Data Fusion Techniques Applied to Scenarios Including ADS-B and Radar Sensors for Air Traffic Control

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1 1th International Conference on Information Fusion Seattle, WA, USA, July 6-9, 9 Data Fusion Techniques Applied to Scenarios Including ADS-B and Radar Sensors for Air Traffic Control Julio L. R. da Silva Technological Development EMBRAER São José dos Campos, SP, Brazil julio.lana@embraer.com.br Jose F. B. Brancalion Technological Development EMBRAER São José dos Campos, SP, Brazil jose.brancalion@embraer.com.br David Fernandes Electronic Eng. Department Instituto Tecnológico de Aeronutica São José dos Campos, SP, Brazil david@ita.br Abstract The perspectives of expansion in air traffic volume for the next years create important challenges in monitoring and control fields. In this scenario a new concept named ADS-B is rising based on cooperative aircrafts to provide air traffic control. The technique has been disseminated by regulatory agencies of all over the world and its popularity is increasing. It seeks for integration with the actual radar based sensors to provide information with better accuracy to traffic monitoring using parameters supplied by airborne position and navigation systems based on satellite communication. The present work evaluates the efficient use of both sensors data - radar and ADS-B - through the use of data fusion techniques. Centralized and distributed fusion are evaluated showing improvements in aircraft track estimation in both cases, when information from a simulated GPS system is used. The conclusions point to the fact that the system is able to accommodate the expected traffic growth with reduction in aircraft separation rules with greater predictability of its movement. Keywords: Air Traffic Control, ATC, ADS-B, radar, centralized, decentralized. 1 Introduction Position estimation of an aircraft within an airspace is a well known problem with correlated specific algorithm and techniques. The solution of this problem, known as target tracking, is a fundamental requirement for monitoring systems such as Air Traffic Control (ATC) where information as the aircraft position are used to support controlling decisions. In this context one or more sensors coupled to computational systems shall provide an efficient picture of the real scenario, in other words, traffic control is based on the monitoring of the current status of the air traffic. Typically the ATC has its characteristics based on the characteristics of the sensors used to monitor the airspace. The currently used sensors are based on radar system which were mainly developed during the Second World War. But despite the evolution of this type of sensors the system apparently has some disadvantages, such as ground base cost, to support the traffic growth expected to the next following years without any improvement. One of its main role, related to aircraft separation, might be highly degraded in case inaccurate measurements are used. A new type of solution to support the expected air traffic growth has been pursued with the objective of providing a satisfactory infrastructure to this context. The concept CNS/ATM (Communication, Navigation and Surveillance / Air Traffic Management) is the result of this pursuit and has become a world reality. Based on three important concepts communication, navigation and surveillance, this new approach shall enhance the overall Air Traffic Management. From the monitoring point of view it has been considered the utilization of a different configuration of track monitoring based on new sensors. This new approach has been named Automatic Dependent Surveillance - Broadcast (ADS-B) and uses airborne sensors based on a Global Positioning System (GPS) to provide Air Traffic Management with an accurate measurement position. The simplifications and benefits brought by the utilization of this new concept can transcend the limits of target tracking. Along with the possibility of the accommodation of a greater aircraft density due to a more accurate position estimation, a low cost of implementation is expected by authorities such as FAA and JAA. For aircraft infrastructure some issues have been stated in order to have a simple solution based on already used airborne systems. A simple architecture, depicted on Figure 1, represents how this information is to be generated on the aircraft, and latter transmitted to ATC. On the other side this new approach may not fully overcome the well established monitoring system based on radars which has already an installed infrastructure. The utilization of data fusion techniques has the major impact of extract the main benefits of each solution and provide a better scenario for the ATC point of view. This approach has been used today using information of a multi-sensor scenario based on radars. Therefore techniques can be easily extended to applications using ADS-B sensors and enhancing the overall system ISIF 1481

2 Figure 1: ADS-B system architecture This paper focus on the efficient use of data from both sensors and is organized as follows: Section presents a simple mathematical formulation used for a simulated GPS system along with an algorithm to the solution of the pseudorange equations, Section 3 reviews the formulation for the system dynamics model for the Kalman Filter and for architectures used in multisensor data fusion scenarios. Section 4 compares the tracking performance when we consider a multisensor scenario composed by ADS-B sensors and radar sensors, for one simulated scenario. Conclusions are presented in 5. Global Positioning System The Global Positioning System (GPS) has been considered to provide to ADS-B sensors information of position, velocity and time. Being composed by three known segments, the spacial, the control and the user, this system can provide this kind of information with a relative uniform accuracy overall the earth. The user segment uses information transmitted by the spatial segment, which is composed by non-geostationary satellites, to calculate its position. In order to perform this calculus the position and time base of the satellites must be well known. The control segment is responsible to correctly provide this kind of information parameters and apply corrections if necessary allowing users the establishment of its own position with the lowest value of error..1 Pseudorange equations The most important operational characteristic of the GPS system is the fact that it is based on time measurements. This dimension is related to the delay due to propagation of signals from satellites to receptors and can be rightly correlated to distance allowing further calculation. Nevertheless, this important property can infringe the simplicity of a time measurement as kinematics of satellites and receptors takes place. Despite kinematics, signals are subjected to noise due to propagation environment and to transmission and reception specific characteristics. Therefore calculated distances are no longer the simple representation of geometric distances. This parameter has been stated as pseudorange, meaning that range measurements calculated from propagation time have been contaminated with unknown quantities of time delays. Considering a given receptor positioned in (l,m,n) on a three-dimensional Cartesian space and a satellite constellation, each one positioned in (L (i),m (i),n (i) ) the pseudorange measurements ρ (i) can be expressed as the sum of two components. The first is the geometric tridimensional component ρ (i) g and the second represents the errors χ (i) ρ (i) = ρ (i) g + χ (i). (1) Considering an Earth-Centered Earth-Fixed (ECEF) referential frame these components can be expressed as [1, ]: ρ (i) g = (L (i) l) + (M (i) m) + (N (i) n) ; () and: χ (i) = c t r + c t (i) SV + c t(i) a + E (i) + η (i) ; (3) where each of the terms represent: t r t (i) SV t (i) a - Deviation on receptor s clock; - Deviation on satellite i clock; - Delay due to atmospheric propagation to the signal from satellite i; E (i) - Errors in transmitted data from satellite i; η (i) - Errors due to measurement noise of signal from satellite i; c - Speed of light; where it is not being considered the deliberated corruption of satellite s signal (Selective Availability). The basic problem of determining the receptor s position has now to be defined as a solution of a set of pseudoranges equations from visible satellites, where visible means that receptor is able to receive its signal. As pseudoranges are contaminated measurements, the receptors have to be able to minimize the errors at least for the major contributions. One term that has a major impact in this solution is the deviation of receptor s clock, and by construction the GPS receivers must be able to evaluate this. Therefore three range components and one time component have to be calculated. This problem is often referred as trilateration. One of the well known solutions described by many authors, as [1] and [], is based on the linearization of a set of pseudorange equations and the use of an iterative process. As stated a minimum of four equations required to determine the four unknown quantities. 148

3 ρ (1) (x) ρ () (x) ρ (3) (x) ρ (4) (x) = H ρ (1) (x ) ρ () (x ) ρ (3) (x ) ρ (4) (x ) (l l ) (m m ) (n n ) c t r + + χ (1) χ () χ (3) χ (4) + ς; where (l,m,n ) represents the linearization point and ς the higher order terms in the expansion of the radical of Equation. The matrix H can be expressed as where: δρ (i) H = = δρ (1) δρ () δρ (3) δρ (4) δρ (1) δm δρ () δm δρ (3) δm δρ (4) δm δρ (1) δn 1 δρ () δn 1 δρ (3) δn 1 δρ (4) δn 1 (l,m,n ) (4) ; (5) (L (i) l) (L (i) l) + (M (i) m) + (N (i) n) ; (6) δρ (i) δm = (M (i) m) (L (i) l) + (M (i) m) + (N (i) n) ; (7) δρ (i) δn = (N (i) n) (L (i) l) + (M (i) m) + (N (i) n). (8) Thus rows of Equation 4 may be rewritten as: δˆρ (i) = ρ (i) (x) ρ (i) (x ) = h (i) δx + χ (i) + ς; (9) where the term h (i) represents the ith row of the matrix H and δx i the matrix that multiply H. Assuming that H rows are linearly independent the set of equations can be solved by the simple inverse matrix operation applied to this matrix: δx i = H 1 δˆρ (1) δˆρ () δˆρ (3) δˆρ (4) H 1 χ (1) χ () χ (3) χ (4) + ς. (1) This can also be represented as the quantity: δˆρ (1) δ x i = H 1 δˆρ () δˆρ (3) ; (11) δˆρ (4) with an error given by: H 1 χ (1) χ () χ (3) χ (4) + ς. (1) This solution can also be generally represented in a matrix form allowing the use of more than four pseudorange measurements: δ x = (H T H) 1 H T δˆρ. (13) The knowlodge of the positioning error allows the determination of the actual position as: x = x + δ x; (14) The use of an interactive process shall reduce the contribution of the parameter δˆx to acceptable values, even when ˆx has as a initial point (,,) in ECEF referential frame, leading to a good estimative of the real position. Although this method may not be the best, it has been sucessfully applied to position determination. 3 Modeling The key for a correct aircraft tracking is the use of good estimation algorithms along with sensors that provide efficient measurements. Therefore one of the main interests in the area is the acknowledgment of the mathematical models that represent the movement of the objects in a threedimensional space, and also the technique that makes possible the processing and use of this information. In this context the algorithm of Kalman Filter herein presented has received widespread use. One of its advantages is its ability of integration of a great number of sensors. Besides, other advantages of its well known characteristics are its low computational cost. 3.1 Dynamic Model Although aircraft are almost never really a point in space and information about its orientation may be useful, these objects are usually treated as a point source in the field of target tracking. Dynamical models are capable of describing the evolution of its states with respect to time. State space models are currently used in this representation and are discussed from here on. The state x R of a discrete-time controlled process is governed by the linear stochastic difference equation: x k+1 = f k (x k,u k ) + v k ; (15) z k = h k (x k ) + w k ; (16) where z k R represents the actual measurement of x at time k, u k represents the input to the system on a discrete instant of time k, the random variables v k and w k represents the process and the measurement noise respectively. This kind of approach can be further extended to systems with more than one state. For linear dynamic systems some considerations may be taken into account to better suit the model for each application. The current work has considered aircraft dynamics with acceleration as white noise as described in reference [3]. In this representation the model 1483

4 is considered to have constant velocity and the white noise that represents the acceleration is not influenced by previous noise states - no correlation in time. Without loss of generality the following representation is considered: x k+1 = Fx k + Γ k v k. (17) knowing that each of the terms can be described as: F - System state transition matrix; Γ - Noise state transition matrix; x k+1 - System next state; x k - System actual state; The measurement state equation can also be extended: in which: z k = Hx k + w k ; (18) H - State observation matrix - commonly known as the measurement matrix; For purposes related to the dynamics of an object such as those used for target tracking, it is of interest to define the space state vector as: x k = [ x y z ẋ ẏ ż ] T ; (19) where x,y,z are the position of the system in ECEF referential system, and ẋ, ẏ, ż the respective velocities associated with each of the referential system axis. In the representation suggested by [3] the matrix associated to system noise are used to model the effects of the system s inputs u. Advantage of simplicity is obtained as the state and noise transition matrix are mathematical discrete equations of a system dynamics with constant velocity, and therefore represented by: F k = 1 t k+1 1 t k+1 1 t k Γ k = t k+1 t k+1 t k+1 t k+1 t k+1 t k+1 ; () ; (1) in which t k+1 = t k+1 t k. Considering white noise with zero mean disturbing the process: E[v k ] =. () The noise covariance is given by: Q k = E[[Γ k v k ][Γ k v k ] T ] = Γ k qγ T k ; (3) where in case Γ k is given by Equation 1, can be restated as: ] Q k = [ t 4 k+1 4 q t 3 k+1 q = E[v k v T k ] = t 3 k+1 q q t k+1 q σx σy σz ; (4). (5) In this q k is associated with the variances of acceleration σ x, σ y and σ z. These are defined by the intensity of noise in the process of constant velocity. 3. Kalman Filter The technique of the Kalman Filter [4] has received widespread use and, although the iterative algorithm has general application to state estimation, it is very well suited for use in target tracking problems. Given the equations of state evolution aforementioned and also the equations of state measurement, the algorithm produces an optimal estimate of the real state of the system with low computational cost. It is considered that the evolution of the states of the system, represented by the Equation 17 is a property of dynamics of the system itself. Despite that, measurements represented by Equation 18 are influenced by the sensors used resulting on non direct measures of the real state, been affected by some kind of noise. Also, the majority of measurements provide only partial information of the complete state, what imposes restrictions to the matrix H. The filter consider known the matrix H, as property of the sensor used, and also that the stochastic variables associated to the measurement noise have well known properties such as mean and covariances: E[w k ] = ; (6) E[w k w k T ] = Rδ(k l). (7) It can be noticed that the noise has been considered time stationary. It is also considered that process and measurement noises are not correlated: E[w k v l T ] = k,l. (8) The recursive estimator based on the system of equations presented that has an optimal solution for the covariance error of the stationary state is given by the Kalman Filter [5]. The filtering process is based on two well known distinct steps: prediction and update. Gathering the information of these steps the algorithm can be represented in a very useful form, know as the inverse form: ˆP 1 k+1 k+1 = [F k ˆP k k F T k + Q ] 1 + H k+1 R 1 H T k+1 (9) 1484

5 ˆx k+1 k+1 =F kˆx k k + ˆP k+1 k+1 H T k+1 R 1 z k+1 ˆP k+1 k+1 H T k+1 R 1 H k+1 F kˆx k k (3) Despite the fact that the majority of the problems of interest are non-linear and that uncertainties of process and measurements cannot be all the time well modeled as Gaussian distributions, the Kalman Filter has widespread applications in the field of aircraft tracking. In practice simplified models are used to approximate aircraft dynamics. 3.3 Centralized data fusion In the centralized data fusion, the combination of observations (measurements) of each sensor are combined in order to give a global estimative better than that obtained with the use of only one measurement. In this type of data fusion architecture the central processor generates optimum global state estimation and error covariances based exclusively in its previous estimate and in measurements provided by each sensor implemented by the use of a Kalman Filter. One of the methods used to implement this type of data fusion is the well known parallel fusion. The method is based on the utilization of a vector with the measurements so these can be processed in parallel. The effect in the algorithm is the inclusion of other observation states. Therefore, the algorithm presented before can be conditioned to this new approach and some parameters are redefined: z k = H k x k + w k ; (31) z k = [ z T 1 k,...,z T N k ] T ; (3) H k = [ H T 1 k,...,h T N k ] T ; (33) w k = [ w T 1 k,...,w T N k ] T ; (34) R = diag[r 1,...,R N ]; (35) where the terms described represent different measurements and characteristics from each sensors. The optimal solution is obtained by the application of the Kalman Filter algorithm given by the Equations 9 and Decentralized data fusion A track-level fusion method uses the fact that each sensor can perform its own preprocessing using its measurements in order to obtain a first state estimation generating local tracks. In this kind of approach each sensor must have its own algorithm to perform data processing and memorization. The tracks of each sensor are than transmitted to a central data processor responsible for the fusion process. The fact that this central processor uses a set of information from different sources can enable it to provide a more accurate state estimation. The use of Kalman Filter to derive other algorithms to perform this operation can also provide an optimal estimation and different forms of approaches have been considered [6]. Covariance Intersection algorithm has been considered in this work. This technique provides a method to fuse track level information without taking into account the dependence of the measurements. An analogy to the geometric representation of covariance of the measurements is the main argument of this technique [6]. In the case of tracking in which two sensors process their measurements and have local tracks, each one will have along with the position estimation a covariance of this process. Given that for sensors 1 and respectively these parameters can be stated as: (ˆx 1, ˆP 1 ) and (ˆx, ˆP ). the algorithm based on Kalman Filter with the steps of Prediction and Update can be described as follows [7]: Prediction Update ˆx k+1 k = F kˆx k k ; (36) ˆP k+1 k = F k ˆP k k F T k + Q; (37) ˆP 1 k+1 k+1 =ω 1 ˆP k+1 k + ω 1 ˆP 1 1 (k+1 k) + ω ˆP 1 (k+1 k) ; ˆP 1 k+1 k+1ˆx k+1 k+1 =ω ˆP 1 k+1 kˆx k+1 k+ ω 1 ˆP 1 1 (k+1 k)ˆx 1(k+1 k) + ω ˆP 1 (k+1 k)ˆx (k+1 k). (38) (39) the terms ˆP 1 1 (k+1 k), ˆP 1 (k+1 k), ˆx 1(k+1 k) and ˆx (k+1 k) are associated to filtering processes performed by sensors 1 and, that uses in the present case Kalman Filter algorithms. The above mentioned steps are subjects to the following conditions: ω + ω 1 + ω = 1; (4) ω j, j. (41) It s interesting to note that the parameters ω j provide a new degree of freedom to the technique. That allows a further optimization process to be implemented in the central element that fuses data. Some alternative proposal to this kind of optimization have been presented on the reference [6], although the current work does not emphasize the use of those. 4 Results The present work deals with an actual air traffic monitoring problem. The focus is on target tracking in areas covered by ADS-B and radar sensors. Data from these different sensors are used to calculate a best estimate of aircraft position. In 1485

6 order to investigate the benefits of using ADS-B sensors in ATM systems a single target tracking simulation was performed, according to the system represented in the Figure. The monitoring entity is connected to the radar sensor and to the ADS-B sensor, being responsible for the fusion of sensors data. The aircraft has its own position provided by an embedded GPS system integrated with ADS-B Out equipment. The simulated scenario also implements the satellite configuration for the GPS system. Measurement errors: noise standard deviation (σ) in range 5 meters, azimuth,5 and elevation,5. The radar sensor generates measurements in polar coordinates. The ADS-B sensor generates data in ECEF referential frame (Cartesian coordinates). In order to perform the data fusion all measurements need to be represented in the same referential frame, and therefore alignment of measurements were made according to the algorithm reported by Peters in [9]. The objective is to present the significant improvement in target tracking results, evaluating the gains provided by the employment of the new sensor in ATM systems. In order to provide comparison some random scenarios were simulated and therefore simulated scenario did not represent a realistic aircraft route. The first one considers only the radar sensor (case 1) and the second one considers the radar sensor and the ADS-B sensor using a specific data fusion architecture (case ). A third case (case 3) with the use of only ADS- B sensors was also considered in order to provide a more relevant comparison between scenarios. The results were compared using statistics techniques. Error histograms for the cases 1 and are presented on Figures 3 and 4 respectively. The quantitative gain was not considered. The histograms clearly show the improvement when more accurate information is used, as those provide by ADS-B. Figure : Simulated scenario The following considerations were taken into account in the simulation scenario: The radar sensor position is well known in ECEF referential frame; Both ADS-B and radar sensors are able to monitor the same airspace; Stochastic characteristics of errors from ADS-B system are obtained from GPS position; No filtering algorithms are used to enhance the solution in the embedded GPS, resulting on a lower performance than the actual equipments; There are no losses on ADS-B messages that can affect the target tracking algorithm; There is enough bandwidth for data transmission between sensors and the central control system; The sensors are assumed to have the same sampling rates and no communication delays are considered; Radar generated measurements were modeled according to formulation presented on [8] with the following assumptions: sea-level altitude and rotations period of 1 r.p.m. Frequencia (admensional) Erro absoluto (m) Figure 3: Error histogram for case 1 For the case 3, considering the use of the ADS-B sensor only, error histogram is presented on Figure 5. As can be seen this histogram is quite similar to the one representing case where absolute errors are condensed bellow 3 meters. Despite this fact errors above 3 meters are found in a significant quantity in case, what affects the cumulative error count represented on both histograms by the solid line. Above 9% the difference between them becomes more clear with a smoothing in the cureve representing case. This result is assigned to the fact of using only accurate measurements. 1486

7 1 9 8 Frequency (dimensionles) Absolute error (m) Figure 4: Error histogram for case 1 9 Figure 6: Comparison of cumulative errors on both cases 1 and 8 Frequency (dimensionless) Absolute error (m) Figure 5: Error histogram for case 3 The cumulative error comparison of cases 1 and is shown in Figure 6. The discrepancies between both cases can be clearly studied quantitatively. The literature frequently addresses tracking problems like this comparing the performance related to 95% of cumulative error [1]. At this point the difference between both cases may reach 4 meters. This value represents approximately.6 times the value of the error presented using centralized data fusion algorithms with both sensors. As the use of centralized data fusion is sometimes restricted by data bandwidth communication, the above cited decentralized data fusion algorithm were also evaluated in this study. As mentioned this technique provides another degree of freedom to the optimization of the tracking results, which were generated varying the values of the parameters ω in the Equation 4. For a wide range variation on these parameters cumulative errors are represented by the Figure 7. No effort has been taken to choose the best parameters for the presented scenario. Figure 7: Cumulative errors of decentralized data fusion Results of decentralized data fusion show that cumulative errors can range from a situation close to the one provided by centralized one to worst cases as the ones provided with the use of only radar sensors. To provide a better view of the situation the cases were plotted in Figure 8 as a function of the parameters ω related with the value of error at a cumulative error of 95%. 1487

8 [3] Y. Bar-Shalom, X. -Rong Li and T. Kirubarajan, Estimation with Applications to Tracking and Navigation, John Wiley and Sons Inc, 1. [4] R. E. Kalman, A New Approach to Linear Filtering and Prediction Problems, Transactions of the ASME Journal of Basic Engineering, Vol 8, No. SeriesD, pp , 196. [5] S. M. Bozic, Digital and Kalman Filtering, Edward Arnold Ltd, Figure 8: 95% of cumulative errors for decentralized data fusion The influence of utilization of parameters ω different of zero can be clearly noted. What is really outstanding is the fact that the parameter ω related to ADS-B sensor is much more efficient in the reduction of cumulative error. The higher the weight of ADS-B sensor data the lower is the resulting error. However it is not desirable to make radar parameter zero, and therefore for applications using this technique either a consistent choice of the parameters must be made, for example ω radar =. and ω ADS B =.6, or the use of a well established algorithm for the optimization on the new degree of freedom as described in reference [6]. 5 Conclusions The redesign and enhancement of the Air Traffic Management to accommodate the expected rise in demand from air transportation demands the development of a new technology. The results presented in this paper show that the emerging ADS-B technique is able to substantially increase capacity and efficiency of ATM systems, while maintaining and possibly improving safety. The simulations show that both centralized and decentralized data fusion can bring more accuracy to the scenario, but restrictions to the last one demand an efficient choice of data weight parameters. Despite the benefits of both the use of one or another may be restricted to practical issues, but it is clear that the scenario can be enhanced in order to allow a more efficient use of airspace to cater for the expected traffic growth. [6] D. Smith and S. Singh, Approaches to Multisensor Data Fusion in Target Tracking: A Survey, IEEE Transactions on Knowledge and Data Engineering, Vol 18, No. 1, pp , 6. [7] S. J. Julier and J.K. Uhlmann, A Non-Divergent Algorithm in the Presence of Unknown Correlation, Proceeding of the American Control Conference, Vol 4, pp ,1997. [8] Y. Zhou, A Kalman filter based registrations approach for multiple assynchronous sensors, Defence R&D Canada Reports, No.DRDC-OTTAWA-TR-3-, Ottawa, 3. [9] D. J. Peters, A pratical guide to level one data fusion algorithms, Defence R&D Canada Reports, Dartmouth, 1. [1] A. Smith, R. Cassell, T. Breen, R. Hulstrom and C. Evers, Methods to Provide System-Wide ADS-B Back- Up, Validation and Security, 5th Digital Avionics Systems Conference, pp. 1-7, 6. References [1] W. Hofmann, H. Lichtenegger and J. Colling Global Positioning System Springer, [] J. Farrel and M. Barth, The Global Positioning System and Inertial Navigation, Addison-Wesley,