estimator (e.g., an extended Kalman filter), a global statistical estimator (e.g., a particle filter, a point mass filter), or other statistical filtering techniques) to combine measurements acquired by GNSS receivers 114, 116 with measurements acquired from inertial sensor 118 and other sensors 120. When navigation computer 102 uses a Kalman filter to combine measurements, it may use a dynamic model, control inputs to navigation system 100, and multiple sequential measurements acquired from inertial sensor 118, other sensors 120, and via GNSS receivers 114, 116, and optionally GNSS receiver 117 to form an estimate of navigation parameters for navigation system 100 that is superior to measurements acquired from any one of the measurement sources.

[0031] When implementing a Kalman filter, navigation computer 102 (or another computing system communicating with navigation computer 102) can perform a prediction step and an update (correction) step. In the prediction step, navigation computer 102 can predict the state estimate and estimated covariance of the navigation solution for navigation system 100. In the update / correction step, navigation computer 102 can create weighted measurement results by applying a Kalman gain to measurement results obtained from measurement sources, and add the weighted measurement results to the predicted state estimate calculated in the prediction step. Furthermore, when performing the update step, navigation computer 102 calculates measurement residuals. To calculate the measurement residuals, navigation computer 102 compares the observed measurement results with the predicted state estimate. While the calculations of navigation computer 102 have been described as being applied to a Kalman filter, it should be understood that this is an example, and the calculations can also be applied to extended Kalman filters, unscented Kalman filters, and other statistical filters. For example, an extended Kalman filter can be applied when integrating INS and GNSS measurement results.

[0032] As described above, when using the low-level inertial sensor 118, the navigation system 100 needs to obtain heading information from another source during the static or stable phase of flight / operation. Figure 1 In the example shown, navigation computer 102 is configured to estimate two of the three attitudes and heading angles of navigation system 100 using raw carrier phase measurements received by GNSS antennas 110, 112 (and optionally GNSS antenna 113, if applicable) via GNSS receivers 114, 116 (and optionally GNSS receiver 117, if applicable). The heading and pitch angles are directly observable if the baseline between the GNSS antennas is collinear with the x-axis of the aircraft / vehicle / object's main frame.

[0033] Figure 2 This is an exemplary method 200 for determining the attitude and heading of a navigation system (such as, for example, navigation system 100) that is used to calculate valid measurements and ensure the integrity of the results used to determine attitude and heading. The above is in contrast to... Figure 1 The common features discussed in navigation system 100 may include features similar to those discussed with respect to method 200, and vice versa.

[0034] Method 200 includes obtaining inertial measurement results from an inertial sensor (box 201). In some examples, the inertial sensor includes one or more accelerometers and one or more gyroscopes.

[0035] Method 200 includes obtaining raw carrier phase measurements from two or more GNSS receivers (box 202). In some examples, the GNSS receivers are communicatively coupled to corresponding GNSS antennas separated by known baselines.

[0036] Method 200 further includes determining carrier phase double-difference (CDD) measurements from the raw carrier phase measurements (box 204). In some examples, CDD measurements are obtained by determining a single difference (which is the difference between measurements from two antennas of the same satellite) and then determining a second difference of the single difference associated with the defined pair of selected satellites. Using CDD measurements generally eliminates the need to estimate the clock offset between two GNSS receivers, which is necessary when using single differences. In some examples, at least one satellite (master satellite) in each correspondingly defined pair of selected satellites is selected based on a specific satellite having the minimum variance of the single-difference measurement residuals. In some such examples, the master satellite is deployed in each CDD measurement to form all possible second differences (between satellites in the field of view). In some such examples, the CDD measurement residuals are refined by applying a wrapper function with limits of ± half the wavelength of the GNSS carrier signal. In some such examples, selecting a master satellite with the minimum variance of the (refined) single-difference measurement residuals allows a larger number of CDD measurements to pass the validity test of box 212 discussed below.

[0037] In the case of a third GNSS antenna (or using a greater number of GNSS antennas) and a third GNSS receiver (or using a greater number of GNSS receivers), CDD measurement results can be used in conjunction with some or all of the additional combinations of two of the GNSS receivers. For example, when using three GNSS antennas and receivers, CDD measurement results can be determined using the first and second GNSS antennas and receivers, the first and third GNSS antennas and receivers, and / or the second and third GNSS antennas and receivers.

[0038] Method 200 further includes determining a predicted CDD value based on the predicted state (box 206). In some examples, the predicted CDD value is determined by a navigation computer (e.g., using an extended Kalman filter). In such examples, the predicted state of the extended Kalman filter used to determine the predicted CDD value includes the position of the navigation system, the positions of satellites determined according to ephemeris, attitude, and heading, and other estimated CDD quantities based on the previous state of the navigation system (e.g., errors in the GNSS antenna baseline).

[0039] Method 200 further includes determining the CDD measurement residuals and related variances based on the CDD measurement results and predicted CDD values ​​(box 208). The CDD measurement residuals are determined by obtaining the difference between the CDD measurement results and the predicted CDD values.

[0040] Since the dynamics of all states required for measurement residual prediction, except for integer ambiguity of the carrier wavelength, can be well predicted using performance significantly lower than that of the carrier signal wavelength, the CDD measurement residuals can be refined. Because the sign of the CDD measurement residuals cannot be reconstructed, method 200 further includes applying a wrapping function (box 210) to the CDD measurement residuals with limits of ± half the GNSS carrier signal wavelength.

[0041] To ensure the integrity of the CDD measurement results, method 200 further includes validating the refined CDD measurement residuals (box 212). For the validity test in box 212, it is assumed that the navigation system will be able to measure changes in attitude and heading via initial predictions (e.g., via attitude alignment algorithms and independent GNSS heading algorithms, magnetometers, etc.), and that both the predicted and measured CDD errors have a Gaussian distribution. The CDD measurement residuals are validated by determining whether the covariance of the refined CDD measurement residuals meets a threshold. In some examples, the threshold is determined using the desired probability of hazard misleading information (PHMI) value (which is an integrity requirement for the specific application) and the independent sampling rate (ISR). The PHMI value and ISR are used to determine the σ multiplier applied to the covariance of the CDD measurement residuals. To validate the CDD measurement residuals, the following condition must be met:

[0042]

[0043] Where λ is the wavelength of the GNSS carrier signal, and It is the σ multiplier, which is defined as:

[0044]

[0045] Q -1 Find the inverse of the following:

[0046]

[0047] In some examples, the validity test described in box 212 is applied for each measurement update (e.g., extended Kalman filter measurement update). In such examples, the original carrier phase measurement or the carrier phase range measurement, determined based on the pseudorange, the original carrier phase, and the Δ range, can be used.

[0048] Using a validity test for each measurement update limits the number of CDD measurements that can be used to determine the attitude and heading of a navigation system. In some examples, the validity test discussed above is applied only to the first iteration. In such examples, the integer ambiguity of the carrier phase range is determined, and the accumulated carrier phase, typically expressed as a Δ range, is used to propagate them during subsequent iterations. Because the validity test is applied only once in such examples, the threshold can be relaxed (e.g., the ISR can be set to 1), and more CDD measurements can be used in the determination of attitude and heading.

[0049] Due to the second difference applied between satellite measurements, CDD measurements are correlated with each other even if carrier phase measurements from GNSS receivers are uncorrelated. This correlation prevents efficient sequential processing of CDD measurements from being directly utilized in the filtering step of the Kalman filter. To overcome this limitation and utilize sequential measurement processing, a first possible option is to compute the inversion of the CDD measurement noise covariance matrix at each time step (fully, e.g., off-diagonally). However, such an option introduces additional computational complexity due to the need to perform covariance matrix inversion calculations at every time step.

[0050] A second possible option includes a computationally efficient implementation that allows for sequential measurement processing using correlated measurement noise. In some examples, it can be reasonably well assumed that the carrier phase noise statistics are nearly identical for a sufficiently large set of satellite measurements at high altitudes, and method 200 optionally includes offline (and potentially computationally intensive) pre-computation of the inversion of the CDD measurement noise covariance matrix (at most a scaling parameter associated with the measurement noise statistics) and subsequent online (and computationally inexpensive) decorrelation of efficient CDD measurements (box 214). In some such examples, the pre-computation / predetermined factorization (at most scaling) of the covariance matrix reflecting the transformation matrix between single and double differences is based on Cholesky factorization, singular value decomposition, or other matrix decompositions. The factorization matrix can be computed for the maximum expected number of satellites in the field of view, and a specific portion (top left portion) of the matrix used for decorrelation is determined based on the current number of satellites in the field of view. In this way, only a single matrix needs to be pre-computed and stored, and this matrix can be used for any number of satellites in the field of view.

[0051] Method 200 further includes using valid CDD measurements and inertial measurements to estimate attitude and heading (box 216). In some examples, the navigation computer (e.g., a navigation computer implementing a Kalman filter) integrates / hybridizes / mixes the CDD measurements with inertial measurements from inertial sensors to estimate the attitude and heading of the navigation system. By utilizing only CDD measurements that have passed the validity test in box 212, method 200 does not require resolving integer ambiguities and the integrity of the CDD measurements used in the attitude and heading estimation is assured.

[0052] Figure 3 This is another exemplary method 300 for determining the attitude and heading of a navigation system (such as, for example, navigation system 100) used to calculate valid measurements and to ensure the integrity of the results used to determine attitude and heading. (The above is in contrast to...) Figure 1 The common features discussed in navigation system 100 may include features similar to those discussed with respect to method 300, and vice versa.

[0053] Method 300 includes obtaining inertial measurement results from an inertial sensor (box 301). In some examples, the inertial sensor includes one or more accelerometers and one or more gyroscopes.

[0054] Method 300 includes obtaining raw carrier phase measurements from two or more GNSS receivers (box 302). In some examples, the GNSS receivers are communicatively coupled to corresponding GNSS antennas separated by known baselines.

[0055] Method 300 further includes determining a carrier phase single difference (CSD) measurement result from the original carrier phase measurement result (box 304). The CSD measurement result includes determining the difference between measurements from two antennas from the same satellite.

[0056] In the case of a third GNSS antenna (or using a greater number of GNSS antennas) and a third GNSS receiver (or using a greater number of GNSS receivers), CSD measurements can be used in combination with some or all of the additional combinations of two of the GNSS receivers. For example, when using three GNSS antennas and receivers, CSD measurements can be determined using the first and second GNSS antennas and receivers, the first and third GNSS antennas and receivers, and / or the second and third GNSS antennas and receivers.

[0057] Because CSD measurements are used in method 300 instead of CDD measurements as in method 200, the clock skew between GNSS receivers is not eliminated as in method 200. Therefore, method 300 further includes estimating the clock skew between GNSS receivers based on the CSD measurements (box 305). In some examples, the clock skew between GNSS receivers is estimated using a global statistical estimator (e.g., a particle filter) and a first CSD measurement. This global statistical estimator is then used to hybridize all available sensor measurements. In some examples, the clock skew between GNSS receivers may first be identified based on all CSD measurements (e.g., using a trigonometric-based averaging algorithm), and then fine-tuned by a local statistical estimator, which may also be deployed to hybridize all available sensor measurements. In some examples, the clock skew between GNSS receivers is estimated before verifying any CSD measurement residuals, as described below with respect to boxes 306 through 312. In some examples, CSD measurements are provided to a navigation computer (e.g., a navigation computer that implements a global statistical estimator), and clock offsets between GNSS receivers are estimated before the predicted CSD value is determined based on the predicted state, as described below with respect to box 306.

[0058] Method 300 further includes determining a predicted CSD value based on the predicted state (box 306). In some examples, the predicted CSD value is determined by the navigation computer using a global statistical estimator (e.g., a particle filter). In such examples, the predicted state of the global statistical estimator used to determine the predicted CSD value includes the position of the navigation system, the positions of satellites determined according to ephemeris, attitude, and heading, and other estimated CSD quantities based on the previous state of the navigation system (e.g., errors in the GNSS antenna baseline). In some examples, the predicted CSD value is determined using the estimated clock offset between the GNSS receivers determined in box 305, and the CSD value is predicted only for subsequent iterations of the CSD measurement results after the first CSD measurement results used to estimate the clock offset between the GNSS receivers.

[0059] Method 300 further includes determining the CSD measurement residuals and related variances based on the CSD measurement results and the predicted CSD values ​​(box 308). The CSD measurement residuals are determined by obtaining the difference between the CSD measurement results and the predicted CSD values.

[0060] Since the dynamics of all states required for measurement residual prediction, except for carrier wavelength integer ambiguity and clock skew between the GNSS receiver (determined in box 305), can be well predicted using performance significantly lower than the carrier signal wavelength, the CSD measurement residual can be refined. Because the sign of the CSD measurement residual cannot be reconstructed, method 300 further includes applying a wrapping function (box 310) to the CSD measurement residual with limits of ± half the GNSS carrier signal wavelength.

[0061] To ensure the integrity of the CSD measurement results, method 200 further includes validating the refined CSD measurement residuals (box 312). For the validity test in box 312, it is assumed that the navigation system will be able to measure changes in attitude and heading via initial predictions (e.g., via attitude alignment algorithms and independent GNSS heading algorithms, magnetometers, etc.), and that both the predicted and measured CSD errors have a Gaussian distribution. The CSD measurement residuals are validated by determining whether the covariance of the refined CSD measurement residuals meets a threshold. In some examples, the threshold is determined using the desired Probability of Hazardous Misleading Information (PHMI) value (which is an integrity requirement for the specific application) and the Independent Sampling Rate (ISR). The PHMI value and ISR are used to determine the σ multiplier applied to the CSD measurement residual covariance. To validate the CSD measurement residuals, the following condition must be met:

[0062]

[0063] Where λ is the wavelength of the GNSS carrier signal, and It is the σ multiplier, which is defined as:

[0064]

[0065] Q -1 Find the inverse of the following:

[0066]

[0067] In some examples, the validity test described in box 312 is applied for each measurement update (e.g., particle filter measurement update). In such examples, raw carrier phase measurements or carrier phase range measurements determined based on pseudorange, raw carrier phase, and Δ range can be used.

[0068] Using a validity test for each measurement update limits the number of CSD measurements that can be used to determine the attitude and heading of a navigation system. In some examples, the validity test discussed above is applied only to the first iteration. In such examples, the integer ambiguity of the carrier phase range is determined, and the accumulated carrier phase, typically expressed as a Δ range, is used to propagate them during subsequent iterations. Because the validity test is applied only once in such examples, the threshold can be relaxed (e.g., the ISR can be set to 1), and more CSD measurements can be used in the determination of attitude and heading.

[0069] Method 300 further includes using valid CSD measurements and inertial measurements to estimate attitude and heading (box 314). In some examples, a global statistical estimator (e.g., a particle filter) integrates / mixes / hybrids the CSD measurements with inertial measurements from inertial sensors to estimate the attitude and heading of the navigation system.

[0070] By applying a wrapping function and using only CSD measurements that pass the validity test in box 312 to estimate attitude and heading, method 300 does not require resolving integer ambiguities, and the integrity of the CSD measurements used in attitude and heading estimation is assured.

[0071] Exemplary Implementation

[0072] Example 1 includes a method for estimating the attitude and heading of a system, comprising: obtaining inertial measurements from one or more inertial sensors; obtaining raw carrier phase measurements from two or more Global Navigation Satellite System (GNSS) receivers communicatively coupled to corresponding GNSS antennas; determining carrier phase double difference (CDD) measurements from the raw carrier phase measurements; determining predicted CDD values ​​based on statistical filter prediction states; determining CDD measurement residuals and corresponding variances based on the CDD measurements and predicted CDD values; applying a wrapping function with limits of ± half the wavelength of the GNSS carrier signal to the CDD measurement residuals to generate refined CDD measurement residuals; verifying the refined CDD measurement residuals to determine effective CDD measurements; and using the effective CDD measurements and inertial measurements to estimate the attitude and heading of the system.

[0073] Example 2 includes the method according to Example 1, further comprising: decorrelating the effective CDD measurement results; and wherein using the effective CDD measurement results and inertial measurement results to estimate the attitude and heading of the system includes sequentially processing the decorrelated effective CDD measurement results.

[0074] Example 3 includes the method according to Example 2, wherein decorrelation of the effective CDD measurement results includes applying a predetermined factorized measurement noise covariance matrix, which is at most a scaling parameter, to the effective CDD measurement results.

[0075] Example 4 includes the method according to any one of Examples 1 to 3, wherein verifying the refined CDD measurement residuals to determine the effective CDD measurement results includes comparing the covariance of the refined CDD measurement residuals with a threshold.

[0076] Example 5 includes the method according to any one of Examples 1 to 4, wherein the refined CDD measurement residuals are verified to determine that valid CDD measurement results are applied to each measurement result update.

[0077] Example 6 includes the method according to any one of Examples 1 to 4, wherein the refined CDD measurement residual is verified to determine that the effective CDD measurement result is applied only to the first iteration of the measurement result update; and wherein the method further includes determining the integer ambiguity of the carrier phase range and using the accumulated carrier phase to propagate the carrier phase range during subsequent iterations of the measurement result update.

[0078] Example 7 includes a system comprising: one or more inertial sensors configured to capture inertial measurement results; a first Global Navigation Satellite System (GNSS) receiver communicatively coupled to a first GNSS antenna, wherein the first GNSS receiver is configured to receive signals from a plurality of GNSS satellites; a second GNSS receiver communicatively coupled to a second GNSS antenna, wherein the second GNSS receiver is configured to receive signals from a plurality of GNSS satellites; and at least one processor communicatively coupled to a memory, the one or more inertial sensors, the first GNSS receiver, and the second GNSS receiver, wherein the at least one processor is ... One processor is configured to: acquire inertial measurement results from one or more inertial sensors; acquire raw carrier phase measurement results from a first GNSS receiver and a second GNSS receiver; determine carrier phase double difference (CDD) measurement results from the raw carrier phase measurement results; determine predicted CDD values ​​based on statistical filter prediction states; determine CDD measurement residuals and corresponding variances based on the CDD measurement results and predicted CDD values; apply a wrapping function with limits of ± half the wavelength of the GNSS carrier signal to the CDD measurement residuals to generate refined CDD measurement residuals; verify the refined CDD measurement residuals to determine effective CDD measurement results; and use the effective CDD measurement results and inertial measurement results to estimate the attitude and heading of the system.

[0079] Example 8 includes the system according to Example 7, wherein at least one processor is further configured to decorrelate effective CDD measurements; and wherein at least one processor is configured to use effective CDD measurements and inertial measurements to estimate the attitude and heading of the system, including sequentially processing the decorrelated effective CDD measurements.

[0080] Example 9 includes the system according to Example 8, wherein at least one processor is configured to decorrelate the effective CDD measurement results by applying a predetermined factorized measurement noise covariance matrix, which is at most a scaling parameter, to the effective CDD measurement results.

[0081] Example 10 includes a system according to any one of Examples 7 to 9, wherein at least one processor is configured to verify the refined CDD measurement residuals by comparing the covariance of the refined CDD measurement residuals with a threshold to determine valid CDD measurement results.

[0082] Example 11 includes a system according to any one of Examples 7 to 10, wherein at least one processor is configured to verify refined CDD measurement residuals to determine valid CDD measurement results for each measurement result update.

[0083] Example 12 includes a system according to any one of Examples 7 to 10, wherein at least one processor is configured to verify refined CDD measurement residuals to determine valid CDD measurement results through a first iteration that updates only for measurement results; and wherein at least one processor is further configured to determine carrier phase range integer ambiguity and propagate the carrier phase range using accumulated carrier phase during subsequent iterations of measurement result updates.

[0084] Example 13 includes the system according to any one of Examples 7 to 12, further including one or more sensors communicatively coupled to at least one processor, wherein the one or more sensors are configured to provide additional navigation information to at least one processor.

[0085] Example 14 includes the system according to any one of Examples 7 to 13, wherein the system is mounted on or incorporated into a vehicle.

[0086] Example 15 includes the system according to any one of Examples 7 to 14, further comprising: a third GNSS receiver communicatively coupled to a third GNSS antenna, wherein the third GNSS receiver is configured to receive signals from a plurality of GNSS satellites, wherein the third GNSS receiver is communicatively coupled to at least one processor; wherein the at least one processor is further configured to: obtain raw carrier phase measurement results from the third GNSS receiver; and determine CDD measurement results from the raw carrier phase measurement results obtained from the third GNSS receiver.

[0087] Example 16 includes a system comprising: one or more inertial sensors configured to capture inertial measurement results; a first Global Navigation Satellite System (GNSS) receiver communicatively coupled to a first GNSS antenna, wherein the first GNSS receiver is configured to receive signals from a plurality of GNSS satellites; a second GNSS receiver communicatively coupled to a second GNSS antenna, wherein the second GNSS receiver is configured to receive signals from a plurality of GNSS satellites; and at least one processor communicatively coupled to a memory, the one or more inertial sensors, the first GNSS receiver, and the second GNSS receiver, wherein the at least one processor is configured to: receive signals from the one or more inertial sensors The system acquires inertial measurement results; obtains raw carrier phase measurements from a first GNSS receiver and a second GNSS receiver; determines carrier phase single difference (CSD) measurements from the raw carrier phase measurements; estimates the clock offset between the first and second GNSS receivers based on the CSD measurements; determines predicted CSD values ​​based on statistical filter prediction states; determines CSD measurement residuals and corresponding variances based on the CSD measurements and predicted CSD values; applies a wrapping function with limits of ± half the wavelength of the GNSS carrier signal to the CSD measurement residuals to generate refined CSD measurement residuals; verifies the refined CSD measurement residuals to determine valid CSD measurements; and uses the valid CSD measurements and inertial measurement results to estimate the system's attitude and heading.

[0088] Example 17 includes the system according to Example 16, wherein at least one processor is configured to verify refined CSD measurement residuals to determine valid CSD measurement results by comparing the covariance of the refined CSD measurement residuals with a threshold.

[0089] Example 18 includes a system according to any one of Examples 16 to 17, wherein at least one processor is configured to verify refined CSD measurement residuals to determine valid CSD measurement results for each measurement result update.

[0090] Example 19 includes a system according to any one of Examples 16 to 17, wherein at least one processor is configured to verify refined CSD measurement residuals to determine valid CSD measurement results through a first iteration that updates only for measurement results; and wherein at least one processor is further configured to determine carrier phase range integer ambiguity and propagate the carrier phase range using accumulated carrier phase during subsequent iterations of measurement result updates.

[0091] Example 20 includes the system according to any one of Examples 16 to 19, further comprising: a third GNSS receiver communicatively coupled to a third GNSS antenna, wherein the third GNSS receiver is configured to receive signals from a plurality of GNSS satellites, wherein the third GNSS receiver is communicatively coupled to at least one processor; wherein the at least one processor is further configured to: obtain raw carrier phase measurement results from the third GNSS receiver; and determine CDD measurement results from the raw carrier phase measurement results obtained from the third GNSS receiver.

[0092] Although specific embodiments have been illustrated and described herein, those skilled in the art will recognize that any arrangement calculated to achieve the same purpose may replace the specific embodiments shown. Therefore, it is apparent that the invention is limited only by the claims and their equivalents.

Claims

1. A method for estimating the attitude and heading of a system, comprising: Inertial measurement results are obtained from one or more inertial sensors; Raw carrier phase measurements are obtained from two or more Global Navigation Satellite System (GNSS) receivers coupled to the corresponding GNSS antenna at the communication ground. The carrier phase double-difference CDD measurement result is determined from the original carrier phase measurement result; The predicted CDD value is determined based on the state predicted by the statistical filter. Based on the CDD measurement results and the predicted CDD values, determine the CDD measurement residuals and the corresponding variances; A wrap function of half the wavelength of the GNSS carrier frequency is applied to the CDD measurement residual to generate a refined CDD measurement residual; The refined CDD measurement residuals are validated to determine valid CDD measurement results by comparing the covariance of the refined CDD measurement residuals with a threshold based on the integrity requirements and independent sampling rate (ISR) for a specific application, wherein the threshold is determined using the required probability of dangerous misleading information (PHMI) value and the independent sampling rate (ISR). as well as The attitude and heading of the system are estimated using the effective CDD measurement results and the inertial measurement results.

2. A system for estimating attitude and heading, comprising: One or more inertial sensors, the one or more inertial sensors being configured to capture inertial measurement results; A first Global Navigation Satellite System (GNSS) receiver is communicatively coupled to a first GNSS antenna, wherein the first GNSS receiver is configured to receive signals from a plurality of GNSS satellites; A second Global Navigation Satellite System (GNSS) receiver is communicatively coupled to a second GNSS antenna, wherein the second GNSS receiver is configured to receive signals from multiple GNSS satellites; and At least one processor, communicatively coupled to a memory, one or more inertial sensors, a first GNSS receiver, and a second GNSS receiver, wherein the at least one processor is configured to: The inertial measurement results are obtained from the one or more inertial sensors; Raw carrier phase measurement results are obtained from the first and second global navigation satellite system GNSS receivers; The carrier phase double-difference CDD measurement result is determined from the original carrier phase measurement result; The predicted CDD value is determined based on the state predicted by the statistical filter. Based on the CDD measurement results and the predicted CDD values, determine the CDD measurement residuals and the corresponding variances; A wrap function of half the wavelength of the GNSS carrier frequency is applied to the CDD measurement residual to generate a refined CDD measurement residual; The refined CDD measurement residuals are validated to determine valid CDD measurement results by comparing the covariance of the refined CDD measurement residuals with a threshold based on the integrity requirements and independent sampling rate (ISR) for a specific application, wherein the threshold is determined using the required probability of dangerous misleading information (PHMI) value and the independent sampling rate (ISR). as well as The attitude and heading of the system are estimated using the effective CDD measurement results and the inertial measurement results.

3. A system for estimating attitude and heading, comprising: One or more inertial sensors, the one or more inertial sensors being configured to capture inertial measurement results; A first Global Navigation Satellite System (GNSS) receiver is communicatively coupled to a first GNSS antenna, wherein the first GNSS receiver is configured to receive signals from a plurality of GNSS satellites; A second Global Navigation Satellite System (GNSS) receiver is communicatively coupled to a second GNSS antenna, wherein the second GNSS receiver is configured to receive signals from multiple GNSS satellites; and At least one processor, communicatively coupled to a memory, one or more inertial sensors, a first GNSS receiver, and a second GNSS receiver, wherein the at least one processor is configured to: The inertial measurement results are obtained from the one or more inertial sensors; Raw carrier phase measurement results are obtained from the first and second global navigation satellite system GNSS receivers; The carrier phase single-difference CSD measurement result is determined from the original carrier phase measurement result; Based on the CSD measurement results, an estimate of the clock offset between the first GNSS receiver and the second GNSS receiver is determined; The predicted CSD value is determined based on the state predicted by the statistical filter. The CSD measurement residuals and corresponding variances are determined based on the CSD measurement results and the predicted CSD values. A wrap function of half the wavelength of the GNSS carrier frequency is applied to the CSD measurement residual to generate a refined CSD measurement residual; The refined CSD measurement residuals are validated to determine valid CSD measurement results by comparing the covariance of the refined CSD measurement residuals with a threshold based on the integrity requirements and independent sampling rate (ISR) for a specific application, wherein the threshold is determined using the required probability of dangerous misleading information (PHMI) value and the independent sampling rate (ISR). as well as The attitude and heading of the system are estimated using the effective CSD measurement results and the inertial measurement results.

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