Method for providing data association assurance in navigation and radar systems

Abstract

A method for providing data association assurance, the method comprising: formulating a trajectory permutation matrix of measurement statistics based on sensor measurement returns; receiving a first set of correlation trajectories (set a) from the correlator module, the first set of correlation trajectories being identified as originating from the target; selecting a second correlation trajectory set (set b) from the trajectory permutation matrix based on a branch and bound technology; reconstructing verification of the data association framework into a linear inequality, where a first portion of the linear inequality is based on the set a and a second portion of the linear inequality is based on the set b; and performing a verification process based on the formal method to determine whether the characteristics of the set a are defined by the characteristics of the set b. If the characteristics of the associated trajectories within the set a are defined by or less than or equal to the characteristics of the associated trajectories within the set b, the associated trajectories are validated.

Description

Background Art

[0001] Data or feature association is a key component of navigation systems using vision-based sensors or detect-and-avoid (DAA) systems using non-cooperative surveillance sensors such as radar or cameras. For vision-assisted navigation systems, data association is used to identify identical features in consecutive measurement frames to enable the navigation system to calculate vehicle kinematic state statistics (such as position, velocity, or angular orientation). In DAA systems, sensor-level data association is used to identify sequences of measurements originating from the same target. Additionally, in DAA systems, system-level data association is used to identify measurements originating from different sensors that originate from the same target.

[0002] The performance of navigation or tracking systems is highly dependent on the correctness of the correlations performed by data association algorithms. Therefore, it is crucial to guarantee the correctness of these data association algorithms with a high degree of confidence. The most rigorous way to guarantee that a software system can be certified is to use verification based on formal methods. To date, formal methods have only been used to guarantee linear systems, because the complexity of the behavior defined by nonlinear systems, such as data association algorithms (i.e., their statistical properties and nonlinear dynamics), makes them unsuitable for formal verification methods without substantial abstraction / simplification.

[0003] Currently, in the avionics field, testing and simulation are the most common methods for achieving some confidence in data association implementations, but these methods are insufficient to guarantee the correctness of the association. Some previous research efforts have attempted to define abstractions of such algorithms in formal notations and use theorem provers to prove high-level properties. However, such approaches are not scalable to analyze full-scale models or implementations of such algorithms without abstractions. Summary of the Invention

[0004] A system includes: at least one processor onboard a vehicle; and a plurality of sensors in operative communication with the at least one processor, the sensors including at least one non-cooperative sensor. The at least one processor is configured to host: a correlator module in operative communication with the sensors, wherein the correlator module is configured to receive measurement returns from the at least one non-cooperative sensor and output a correlated trajectory based on the measurement returns; and a verification module in operative communication with the plurality of sensors and the correlator module, wherein the verification module is configured to receive the measurement returns and the correlated trajectory. The verification module includes program instructions executable by at least one processor to perform a method comprising the following steps: formulating a trajectory permutation matrix of measurement statistics based on measurement returns; receiving a first set of correlated trajectories (set a) from a correlator module, the first set of correlated trajectories identified as originating from at least one target; selecting a second set of correlated trajectories (set b) from the trajectory permutation matrix based on a branch-and-bound technique; reformulating verification of a data association framework as a linear inequality, wherein a first part of the linear inequality is based on set a and a second part of the linear inequality is based on set b; and performing a formal method-based verification process to determine whether a characteristic of set a is bounded by a characteristic of set b. If the characteristic of the correlated trajectories in set a is bounded by the characteristic of the correlated trajectories in set b or is less than or equal to the characteristic of the correlated trajectories in set b, then verifying the correlated trajectories from the correlator module. If the characteristic of the correlated trajectories in set a is not bounded by the characteristic of the correlated trajectories in set b or is not less than or equal to the characteristic of the correlated trajectories in set b, then not verifying and deleting the correlated trajectories from the correlator module. BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Features of the present invention will become apparent to those skilled in the art from the following description, which proceeds with reference to the accompanying drawings. Understanding that the drawings depict only typical embodiments and are not therefore to be considered limiting of the scope of the invention, the invention will be described with additional specificity and detail through use of the accompanying drawings, in which:

[0006] Figure 1A is a block diagram of a system for providing data association guarantees during vehicle navigation, according to one embodiment;

[0007] Figure 1B It is implemented according to the example Figure 1A A flowchart of a method for providing data association guarantee executed in a system;

[0008] Figure 2 Shows the operability Figure 1A Example sensor measurement scenarios for the system;

[0009] Figure 3 Describes the Figure 2 The trajectory permutation matrix of the sensor measurement scene;

[0010] Figure 4 According to one embodiment, Figure 1A A block diagram of a correlator system employed in a system of

[0011] Figure 5 is a block diagram of a tracking system employing a correlator system algorithm according to an alternative embodiment. DETAILED DESCRIPTION

[0012] In the following detailed description, the embodiments are described in sufficient detail to enable those skilled in the art to practice the present invention. It should be understood that other embodiments may be utilized without departing from the scope of the present invention. Therefore, the following detailed description should not be considered to have a limiting meaning.

[0013] Systems and methods for providing data association assurance in navigation and radar systems are described herein.

[0014] This method applies formal methods to ensure stationary feature / moving object correlation. Formal methods include tools that provide a way to ensure results for linear systems. This method reformulates the inherently nonlinear feature correlation problem as a linear inequality suitable for the application of formal methods.

[0015] The present approach addresses the lack of a technique that provides guarantees about the correct feature associations computed by data association algorithms. Applying formal methods to the data association problem provides a path for certifying vision-based navigation systems and DAA systems.

[0016] In this approach, a formal methods framework is developed by using the output of a data association algorithm, rewriting verification tests as affine inequalities, and using these affine inequalities to develop performance guarantees. This approach enables the extension of formal methods to nonlinear systems, and therefore to data association algorithms in general. This formal methods framework addresses the primary shortcoming of guaranteeing the integrity of systems using data association.

[0017] The present method provides formal verification and is generally operated to: reformulate the feature association problem as a linear inequality; formulate a complete trajectory permutation matrix that describes all possible trajectories; determine a suitable subset of trajectories from the trajectory permutation matrix using an efficient search method (such as a branch and bound method based on the kinematic equations); define the verification target as a synchronous observer of the correlator system, which checks whether the trajectory output of the correlator is always within the appropriate trajectory subset; and perform formal verification and observe the result. When the result is true, this proves the correctness of the trajectory from the correlator. When the result is false, the trajectory output from the correlator is not verified and is deleted. In this formal verification method, the synchronous observer is an attachment to the system that monitors the inputs and outputs of the system, with the purpose of continuously verifying whether the expected behavioral characteristics of the system (expressed in terms of inputs and outputs) are met, while keeping the original behavior of the system intact. The method provides a mathematically proven proof of correctness, which serves as a strict assurance component for the certification of systems by regulatory agencies.

[0018] The various benefits of this approach include: generating formal guarantees of feature correlator functionality for navigation and DAA systems; providing a path to guarantee the integrity of data / feature associations; and providing a path to certification arguments to regulators. For sensor-level DAA systems, this approach guarantees the integrity of the data associations used by the correlator software to generate measurement trajectories, which can then be used for certification arguments to regulators. Similar formal methods can be extended to other systems, such as map-based visual navigation systems or DAA systems that rely on data association.

[0019] This technique can be implemented in software to ensure feature correlator correctness and provides a way to ensure that measurements taken over time are correlated and originate from the same target (e.g., an intruder aircraft). This approach is used to apply formal methods to the feature correlation problem by defining the verification objective as a simultaneous observer of the correlator. The verification objective consists of a mathematical formula that describes the desired behavior of the correlator that must be met. For example, the distance between consecutive correlator output traces from the correlator must never be greater than a user-selected threshold.

[0020] In a data association implementation, a correlator for a non-cooperative DAA monitoring sensor receives measurements from the sensor (which detects a target) and determines whether a sequence of consecutive measurements originates from the same target. This method is used to formally verify and validate that measurement associations performed over time do indeed originate from the same target—in other words, to verify the correctness of the associations performed by the correlator.

[0021] This method reformulates the data association framework as a linear inequality suitable for applying formal methods: a≤b; where a≡the set of trajectories from the correlator and b≡the set of most likely trajectories (selected from all measurement combinations starting from the encounter scenario). The method mathematically formulates set b using all measurement returns starting from the encounter scenario. Starting from an encounter between a target and a friend vehicle defined for a finite time horizon, a complete trajectory permutation matrix is ​​defined that enumerates all possible association sequences of the target relative to the friend vehicle. Within the trajectory permutation matrix, a kinematic model describing the relative motion between the target and friend vehicle is used to identify the most likely sequence of measurements from the encounter scenario using all measurement returns. The method exploits the target's (relative) motion to branch and bound the measurement combinations and select the set of most likely trajectories—set b—for use by the synchronous observer in the correlator. The method uses model checking to thoroughly verify that the correlated trajectories from the correlator (set a) are within the set of most likely trajectories (set b). A successful verification result guarantees that the sequence of measurement returns identified by the data association algorithm as originating from the same target is correct, and serves as a rigorous proof of correctness that can be presented at authentication time.

[0022] The present technique provides assurance that measurement results are correctly identified as metrics originating from the same target. In particular, the use of formal method techniques to specify and verify measurement associations provides assurance that the associations are performed correctly and that the association requirements are met.

[0023] The present method uses formal methods to ensure the integrity of the data association algorithm used by the correlator to generate measurement tracks for DAA applications. Although the correlator algorithm is nonlinear, the data association algorithm that determines whether a measurement return originates from a target can be expressed using a simple expression: a≤b. In this expression, set a refers to the three-dimensional (3D) position estimates of the measurement tracks calculated by the correlator and identified as originating from the same target over time, and set b refers to the combination of the 3D position measurement returns or measurement mean vectors of the target buffered by an additional tolerance for sensor errors. Applying formal methods to data association involves mathematically capturing the definitions of set a and set b so that they can be used as properties for verification.

[0024] In one embodiment, set b includes the 3D positions of the targets, where each position is augmented by a function of the sensor measurement error that enables the sensor performance to be included in the definition of the target position. Set b uses the difference between two target position measurements at the same measurement time or consecutive measurement times and the relative vehicle kinematic model to determine whether the measurements are likely to originate from the same target. Set b is incorporated into the establishment of a correctness property for the correlator, which is then subjected to formal verification. This property requires that certain properties of the trajectories calculated by the correlator (set a) should always be within (≤) the corresponding properties of the selected trajectories in set b. A successful formal verification result a≤b asserts that the measurements do originate from the same target, and a negative result a>b indicates that the measurements do not originate from the same target.

[0025] Further details regarding the present systems and methods are described below and with reference to the accompanying figures.

[0026] Figure 1A A system 100 for providing assurance of data association performed during DAA is shown, according to one embodiment. The system 100 generally includes at least one processor 110 onboard a vehicle 102, and a plurality of onboard sensors 120 in operative communication with the processor 110. Additionally, one or more offboard sensors 126 may be in operative communication with the vehicle 102. The vehicle 102 may be an unmanned aerial system (UAS) vehicle, an urban air mobility (UAM) vehicle, or other similar aircraft.

[0027] Onboard sensors 120 may include one or more cooperative sensors 122 and one or more non-cooperative sensors 124. Cooperative sensors 122 operate to provide measurement tracks for one or more targets in the environment surrounding vehicle 102, where each respective measurement track includes a track identifier (ID). Examples of cooperative sensors 122 include Automatic Dependent Surveillance-Broadcast (ADS-B) sensors and Traffic Collision Avoidance System (TCAS) Mode-S sensors. Non-cooperative sensors 124 may include: sensors that provide measurement tracks originating from the same target while providing inconsistent, varying IDs for the tracks; sensors that provide multiple measurement tracks for a target with consistent IDs but provide multiple measurement tracks for the same target in a single measurement epoch; or sensors that provide measurement returns for targets without measurement correlations or IDs. Examples of non-cooperative sensors 124 include air-based radar, airborne visual sensors (e.g., electro-optical cameras or infrared cameras), or other similar sensors. When present, one or more offboard sensors 126 may include one or more non-cooperative surveillance sensors, such as ground-based radar.

[0028] The processor 110 hosts a correlator module 130 that is in operative communication with the non-cooperative sensors 124. The correlator module 130 is configured to receive measurement returns from the sensors 124 and to output correlation traces based on the measurement returns.

[0029] The processor 110 also hosts a verification module 140 that is in operative communication with the sensor 124 and the correlator module 130. The verification module 140 is configured to receive measurement returns from the sensor 124 and correlation traces from the correlator module 130. The verification module 140 includes program instructions that are executable by the processor 110 to perform a method for providing data association assurance, which is described in further detail below and in Figure 1B Shown in.

[0030] In some embodiments, the off-board processor 131 hosts a correlator module 132 in operative communication with the off-board sensor 126. The correlator module 132 is configured to receive measurement returns from the sensor 126 and output a correlation trajectory based on the measurement returns. The verification module 140 is also configured to receive the measurement returns from the sensor 126 and the correlation trajectory from the correlator module 132.

[0031] The system 100 may also include a DAA system 150 hosted by the processor 110. The DAA system 150 is configured to receive verified correlation trajectories from the correlator module 130 and the correlator module 132 (when present). The DAA system 150 is also configured to receive measurement trajectories from the cooperative sensor 122.

[0032] The onboard vehicle navigation system 154 is in operative communication with the DAA system 150, the non-cooperative sensors 124, and the correlator module 130. In some embodiments, the onboard vehicle navigation system 154 is also in operative communication with the offboard sensors 126 and the correlator module 132.

[0033] The vehicle navigation system 154 operates to calculate a navigation solution for the vehicle 102. The DAA system 150 operates to fuse the verified relevant trajectories to estimate an optimal trajectory for at least one target (e.g., an intruder aircraft). The DAA system 150 uses the optimal trajectory to provide guidance commands to the onboard vehicle guidance system 158 to ensure that the vehicle 102 remains clear of other air traffic.

[0034] As described above, the verification module 140 includes program instructions to perform the method for providing data association assurance. Figure 1BThe method includes: formulating a complete trajectory permutation matrix of measurement statistics based on measurement returns starting from an encounter scenario (box 142); receiving a first set of correlated trajectories (set a) from a correlator module, the first set of correlated trajectories being identified as originating from at least one target (box 143); and selecting the most likely second set of correlated trajectories (set b) from the trajectory permutation matrix based on a branch and bound technique (box 144). The method then performs a validation of the data association framework by reconstructing it into a linear inequality, wherein the first part of the linear inequality is based on the first set of correlated trajectories (set a) from the correlator module and the second part of the linear inequality is based on the most likely second set of correlated trajectories (set b) from the trajectory permutation matrix (box 145). The method performs a formal method-based validation process to determine whether the characteristics of the first set of correlated trajectories (set a) from the correlator module are bounded by the characteristics of the most likely second set of correlated trajectories (set b) from the trajectory permutation matrix (box 146). If the characteristics of the correlation traces in set a are bounded by the characteristics of the most likely correlation traces in set b or are less than or equal to the characteristics of the most likely correlation traces in set b, then the correlation traces from the correlator module are verified (block 147). If the characteristics of the correlation traces in set a are not bounded by the characteristics of the most likely correlation traces in set b or are not less than or equal to the characteristics of the most likely correlation traces in set b, then the correlation traces from the correlator module are not verified and are deleted (block 148).

[0035] For example, the characteristics of sets a and b, as well as the thresholds used to evaluate the proximity of these sets during verification, are established based on the specific vehicle types within the correlation domain. This is mathematically formulated as a verification target, which serves as a synchronous observer for the correlator and is subsequently formally verified. Through an exhaustive analysis of the correlator's state space, the formal verification process determines that there are no potential violations of the verification target. In other words, if the characteristics of the correlation trajectory in set a are bounded by, or are less than or equal to, the characteristics of the most likely correlation trajectory in set b, then the correlation trajectory is verified.

[0036] The method of applying formal methods based verification to ensure the correctness of correlation features based on a set of scalar expressions a≤b has various tasks. These tasks include clustering these target position measurements using data association, filtering the clustered measurements, and generating the input of set a. These tasks also include formally defining the data association, that is, specifying a notion of correctness for set b, or more specifically, identifying the most likely correlation trajectories from a trajectory permutation matrix. This is provided by a threshold at which a measurement combination can be clustered. The sensor provides multiple measurement returns of the same target and different targets at each measurement time or epoch. Formal methods based verification involves capturing the formal specification in a notation that supports feature verification and performing the verification of the correlators.

[0037] Further details about this method are described below.

[0038] Linear inequalities related to features

[0039] When reframing the data / feature association as a linear inequality suitable for applying formal methods: a≤b, where:

[0040] a≡set of correlated tracks, and

[0041] b≡set of most likely tracks

[0042] (selected from all measurement combinations from the start of an encounter scenario), formal verification methods operate to identify and guarantee the set b.

[0043] For set a, related trajectories are provided by the correlator and are identified as originating from the same target. The measurement result sequences are identified using: a relative motion model, such as a white noise model, a Markov process model, or a semi-Markov jump process model, such as described in Li et al., "Survey of Maneuvering Target Tracking. Part I: Dynamic Models", IEEE Transactions on Aerospace and Electronic Systems, Vol. 39, No. 4, pp. 1333-1364 (2003); an association algorithm, such as joint probabilistic data association with nearest neighbors or multiple hypothesis testing, such as described in Smith et al., "Approaches to Multisensor Data Fusion in Target Tracking: A Survey", IEEE Transactions on Knowledge and Data Engineering, Vol. 18, No. 12, pp. 1696-1710 (2006), and Kalandros et al., "Tutorial on Multisensor Management and Fusion Algorithms for Target Tracking", Proceedings of the 2004 American Control Conference, Boston, Massachusetts, pp. 1-15 (2004); and the measurement returns from the current epoch. The disclosures of Li et al., Smith et al., and Kalandros et al. are incorporated herein by reference. At each measurement epoch, the correlator outputs a track for each visible target, including the target's track statistics, such as the mean and variance calculated from the measurement returns.

[0044] For set b, the most likely correlation trajectory is selected from the trajectory permutation matrix. The measurement sequence is identified using a higher-order relative vehicle kinematic model than the one used by the correlator, such as a coordinated turn model using all measurement returns from the encounter scenario. The trajectory permutation matrix is ​​then used to branch and bound the measurement combinations, narrowing down the possible measurement combinations from the encounter scenario by utilizing the target's motion relative to the own vehicle, its geometry (to account for sensor errors), and other factors such as infeasibility conditions and constraints.

[0045] Trajectory permutation matrix

[0046] Figure 2 An example sensor measurement scenario 200 is shown in which the present system may operate. At a first time epoch 210, there are two measurement traces (1 and 2). At a second time epoch 220, there are two measurement returns (C and D). At a third time epoch 230, there are two other measurement returns (E and F). Measurement statistics include mean and variance. Data association and branch-and-bound techniques require operating on all measurement statistics provided by the sensors.

[0047] Figure 3 Describes the Figure 2 The trajectory permutation matrix for sensor measurement scene 200 is shown in Figure 2. As shown, even after three epochs, the number of permutations becomes unwieldy for two measurement returns. The aforementioned set b needs to be identified and guaranteed based on the trajectory permutation matrix. Using a branch-and-bound method (which exploits the kinematic equations of relative motion, accounts for outliers, and eliminates infeasible measurement permutations), a subset of trajectories, set b, is selected from the trajectory permutation matrix.

[0048] Correlator

[0049] The correlator is configured to provide a measurement track for the DAA system. The correlator uses the surveillance sensor to provide the measurement track and, if the DAA processor is located on the sensor's processor and the sensor is located on the own aircraft, can limit the computation time of the DAA processor. A sensor measurement track is a sequence of measurement returns originating from the same target (e.g., an intruder aircraft with an International Civil Aviation Organization (ICAO) identification number (ID) or a unique sensor-specific ID).

[0050] The sensors used in the present system may include cooperative sensors, such as Automatic Dependent Surveillance-Broadcast (ADS-B) sensors, or active surveillance sensors (e.g., Traffic Collision Avoidance System (TCAS) Mode-S sensors). These sensors provide an ICAO ID to accompany the measurement track. The sensors may also be non-cooperative sensors, such as air-based radar, airborne visual sensors (e.g., cameras), or ground-based radar. For off-board sensors, such as ground-based radar, the correlator may be hosted in the DAA processor. The correlator operates to generate a sensor measurement track with a sensor-specific ID.

[0051] Typically, a correlator identifies sequences of measurements originating from the same target over multiple time epochs. The correlator correlates and statistically fuses multiple returns originating from the same target at the same time epoch, resulting in a single measurement track per target per time epoch. The correlator is also configured to merge multiple measurement returns from the same target at a specific time epoch. The correlator includes a glide function, which enables the measurement track to glide through the sensor scan pattern strategy. For example, measurement returns from an intruder aircraft are provided asynchronously. The glide function also maintains tracking when the sensor misses a detection, such as when power on the target is insufficient. The correlator assigns an ID to a sequence of sensor measurements; identifies an unknown number of targets in the sensor's field of view; and rejects erroneous measurements, which may be false or spurious. The correlator may use range rate measurements to assist in data association, where available. The correlator is also configured to predict the measurement position of the current track for association with the current measurement return. While the correlator is not designed to smooth the track, some degree of smoothing is unavoidable.

[0052] Figure 4 is a block diagram of a correlator system 400 that may be employed in the present system, according to one embodiment. The correlator system 400 generally includes a format measurement unit 410 and a target / feature motion classifier 412, both of which are configured to receive sensor measurement returns and own vehicle navigation statistics. A relative target / feature motion model 414 is responsive to the output from the target / feature motion classifier 412. A correlator unit 416 is responsive to the output from the format measurement unit 410 and the relative target / feature motion model 414. A format trajectory output statistics unit 418 is responsive to the output from the correlator unit 416 and is configured to receive the sensor lever arm. The format trajectory output statistics unit 418 operates to output a measurement trajectory for use by the DAA system. The various components of the correlator system 400 are described in further detail below.

[0053] The format measurement unit 410 operates to use own vehicle navigation statistics to parse received measurement returns into a relative reference frame specific to a given sensor. The target / feature motion classifier 412 operates to classify items measured by the vision-based sensor as moving or stationary for low altitude operations. The target / feature motion classifier 412 is configured to use own vehicle navigation statistics to parse measurement returns into a relative reference frame specific to the non-cooperative sensor - the same coordinate system used by the format measurement unit 410. For vision sensors, the target / feature motion classifier 412 then uses dynamic pattern decomposition to identify foreground (moving) and background (stationary) targets / features from a sequence or scene of vision sensor measurements.

[0054] Relative object / feature motion model 414 uses a relative motion model, such as a white noise model, a Markov process model, or a semi-Markov jump process model. Relative object / feature motion model 414 selects vehicle model parameters based on the own vehicle's speed and altitude, the classification of visual sensor measurements as moving objects or targets or stationary features, and the relative speed between the target / feature and the own vehicle. The own vehicle navigation solution provides the own vehicle's speed and altitude. Relative object / feature motion model 414 selects model parameters based on: 1) the own vehicle's speed and altitude; 2) the speed of the moving object or stationary feature in the scene; and 3) the relative speed of the moving object or stationary feature in the scene.

[0055] The correlator unit 416 can be divided into three sub-functions: data association, trajectory management, and correlation filter. These sub-functions are interdependent because they work together to formulate measurement trajectories for downstream systems and users. An exemplary algorithm for the correlator unit is described in more detail in U.S. application Ser. No. 17 / 846,899, filed on June 22, 2022, entitled “DETECT AND AVOIDTRACKING ARCHITECTURE,” the disclosure of which is incorporated herein by reference.

[0056] The format trajectory output statistics unit 418 is used to output the following trajectory statistics in multiple reference coordinate systems: trajectory ID; measurement time; object or target relative kinematic statistics resolved in the spherical coordinate system of the vehicle body; intruder aircraft range change rate and its measurement statistics; air traffic speed resolved in the local horizontal-local vertical reference coordinate system and its measurement statistics; and validity flags of various measurement results.

[0057] In an alternative embodiment, the correlator algorithm and verification module may reside on the sensor processor so that the correlator functionality does not impact the DAA functionality or computing resources of the DAA processor. An example implementation of such an embodiment is Figure 5 . Here, the DAA tracking system 500 includes at least one surveillance sensor 510 having a sensor emitter / detector 512 and a sensor processor 514 hosting a correlator algorithm 516 and a verification module 517. The surveillance sensor 510 is in operative communication with a DAA module 520. The vehicle navigation system 530 is in operative communication with the DAA module 520 and the surveillance sensor 510. When an off-board sensor (such as a ground radar) is Figure 5 When used with an embodiment of the present invention, the correlator for the off-board sensor can be hosted in the DAA processor.

[0058] The correlator algorithm 516 processes the sensor measurements from the sensor emitter / detector 512 and the navigation data from the vehicle navigation system 530. The verification module 517 provides a method for ensuring the data association of the correlator algorithm 516, such as previously described. The correlator algorithm 516 outputs a correlated measurement trajectory 518 based on the sensor measurements and the navigation data to the DAA module 520 for further processing to provide tracking and guidance data to various vehicle applications. Examples of such vehicle applications may include applications for guidance 522, flight control 524, and display 526.

[0059] The computers or processors used in the present systems and methods may be implemented using software, firmware, hardware, or any suitable combination thereof known to those skilled in the art. These may be supplemented by or incorporated into specially designed application specific integrated circuits (ASICs) or field programmable gate arrays (FPGAs). The computers or processors may also include functionality utilizing software programs, firmware, or other computer-readable instructions for performing the various processing tasks, computations, and control functions used in the present systems and methods.

[0060] 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.

[0061] The instructions for performing the various process tasks, calculations, and generation of other data used in the operation of the methods described herein may be implemented in software, firmware, or other computer-readable or processor-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 may be any available medium that can be accessed by a general-purpose or special-purpose computer or processor or any programmable logic device.

[0062] Suitable processor-readable media may include storage devices or memory media, such as magnetic media or optical media. For example, the storage or memory media may include conventional hard disks, optical disks, DVDs, Blu-ray discs, or other optical storage media; volatile or non-volatile media, such as random access memory (RAM); read-only memory (ROM), electrically erasable programmable ROM (EEPROM), flash memory, etc.; 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.

[0063] Example Implementation

[0064] Embodiment 1 includes a system comprising: at least one processor, the at least one processor being onboard a vehicle; and a plurality of sensors, the plurality of sensors being in operative communication with the at least one processor, the plurality of sensors including at least one non-cooperative sensor; wherein the at least one processor is configured to host: a correlator module, the correlator module being in operative communication with the plurality of sensors, the correlator module being configured to receive measurement returns from the at least one non-cooperative sensor, and to output a correlated trajectory based on the measurement returns; and a verification module, the verification module being in operative communication with the plurality of sensors and the correlator module, the verification module being configured to receive the measurement returns and the correlated trajectory; wherein the verification module includes program instructions executable by the at least one processor to perform a method comprising the steps of: formulating a trajectory permutation matrix of measurement statistics based on the measurement returns; receiving a first phase from the correlator module; A set of related trajectories (set a) is selected, the first set of related trajectories being identified as originating from at least one target; a second set of related trajectories (set b) is selected from a trajectory permutation matrix based on a branch and bound technique; a verification of a data association framework is reconstructed as a linear inequality, wherein a first part of the linear inequality is based on set a and a second part of the linear inequality is based on set b; and a verification process based on a formal method is performed to determine whether a characteristic of set a is bounded by a characteristic of set b; wherein if the characteristic of the related trajectories within set a is bounded by the characteristic of the related trajectories within set b or is less than or equal to the characteristic of the related trajectories within set b, the related trajectories from the correlator module are verified; wherein if the characteristic of the related trajectories within set a is not bounded by the characteristic of the related trajectories within set b or is not less than or equal to the characteristic of the related trajectories within set b, the related trajectories from the correlator module are not verified and are deleted.

[0065] Embodiment 2 includes the system of embodiment 1, further comprising: a detection and avoidance module hosted by at least one processor, the detection and avoidance module configured to receive verified correlation trajectories; and an onboard navigation system operative to calculate a navigation solution for the vehicle, the navigation system operatively communicating with the detection and avoidance module, the plurality of sensors, and the correlator module.

[0066] Embodiment 3 includes the system of embodiment 2, further comprising: an airborne vehicle guidance system in operative communication with the detect and avoid module.

[0067] Embodiment 4 includes the system of embodiment 3, wherein the detect and avoid module is operative to fuse the verified relevant trajectories to estimate an optimal trajectory for at least one target, wherein the optimal trajectory is used by the detect and avoid module to provide guidance to the vehicle guidance system to ensure that the vehicle remains clear of other air traffic.

[0068] Embodiment 5 includes the system of any of embodiments 1-4, wherein the at least one non-cooperative sensor comprises at least one airborne radar or at least one airborne vision sensor.

[0069] Embodiment 6 includes the system of any of embodiments 1-5, wherein the at least one non-cooperative sensor comprises at least one ground-based radar.

[0070] Embodiment 7 includes the system of any one of embodiments 1-6, wherein the vehicle is a friendly aircraft and the at least one target is an intruder aircraft.

[0071] Embodiment 8 includes the system of any one of Embodiments 1-7, wherein the vehicle is an unmanned aerial system (UAS) vehicle or an urban air mobility (UAM) vehicle.

[0072] Embodiment 9 includes the system of any one of embodiments 1 to 8, wherein the correlator module operates to: identify a sequence of sensor measurement returns originating from the same target within multiple time epochs; associate and statistically fuse multiple measurement returns originating from the same target at the same time epoch such that each target has one measurement return at each time epoch; assign an identifier (ID) to the sequence of sensor measurement returns; and reject any erroneous measurement results, which may be erroneous measurement returns or false measurement returns.

[0073] Embodiment 10 includes the system of any one of embodiments 2 to 9, wherein the correlator module comprises: a format measurement unit and a target / feature motion classifier, each of which is configured to receive measurement returns from at least one non-cooperative sensor and navigation statistics from a vehicle navigation system; a relative target / feature motion model, which is responsive to output from the target / feature motion classifier; a correlator unit, which is responsive to output from the format measurement unit and the relative target / feature motion model; and a format trajectory output statistics unit, which is responsive to output from the correlator unit and is configured to receive sensor lever arm data; wherein the format trajectory output statistics unit is operative to calculate a correlated measurement trajectory, which is output to the detection and avoidance module.

[0074] Embodiment 11 includes the system of any of embodiments 1-10, wherein the correlator module and the verification module are hosted on an onboard processor that is part of an onboard sensor of the plurality of sensors.

[0075] Embodiment 12 includes a method comprising: sending measurement returns from at least one monitoring sensor to a correlator, the correlator being operative to output correlated trajectories based on the measurement returns; and sending the measurement returns and the correlated trajectories to a verification module onboard a vehicle, wherein the verification module is operative to perform a method comprising the following steps: formulating a trajectory permutation matrix of measurement statistics based on the measurement returns; receiving a first set of correlated trajectories (set a) from the correlator, the first set of correlated trajectories being identified as originating from at least one target; selecting a second set of correlated trajectories (set b) from the trajectory permutation matrix based on a branch and bound technique; and verifying the data association framework. Reconstructing into a linear inequality, wherein a first part of the linear inequality is based on set a and a second part of the linear inequality is based on set b; and performing a verification process based on a formal method to determine whether a characteristic of set a is bounded by a characteristic of set b; wherein if the characteristic of the correlation trajectory within set a is bounded by the characteristic of the correlation trajectory within set b or is less than or equal to the characteristic of the correlation trajectory within set b, then verifying the correlation trajectory from the correlator; wherein if the characteristic of the correlation trajectory within set a is not bounded by the characteristic of the correlation trajectory within set b or is not less than or equal to the characteristic of the correlation trajectory within set b, then not verifying and deleting the correlation trajectory from the correlator.

[0076] Embodiment 13 includes the method described in embodiment 12, further comprising: sending the verified correlation trajectory from the correlator to an onboard detection and avoidance module; wherein the detection and avoidance module fuses the verified correlation trajectory to estimate an optimal trajectory for at least one target; wherein the optimal trajectory is used by the detection and avoidance module to provide guidance to a vehicle guidance system to ensure that the vehicle remains clear of other air traffic.

[0077] Embodiment 14 includes the method of any one of Embodiments 12-13, wherein the at least one surveillance sensor comprises at least one airborne radar or at least one airborne vision sensor.

[0078] Embodiment 15 includes the method of any one of Embodiments 12 to 14, wherein the at least one surveillance sensor comprises at least one ground-based radar.

[0079] Embodiment 16 includes the method of any one of Embodiments 12 to 14, wherein the correlator and the verification module are hosted on an onboard processor.

[0080] Embodiment 17 includes the method of any one of Embodiments 12 to 16, wherein the vehicle is a friendly aircraft and the at least one target is an intruder aircraft.

[0081] Embodiment 18 includes the method of any one of Embodiments 12 to 17, wherein the vehicle is an unmanned aerial system (UAS) vehicle or an urban air mobility (UAM) vehicle.

[0082] Embodiment 19 includes a program product comprising: a non-transitory processor-readable medium comprising program instructions executable by at least one processor to perform a method for ensuring data association, the method comprising: receiving measurement returns from at least one airborne surveillance sensor in an airborne correlator module, the airborne correlator module outputting correlated trajectories based on the measurement returns; and receiving the measurement returns and the correlated trajectories in an airborne verification module, wherein the verification module performs a process comprising the following steps: formulating a trajectory permutation matrix of measurement statistics based on the measurement returns; receiving a first set of correlated trajectories (set a) from the correlator module, the first set of correlated trajectories being identified as originating from at least one target; and obtaining a set of correlated trajectories from an airborne correlator module based on a branch and bound technique. A second set of correlated trajectories (set b) is selected in the trajectory permutation matrix; verification of the data association framework is restructured into a linear inequality, wherein a first part of the linear inequality is based on set a and a second part of the linear inequality is based on set b; and a verification process based on a formal method is performed to determine whether a characteristic of set a is bounded by a characteristic of set b; wherein if the characteristic of the correlated trajectories in set a is bounded by the characteristic of the correlated trajectories in set b or is less than or equal to the characteristic of the correlated trajectories in set b, then the correlated trajectories from the correlator module are verified; wherein if the characteristic of the correlated trajectories in set a is not bounded by the characteristic of the correlated trajectories in set b or is not less than or equal to the characteristic of the correlated trajectories in set b, then the correlated trajectories from the correlator module are not verified and are deleted.

[0083] Embodiment 20 includes the program product of embodiment 19, wherein the non-transitory processor-readable medium further comprises program instructions for executing a method comprising the steps of: sending verified correlation trajectories from a correlator module to an onboard detection and avoidance module; wherein the detection and avoidance module fuses the verified correlation trajectories to estimate an optimal trajectory for at least one target; wherein the optimal trajectory is used by the detection and avoidance module to provide guidance to a vehicle guidance system to ensure that the vehicle remains clear of other air traffic.

[0084] In light of the foregoing, it will be appreciated that although specific embodiments have been described herein for illustrative purposes, various modifications may be made without departing from the scope of the present disclosure. The embodiments described are therefore to be considered in all respects as illustrative only and not restrictive. Furthermore, all variations that come within the meaning and range of equivalents of the claims are intended to be encompassed within their scope.

Claims

1. A system, comprising: at least one processor, the at least one processor being onboard the vehicle; and a plurality of sensors in operative communication with the at least one processor, the plurality of sensors including at least one non-cooperative sensor; wherein the at least one processor is configured to host: a correlator module in operative communication with the plurality of sensors, the correlator module configured to receive measurement returns from the at least one non-cooperative sensor and to output a correlation trajectory based on the measurement returns; and a verification module in operative communication with the plurality of sensors and the correlator module, the verification module configured to receive the measurement returns and the correlation traces; The verification module includes program instructions, which can be executed by the at least one processor to perform a method comprising the following steps: formulating a trajectory permutation matrix of measurement statistics based on the measurement returns; receiving a first set of correlated trajectories (set a) from the correlator module, the first set of correlated trajectories identified as originating from at least one target; Based on the branch and bound technique, selecting a second set of relevant trajectories (set b) from the trajectory permutation matrix; Reconstructing the verification of the data association framework into a linear inequality, wherein a first part of the linear inequality is based on the set a, and a second part of the linear inequality is based on the set b; as well as performing a verification process based on formal methods to determine whether the properties of the set a are bounded by the properties of the set b; wherein if the characteristics of the correlation traces in the set a are bounded by the characteristics of the correlation traces in the set b or are less than or equal to the characteristics of the correlation traces in the set b, then validating the correlation traces from the correlator module; Wherein if the characteristics of the relevant tracks in the set a are not bounded by the characteristics of the relevant tracks in the set b or are not less than or equal to the characteristics of the relevant tracks in the set b, the relevant tracks from the correlator module are not verified and deleted.

2. The system according to claim 1, further comprising: a detection and avoidance module hosted by the at least one processor, the detection and avoidance module configured to receive the verified correlation trajectory; and an onboard navigation system operative to calculate a navigation solution for the vehicle, the navigation system being in operative communication with the detect-and-avoid module, the plurality of sensors, and the correlator module; and an onboard vehicle guidance system in operative communication with the detect and avoid module; The detection and avoidance module is operative to fuse the validated correlated trajectories to estimate an optimal trajectory for the at least one target, wherein the optimal trajectory is used by the detection and avoidance module to provide guidance to the vehicle guidance system to ensure that the vehicle remains clear of other air traffic.

3. A method comprising: sending measurement returns from at least one monitoring sensor to a correlator, the correlator operative to output a correlation trajectory based on the measurement returns; as well as The measurement returns and the associated trajectory are sent to a verification module onboard the vehicle, wherein the verification module is operative to perform a method comprising the steps of: formulating a trajectory permutation matrix of measurement statistics based on the measurement returns; receiving a first set of correlated trajectories (set a) from the correlator, the first set of correlated trajectories being identified as originating from at least one target; Based on the branch and bound technique, selecting a second set of relevant trajectories (set b) from the trajectory permutation matrix; Reconstructing the verification of the data association framework into a linear inequality, wherein a first part of the linear inequality is based on the set a, and a second part of the linear inequality is based on the set b; as well as performing a verification process based on formal methods to determine whether the properties of the set a are bounded by the properties of the set b; wherein if the characteristics of the correlation traces in the set a are bounded by the characteristics of the correlation traces in the set b or are less than or equal to the characteristics of the correlation traces in the set b, then the correlation traces from the correlator are verified; Wherein if the characteristics of the relevant tracks in the set a are not bounded by the characteristics of the relevant tracks in the set b or are not less than or equal to the characteristics of the relevant tracks in the set b, the relevant tracks from the correlator are not verified and deleted.

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