handling of sensor registration errors in track level ...

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HANDLING OF SENSOR REGISTRATION ERRORS IN TRACK LEVEL FUSION Evrim Anıl EVİRGEN, Orhan AYRAN, Tolga SÖNMEZ, Ziya ULUSOY HAVELSAN, Mustafa Kemal Mahallesi 2120. Cadde No: 39, P.K. 06510 Çankaya, Ankara, Turkey [email protected], [email protected], [email protected], [email protected]

1.0 INTRODUCTION Modern surveillance systems utilize various types of sensors including optical sensors, infrared sensors, electronic support measure sensors (including ELINT and COMINT), automatic identification system (AIS) and primarily radars. Radars are the main sensors of these systems due to their capability to detect targets from long ranges. As HAVELSAN being the main contractor of Turkish Coast Surveillance Radar System Project, HAVELSAN has challenging responsibiliy to effectively utilize the current and the future radars to compile the real time tactical picture.

Figure 1 - Turkish Coast Surveillance Radar System Project Coverage [1]

Decentralized fusion is one the most prominent architectures for distributed systems. A decentralized data fusion system has processing nodes, connected by communication links. The network topology is not transparent to the nodes. Each node communicates with other nodes and processes the relevant information received from other nodes. There is no central node thus more than one node may perform the same task. A node may also own a sensor or sensors. Decentralized systems have certain advantages like failure of a node or link can be tolerated within the system. The system can be scaled easily by adding new nodes without changing the architecture. [2]

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Fusion System

Sensor

Processing Node

Sensor

Processing Node Processing Node

Processing Node

Processing Node

Sensor

Sensor

Figure 2 - Distributed Fusion Architecture

Due to bandwidth requirements, it may be preferable that the radars provide track data. This data includes position, course and speed which must be effectively fused inside the surveillance system. Coverages of different radars may overlap, which implies a target may be detected by more than one radar. In that case different radar tracks corresponding to the same physical target must be identified before the fusion. This is not a straightforward task if there are registration errors embedded in the track data.

Figure 3 – Example Overlapping Radar Coverage Scenario

Track data has two types of errors namely: random and systematic errors. The random errors may be the outcomes of detection and track processing techniques inside the sensor, which reduces the possibility for the fusion system to correct them. The systematic errors or offsets are due to sensor calibration offset, platform flexure, sensor perspective offset, sensor internal clock errors, and coordinate transformations. Systematic errors must be eliminated by fusion systems before the fusion as they degrade the overall performance. This process is named as “sensor registration”. [3]

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2.0 TRACK LEVEL FUSION ALGORITHMS Distributed fusion has been a very popular subject among fusion community. There are two main approaches. First approach aims finding the “best” linear combination of estimates to optimize some criteria, e.g., weighted least squares or minimum variance. If the estimates to be fused are not the sufficient statistics, the optimal linear combination may not be as optimal as the centralized estimate. Some researchers develop a unified model for estimation fusion based upon the best linear unbiased estimation (BLUE) or linear minimum variance approach. [4] The second approach attempts to reconstruct the optimal centralized estimate (by fusing the measurements directly) from the tracks. In particular, the information graph approach has been used to identify additional information needed for complicated fusion architectures. Algorithms for fusing both means and covariances for linear systems and general probability distributions have been developed. This fusion algorithm focuses on decorrelation of common prior information, and is not particularly effective in handling correlation in measurement noise (which may result from common process noise accumulated between fusion instants). It is also a linear combination of estimates when means and covariances are given. The covariance intersection filter has been proposed to fuse estimates without assuming any knowledge on the correlation between the estimates to be fused. It is supposed to be more robust than the linear combination algorithm and provides a bound on the estimation accuracy. However, the covariance intersection filter is conservative and pessimistic yielding larger error ellipsoids than the true one. State estimate of CI:

 = 
 
 + (1 − )
  Error covariance of CI: 
 =  + (1 − ) 

2-sigma contours of first and second covariances Covariance intersection for omega = 0.1 1.5 1.5 1

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Covariance intersection for omega = 0.5 1.5 1

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Covariance intersection for omega = 0.9 1.5

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Figure 4 – Covariance intersection

There are algorithms that can utilize the correlation information between estimates to optimally fuse the estimates.

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3.0 EFFECTS OF SYSTEMATIC ERRORS ON TRACK LEVEL FUSION Covariance Intersection is suitable for data fusion of different mean and covariance estimates. But in practice systematic errors may cause two mutually inconsistent mean and covariance estimates, belonging to the same real-world object, i.e., the differences between their means is much larger than what can be expected based on their respective error covariance estimates. [5] The Covariance Intersection method guarantees consistency as long as the estimates to be fused are consistent. In the deconfliction problem it is only known that one of the estimates, either first mean/covariance pair or second mean/covariance pair is a consistent estimate of the target of interest. If it is not possible to know which estimate is erroneous, the only way to rigorously combine the estimates is to form a unioned estimate that is guaranteed to be consistent with respect to both of the two estimates. This Covariance Union of the two estimates can be subsequently fused with other consistent estimates using Covariance Intersection. 6 Center of estimate 1 Covariance of estimate 1 Center of estimate 2 Covariance of estimate 2 Center of CU estimate Covariance of CU estimate Center of Fast CI estimate Covariance of Fast CI estimate

5 4 3 2 1 0 -1 -2 -3 -6

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Figure 5 – Comparison of Covariance Union with Covariance Intersection

This approach should be used when if no correction can be performed. It is not optimal indeed, implying the need for an effective registration algorithm.

4.0 SIMULTANEOUS SOLUTION OF REGISTRATION ERRORS AND ASSIGNMENT PROBLEM 4.1

Data Correlation (Assignment Algorithms)

A typical fusion tree node architecture is defined in [2]. The data fusion nodes perform the following main tasks: •

Data preparation (common referencing) — time and coordinate conversion of source data, and the correction for known misalignments and data conflicts;

•

Data correlation (association) — associates data to “objects”;

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•

State estimation and prediction — updates and predicts the “object” state (e.g., kinematics, attributes, and ID).

Figure 6 – Data fusion tree node

Data correlation includes three subtasks which are: •

Hypothesis generation: The current data and previous hypotheses are used to create the current correlation hypotheses using feasibility gating, pruning, combining, clustering, and object aggregation. Alternate hypotheses are defined which represent feasible associations of the input data, including existing information. Feasibility is defined in a manner that effectively reduces the number of candidates for evaluation and selection.

•

Hypothesis evaluation: Each of these feasible correlation hypotheses are evaluated using kinematic, attribute, ID, and a priori data as needed to rank the hypotheses (with a score reflecting “closeness” to a candidate object or hypothesis) for more efficient selection searching. Evaluation techniques include numerical (Bayesian, possibilistic), logical (symbolic, nonmonotonic), and neural (nonlinear pattern recognition) methods, as well as hybrids of these methods. The core of this task corresponds to assignment problem in the domain of combinatorial optimization. There are extensive research on this subject and many techniques are proposed like Hungarian, Auction and Jonker-Volgenant-Castanon.

•

Hypothesis selection: Involves a search algorithm that selects one or more association hypotheses to support an improved state estimation process (e.g., to resolve “overlaps” in the measurement/hypothesis matrix). This algorithm may also provide feedback to aid in the generation and evaluation of new hypotheses to initiate the next search. The selection functions include elimination, splitting, combining, retaining, and confirming correlation hypotheses in order to maintain tracks and/or aggregated objects.

In an optimistic scenario this is an elegant way to perform the task. But in some scenarios the registration errors may not be eliminated and propagate to the next step of the process making data correlation a complicated task.

4.2

Registration Errors

As discussed before most track level multiple target tracking and fusion systems are in hierarchical nature. Each sensor processes its own data to generate and maintain sensor-level tracks, while each fusion node fuses the sensor-level tracks into a set of system level tracks. The track-to-track association problem is crucial in the sense that it affects the overall performance in a large extent. A lot of factors can complicate this association. First, participating sensors operating under different principles may track different aspects of the truth. Second, closely spaced objects may be difficult to resolve due to individual sensor sensitivity. A third issue concerns the error due to sensor biases, which results from misalignment of measurement axes and sensor location error often arise and are difficult to estimate. Proper estimation and removal of this error is important to make correct assignments [6].

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Figure 7 – Sensor Bias Errors [7]

There are several potential sources of error that bias removal algorithms attempt to solve. Moore and Blair group these sources into three broad categories: sensor errors, sensor/platform position and heading errors, and transformation errors from one sensor to another. Sensor registration attempts to estimate errors associated with biases that are constant or changing very slowly with time so that they can be removed before filtering takes place. Sensor biases, which may arise in both range and angle dimensions, often account for the majority of the total error. Moreover, they are typically the most difficult to estimate and eliminate. While range error can consist of offset and scaling errors, the angle error is typically the cause of the error that sensor registration seeks to remove. There is vast number of researches in this area to overcome this problem. There are two main categories for sensor registration:

4.3

•

First class of algorithms estimate the errors in a least square sense, if the data association between different sensor tracks are known.

•

Second class of algorithms does not have the data association information a priori. Therefore, second class of algorithms determines the systematic error and the data association simultaneously.

Simultaneous Solution of Registration Errors and Assignment Problem

In some researches some approaches have been proposed to determine systematic sensor registration errors. This approach is applicable to situations where the correspondence of data between the sensors is not known a priori. [6] One approach about track fusion is to decouple the problem of estimating the sensor biases and the problem of track association. There are many researches using this approach but these stem from the fact that these problems are not easily solved independently. That is procedure of one needs the solution of the other and vice versa. It is not easy to solve association without knowing sensor biases. Also it is not easy to estimate sensor biases without knowing the right associations. Levedahl and Kenefic before him were the first ones who attempted to combine and formulate the two problems in order to solve them simultaneously. This approach is called as Global Nearest Pattern Matching (GNPM) problem. Algorithms that solve the GNPM problem generate the K best bias-association hypotheses and rank them according to their corresponding bias-association likelihood. Generating the best hypothesis may not be adequate and misleading because there may be other hypothesis having close likelihoods to the best one. In other words MP-IST-SET-126-Evirgen - 6

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it may be a better choice to present the operator the best sub-hypothesis that is common to the highest likelihoods. GNPM problem can be briefly described as follows: Consider two independent sensor systems –sensor A and sensor B– tracking an unknown number of targets in space. Let  = 1, … ,  and  = 1, … ,  denote the set of tracks formed by sensors A and B, respectively. Without loss of generality, we assume throughout that  ≤  . Due to a host of factors, including geometry and sensor resolution, the number of tracks formed by sensors A and B will often differ from the true number of targets and from one another. Let  and  , for  ∈  , denote the state estimate and error covariance matrix, respectively, of the ith sensor A track. Similarly, let  and  , for  ∈  , denote the state estimate and covariance matrix, respectively, of the jth sensor B track. We assume that estimation errors for each sensor reporting on a common target are uncorrelated. This is only an approximation since; in general, track errors from different sensors are correlated. We assume all state estimates and covariance matrices have been extrapolated to a common time point and have been converted to a common D-dimensional reference frame. A key assumption in this track-to-track association framework is that each track state is corrupted by a constant, but unknown, sensor bias. Ideally, these individual sensor biases would be estimated and removed prior to performing track-to-track association, but this is not always possible. Consequently, a distinguishing facet of this approach is the attempt to estimate the inter-sensor bias, or the relative bias, between the two sensors via maximum a posteriori (MAP) estimation. That is, this is a Bayesian estimation framework. The relative bias b is modelled as a Gaussian random vector having mean 0 and covariance R in a Cartesian coordinate frame. It is assumed that sensor bias only degrades a sensor’s capability of measuring target state, and not its ability to detect a target.

We denote a track-to-track association by the vector j. Consequently, the association of the ith track in  with the jth track in  is denoted by ,  . It is convenient to think of the pair ,  as an undirected arc in a bipartite graph and the vector j as a compact notation for writing 1,  , 2,  , … ,  ,  ಲ . It is possible that the ith track in  is not assigned to any track in  , in which case we still write ,  , but  = 0. We refer to such an assignment as a null assignment, or by saying that track i was assigned to the dummy track. We sometimes refer to partial and complete assignments. A partial assignment is one in which a strict subset of the sensor A tracks are assigned, while in a complete assignment, all sensor A tracks are assigned. A partial assignment can be made complete by assigning the currently unassigned sensor A tracks to the dummy track. It is implicitly assumed that at most one sensor A track can be assigned to a sensor B track and vice versa. We refer to the pair ,  as a bias-association hypothesis, a hypothesis, or a solution to the GNPM problem. A popular objective for track-to-track association is to simultaneously find the most likely track-to-track association and relative bias estimate. To do so, a likelihood function is needed to compare different solutions. The likelihood function for the GNPM problem is based upon the marriage of an a posteriori bias estimation problem and the standard two sensor track-to-track association problem. The first term

 

೅ షభ /

(2) / ||

(where || denotes the determinant of R) is nothing more than a prior probability density on the relative bias, which we assume is available.

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The second term consists of the product of the incremental likelihoods of track assignment. Specifically, given a bias estimate b, the likelihood of assigning track  ∈  and track  ∈  is  

 ೔ೕ ()/ మ

(2) /  !

where • • • •

 is the target density, i.e., the number of targets per unit volume in D-dimensional space;  is the probability that a target is tracked by sensor A and sensor B; ! =  +  ;

    =   −  −  ! "    − −  is the squared Mahalanobis distance between tracks i and j, parameterized by a bias estimate b. 

It is also possible for track  ∈  to be unassigned, in which case the incremental likelihood is the null assignment likelihood   where • • •

 =  ̅ +  represents a target density of no target existing for sensor A, and ̅ is the probability of tracking an object with sensor B but not with sensor A;  =   +  represents a target density of no target existing for sensor B, and  is the probability of tracking an object with sensor A but not with sensor B;

the densities  and  represent the false track densities for sensor A and B, respectively. False tracks are not uncommon when tracking extended objects, i.e., objects for which a sensor may receive multiple detections on a given data frame.

Multiplying these likelihoods together, we arrive at the GNPM likelihood function: #,  =



೅ షభ /

(2) / ||

×$

ಲ



( &  



మ ೔ೕ ()/ ೔

if  > 0 &

(2) /  ! ' , & & %  if  = 0+

It should be noted that we, like many others, abuse terminology by referring to #,  as a likelihood function, when, in fact, it is a posterior joint-probability-massdensity mixture function. Note that we have assumed that assignment likelihoods for track pairs are independent. From a computational perspective, it is more convenient to work with the negative log likelihood. After some algebra and the removal of unnecessary constants, we obtain a modified version of the negative log likelihood function: −log#,  =    + . / ೔ 

ಲ







where

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/  = 0

  + 123 ! 4  ∈  " ವ/మ   ೔ and 3 = −2123 5 ಿ೅ಲ ಿ೅ಳ 6   ೅ ಲಳ 3 4  = 0

is the so-called (log likelihood) gate value, which can be interpreted as a cost incurred for assigning the ith sensor A track to the dummy track j = 0.

4.4

Human Interaction for Enhancing Registration Error Solution

There are ways to incorporate human interaction into the process. These are: •

In a scenario where there are lots of targets to take into account, some focus areas can be selected to apply registration procedure. This is desirable because of the algorithmic complexity of permutation operation ( O(n!) ) required for assignment of large number of targets.

•

There may be situations where targets of opportunity like friendly tracks or known targets which can be distinguished from other tracks. In this case the tracks received from different radars can be associated based on some identification information hence the assignment is not problem anymore and the problem downgrades to a pure registration problem.

•

Based on some threshold received from operators, a fine gating can be applied to eliminate some unlikely hypothesis as a pre-processing step. There may be other ways to pruning of unlikely hypothesis which can speed up the solution.

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If there are known limits for bias values these are used as constraints for optimization

•

In a time varying environment where the own platform is manoeuvring and sensors are changing their orientation some recursive estimation techniques using results of previous estimations can be employed to increase performance.

5.0 MULTI-FRAME PROCESSING The GNPM likelihood function can be evaluated for multiple frames and combined simply as: # ,  = $ #, 

ಾಷ



where nMF is the number of frames to be processed simultaneously and LMF is the multi-frame likelihood function. Also both sensors assumed to have bias thus a correction is performed for both as in Figure 7.

5.1 5.1.1

Simulations Scenario 1

In first situation, the single frame and multi frame approaches are compared when there are bias and random errors at the same time. Radar 1 detects 3 targets, Radar 2 detects 5 targets. 100 Monte Carlo runs are analysed. Targets are distributed uniformly between 2000 – 3000 m for x and 1500 – 2500 m for y coordinates. Target speeds are uniformly distributed between 0 – 20 m/s.  and  are assumed to be 1,  and  are assumed to be 0 for convenience.

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5000 Targets Radar 1 Radar 2

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Figure 7 – Radar coordinates and distribution of initial target locations and for scenario 1

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Results: RMS Bias Estimation Errors

Radar 1 Range Bias (meter)

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Radar 2 Bearing Bias (degree)

Correct Assignment (%)

Single Frame

2.8461

0.4858

2.7252

0.4192

100

Multi Frame (N = 15)

1.2266

0.1666

0.9801

0.1926

100

Bias estimation of multi frame approach is clearly better than single frame approach. Single frame approach fails to estimate range bias while multi frame approach has a better performance. Assignment performance is same for both approaches. 5.1.2

Scenario 2

In second situation, the single frame and multi frame approaches are compared when there are bias and random errors at the same time. But this time targets are closer to each other and the random errors are larger which makes a more challenging case. Radar 1 detects 3 targets, Radar 2 detects 5 targets. 100 Monte Carlo runs are analysed. Targets are distributed uniformly between 2600 – 3000 m for x and 2600 – 3000 m for y coordinates. Target speeds are uniformly distributed between 0 – 20 m/s.  and  are assumed to be 1,  and  are assumed to be 0 for convenience.

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5000 Targets Radar 1 Radar 2

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Figure 8 – Radar coordinates and distribution of initial target locations for scenario 2

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Results: RMS Bias Estimation Errors

Radar 1 Range Bias (meter)

Radar 1 Bearing Bias (degree)

Radar 2 Range Bias (meter)

Radar 2 Bearing Bias (degree)

Correct Assignment (%)

Single Frame

8.5109

1.4034

9.7172

1.3582

100

Multi Frame (N = 15)

0.8470

0.1344

0.8333

0.1401

100

Bias estimation of multi frame approach is clearly better than single frame approach again, but this time the improvement is more significant for the dense environment. Single frame approach again fails to estimate range bias while multi frame approach offer a better performance. Assignment performance is same for both approaches.

5.2

Comparison with Single Frame

The performance advantage of the multiple frame methods over the single frame methods follows from the ability to hold difficult decisions in abeyance until more information is available and the opportunity to change past decisions to improve current decisions. In dense tracking environments the performance improvements of multiple frame methods over single frame methods is very significant, making it the preferred solution for many tracking problems. [8] Multiple frame data association methods are better to handle closely spaced objects caused by dense threats with associated objects, false signals and clutter, radar multi-path, residual sensor registration biases, counter-measures, unresolved closely spaced objects, and data from 2-D sensors. Multiple frame data association methods offer improved performance in, for example, improved accuracy of the target tracks, discriminants, and covariance consistency and also reduced track switches, track breaks, and IST-SET-126

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missed targets. What is more, local sensor corruption can be moderated in a network tracker that uses multiple frame data association. Metrics of concern for consistency of the threat pictures across platforms include common track numbers and also similar target state estimates, error covariance matrices and target discrimination decisions from platform to platform. The only drawback of multi frame processing is delayed decision but it is often preferable to mislead the operators with wrong information. Processing power required is not a crucial issue with modern high performance processors.

6.0 CONCLUSION Efficient fusion of track level data is a crucial issue in distributed fusion systems. Registration and association are some of the most challenging problems in these systems because they are tightly coupled issues. The extension of joint registration and association solution framework to multi frame processing enhances the performance significantly. The drawback of the multi frame processing is its computational burden, but the implementation can be made parallel in modern computing platforms as different hypothesis can be evaluated concurrently.

7.0 ACKNOWLEDGEMENTS We gratefully acknowledge invaluable discussions with many people from whom we have learned much about data fusion and target tracking over the years and supported our studies. We would particularly like to mention Tayfur Yaylagul. We also acknowledge Turkish Coast Surveillance Radar System Project team of HAVELSAN with thanks for supporting our work.

8.0 REFERENCES [1]

http://www.bilisimdergisi.org/s153/ Accessed 30.03.2015

[2] Martin E. Liggins, David Hall, James Llinas, Handbook of Multisensor Data Fusion: Theory and Practice, Second Edition, CRC Press, 2008 [3] Michael J. Hirsch, Panos M. Pardalos, Mauricio G. C. Resende, Sensor Registration in a Sensor Network by Continuous Grasp, IEEE Military Communications Conference, 2006

Chee-Yee Chong, Shozo Mori, Convex Combination and Covariance Intersection Algorithms in [4] Distributed Fusion, FUSION 2001, Fourth International Conference on Information Fusion, 2001 [5] Jeffrey K. Uhlmann, Covariance consistency methods for fault-tolerant distributed data fusion, Information Fusion, Elsevier, Volume 4, Issue 3, 2003 [6] Dimitri J. Papageorgiou, Michael Holender, Track-to-Track Association and Ambiguity Management in the Presence of Sensor Bias, Journal of Advances in Information Fusion Vol. 6, No. 2 December 2011 [7] Dana Martin, Registration Techniques for Multiple Sensor Surveillance, Proceedings of the 9th MIT/LIDS Workshop on C3 Systems, 1986 [8] Suihua Lu, Aubrey B. Poore, Brian J. Suchomel, Network-Centric MFA Tracking Architectures, FUSION 2002, Fifth International Conference on Information Fusion, 2002

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