Space Based Sensor Management Strategies Based on ... - IEEE Xplore

Space Based Sensor Management Strategies Based on Informational Uncertainty Pursuit-Evasion Games Dan Shen, Bin Jia, Genshe Chen

Khanh Pham

Erik Blasch

Intelligent Fusion Technology, Inc. Germantown, Maryland, USA {dshen, bjia, gchen}@intfusiontech.com

Air Force Research Laboratory Albuquerque, NM [email protected]

Air Force Research Laboratory Rome, NY, 13441 [email protected]

measurements [5]. Various space tracking methods have been developed [6, 7, 8, 9] along with space tracking conditions [10, 11, 12] using advanced methods [13].

Abstract— In this paper, a pursuit-evasion (PE) orbital game approach for space situational awareness (SSA) is presented to deal with imperfect measurements and information with uncertainties. The objective function includes the distance to be minimized by pursuers (observers/sensors) and maximized by evaders (space objects being tracked). The proposed PE approach provides a method to solve the realistic SSA problem with imperfect state information, where the evader will exploit the sensing and tracking model to confuse their opponents by corrupting their tracking estimates, while the pursuer wants to decrease the tracking uncertainties. A numerical simulation scenario with one space based space surveillance (SBSS) satellite as a pursuer and one geosynchronous (GEO) satellite as an evader is simulated to demonstrate the PE orbital game approach. Both SBSS and GEO apply the continuous low-thrust such as the Ion thrust in maneuvers. An add-on module is developed for the NORAD SGP4/SDP4 to propagate the satellites with maneuvers. Worst case maneuvering strategies for SBSS satellites are obtained from the Nash equilibrium of the PE game.

However, the optimal control approach doesn't consider the intelligence of the space objects that may change their orbits intentionally to make it difficult for the observer to track it. Such situations are best modeled and investigated using differential games, which was first researched by Isaacs in the 1960s [14]. Game theory has been applied for situation awareness [15], communications [16, 17, 18], and sensor management [19, 20]. In order to address the assessment of maneuverability question, a pursuit-evasion game model can be applied [21, 22, 23]. In this paper, a pursuit-evasion (PE) orbital game approach for space situational awareness (SSA) is presented to deal with imperfect measurements and information with uncertainties, which will be minimized by pursuers (observers/sensors) and maximized by evaders (space objects being tracked). The imperfect measurement information leads to imprecision in the other player’s knowledge of the space picture. The proposed PE approach will solve the realistic SSA problem with imperfect state information, where the evader will exploit the sensing and tracking model to confuse their opponents by corrupting their tracking result, while the pursuer wants to decrease the tracking uncertainties.

Keywords—Pursuit-evasion (PE) games; space situational awareness; tracking uncertainties; SGP4/SDP4, satellite maneuvering strategies

I. INTRODUCTION Space object tracking is an import element of space situational awareness (SSA). Typically, SSA is based on gathering data to track resident space objects, debris, and natural phenomena (e.g., solar flares, comets, asteroids). SSA tracking includes understanding of orbital mechanics, mission policies, and technical purpose (e.g., communications). SSA includes elements of the Dynamic Data-Driven Application System paradigm with models (e.g., orbital mechanics), measurements (e.g., space-based optical sensors), computational software (e.g. tracking), and application-based systems coordination. Knowing the locations of space objects from low-level information fusion supports high-level information fusion tasks of sensor, user, and mission refinement [1, 2]. To accurately provide SSA, space object assessment can be coordinated through a User-Defined Operating Picture (UDOP) [3].

The rest of the paper is organized as follows. Section II presents the general sensor model and tracking. A pursuitevasion game model is detailed in Section III. In Section IV, a typical SSA scenario is simulated to illustrate the game approach. Finally, conclusions are drawn in Section V. II. GENERAL SENSOR MODEL AND TRACKING The ability of a sensor to detect an object is subject to an array of environmental influences and noise sources that make the sensor range estimate unpredictable at best [24, 25]. For the SSA applications, sensor readings can also be subject to electronic countermeasures (ECMs) that are designed to affect sensor inputs in ways that deceive the detection process [26].

Whether deliberate on unintentional, some of space objects may cause confusion to observers (satellites) by performing orbital maneuvers [4]. Generally, the space object tracking problem can be modeled as a one-sided optimization (optimal control) setup or a two-sided optimization (game) problem. In the optimal control setup, the states (positions and velocities) of space objects are computed (filtered) based on the sensor

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We consider space object sensing to be the process of detecting a known target signature either explicit or obscured by background noise. For a given sensor input, the classification process outputs follow one of the four traditional outcomes as detailed in Table I.

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TABLE I. FOUR POSSIBLE OUTCOMES OF THE TARGET-DETECTION PROCESS

Target Detected Target Not detected

Target Present True Positive False Negative

TP), TP classified as FP (TP, FP), FP classified as FP (FP, FP), or FP classified as TP (FP, TP). However, no detection only has the following two possible belief classifications: (ND, TN) or (ND, FN). We denote the six blocks on the right shown in Fig. 1 to be cases 1– 6, with associated probabilities p1, p2, …, p6.

Target Not Presented False Positive True Negative

For a true positive (TP), the target is detected and present; whereas for a false positive (FP), the target is detected but absent (Type II error), for a false negative (FN), the target is present but not detected (Type I error) and in the true negative (TN), the target is absent and not detected. For TP and TN, the sensor works correctly and is reported as a correct classification. FN (FP) corresponds to a Type I (Type II) error in the decision theory. Using Table I and the fact that when a target is present, it is either detected or not detected, P(FN) = 1 í P(TP). Similarly, an absent target is either detected or not, giving P(TN) = 1 í P(FP). Besides target detection, decision theory is used to determine whether a given sensor reading is correct or in error. Therefore, we conclude that a target is present only when P(TP) > P(FP).

p1 =prob(S = TP & D = TP) p2 =prob(S = TP & D = FP) p3 =prob(S = FP & D = TP) p4 =prob(S = FP & D = FP) p5 =prob(S = ND & D = TN) p6 =prob(S = ND & D = FN)

Based on [27], we can derive a posteriori belief functions of the abovementioned cases 1-6 by using the exponentially weighted moving average (EWMA) approach from the statistical control theory. The weights (wold and wnew) can be varied to fit the application, as long as they sum to 1. In our research scenario, we set wold = 0.2 and wnew = 0.8.

We assume that the pursuer and evader have perfect a priori information of each other’s positions at the beginning of the game. After the start of the game (a point in time), both players rely on their sensor inputs. A sensor reading is a tuple consisting of time, detection state, and target coordinates (when a target is detected). When an FP occurs, the sensor returns random coordinates within the effective sensing range. As shown in Fig. 1, at any point in time, the pursuer’s sensor has the following two possible states: target detected or no target detected. If there is a detection event, the pursuer needs to decide whether the detection is a TP or an FP. This classification is done by determining which case is most likely, given the a priori information. When no target is detected (ND), the system needs to determine whether the reading is a TN or an FN, again using a priori information. A non-detection event is a TN if the evader is outside the radar’s effective sensing range.

‫݂݀݌‬ଵ ൌ ‫ݓ‬௢௟ௗ ‫݂݀݌‬௢௟ௗ ൅ ‫ݓ‬௡௘௪ ‫݂݀݌‬ଵǡ௡௘௪ ͳǡ ƒ––Šƒ–’‘•‹–‹‘ ‫݂݀݌‬ଵǡ௪ ൌ ൜ Ͳǡ ‘–Š‡”’‘•‹–‹‘• ‫݂݀݌‬ଶ ൌ ‫݂݀݌‬௢௟ௗ ‫݅݊ݑ‬Ǥ ǡ ƒ–’‘•Ǥ™Ǥ”‡ƒ†‹‰ ൐ ‫݈݀݋݄ݏ݁ݎ݄ݐ‬ ‫݂݀݌‬ଷǡ௪ ൌ ൜ Ͳǡ ‘–Š‡”’‘•‹–‹‘• ‫݂݀݌‬ସ ൌ ‫݂݀݌‬௢௟ௗ ‫݂݀݌‬ହ ൌ ‫ݓ‬௢௟ௗ ‫݂݀݌‬௢௟ௗ ൅ ‫ݓ‬௡௘௪ ‫݂݀݌‬ହǡ௡௘௪ ‫݅݊ݑ‬Ǥ ǡ ƒ–’‘•Ǥ ‘—•‹†‡•‡•‘””ƒ‰‡ ‫݂݀݌‬ହǡ௪ ൌ ൜ Ͳǡ ‘–Š‡”’‘•‹–‹‘• ‫ ଺݂݀݌‬ൌ ‫݂݀݌‬௢௟ௗ

Sensor Reading

Detection

S: FP

No Detection S: ND

(7) (8) (9) (10) (11) (12) (13) (14)

From the initiation of the game (it is assumed that both the pursuer and evader have perfect a priori information of each other’s initial positions), the system can update the probability density functions (pdfs) based on the Eq. (7-14) and the sensor readings associated with player’s current positions.

D: TP S: TP

(1) (2) (3) (4) (5) (6)

D: FP D: TP

Based on these six cases, the probabilities and the probability distribution functions for each case are used to calculate the expected a posteriori belief function (15) ‫݂݀݌‬୉୶୮ୣୡ୲ୣୢ ൌ σ଺௜ୀଵ ‫݌‬௜ ‫݂݀݌‬௜

D: FP D: TN D: FN

Fig. 1. The classification of sensor readings

Then, applying Shannon’s entropy function from the information theory to calculate the amount of uncertainty [28] is:

Fig. 1 shows the classification process. There are three detection states, which are TP, FP, and ND, and for each state, the system can classify it as either true or false. “S” refers to the sensor reading, and “D” refers to the player’s interpretation (classification) of the sensor reading.

‫ܬ‬୉୬୲୰୭୮୷ ൌ ݄ሺ‫ݔ‬ሻ ൌ ൌ

In the perfect information cases, the optimal strategy of evader (E) is to stay, as long as possible, in the portion of its region that the pursuer (P) cannot reach.

෍

െ‫݂݀݌‬୉୶୮ୣୡ୲ୣୢ ሺ‫ݔ‬ሻŽ‘‰ሺ‫݂݀݌‬୉୶୮ୣୡ୲ୣୢ ሺ‫ݔ‬ሻሻ ሺͳ͸ሻ

௫ୀ௔௟௟௣௢௦௜௜௧௢௡௦

To go beyond the information analysis of the sensor measurement model stage, tracking results were integrated, mainly the error covariance matrix P and the estimated state x, to address the effect of the sensor measurement model. In this

A detection event classification can be referred to as one of the following four possible combinations: TP classified as TP (TP,

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μ sinn γ T cos α cos β − m r2 v cos γ T sin α coss β μ cos γ γ = + − r m v r 2v v cos γ cos ζ ξ = r cos φ v cos γ sin ζ φ = r T sin β v cos γ sin φ cos ζ ζ = − m v cos γ r co os φ

paper, we exploit our consensus-based filters [29]. The results of tracking are the estimated satellite states annd the covariance matrix P. From the results, we can generate thhe pdf of satellite positions and velocities as ݂ሺ‫ݔ‬ሻ ൌ 

ଵ ඥሺଶగሻల ୢୣ୲ሺ௉ሻ

݁

భ ି ሺ௫ି௫ොሻ౐ ௉షభ ሺ௫ ௫ି௫ොሻ మ

v =

(17)

where ‫ݔ‬ොis the tracked position/velocity vecttor and P is the error covariance matrix. With the covariance information, the entropy iis [30]: ஶ

݄ሺ‫ݔ‬ሻ ൌ െ ‫ ׬‬ǥ ‫ି׬‬ஶ ݂ሺ‫ݔ‬ሻŽ݂ሺ‫ݔ‬ሻ݀‫ ݔ‬ǥ ݀‫ݔ‬ ଵ

ൌ  ݈݊ሺሺʹߨ݁ሻ଺ ݀݁‫ݐ‬ሺܲሻሻ ‫ߣ ן‬ଵ ߣଶ ߣଷ ߣସ ߣହ ߣ଺ ଶ

(18)

(20) (21) (22) (23) (24)

The set of variables (r, v, Ȗ, ȗ, ȟ, φ) defines the 3-D motions of spacecraft. As shown in Fig. 3, r is the instantaneous radius y magnitude, Ȗ is the flight from Earth center, v is the velocity path angle. ȗ is the velocity azimu uth angle, ȟ is the absolute longitude, and φ is the latitude. Thee control is conducted with the thrust direction, specified by thee two angles Į and ȕ.

where Ȝ1,Ȝ2…Ȝ6 are the eigenvalues of P matriix. Intuitively, the entropy is proportional to the product of eeigenvalues of P matrix. In our following PE game setup, the evvader (GEO) will try to increase the entropy while evader wants it to be minimal. The entropy becomes the confliction parameeter between the evader and the pursuer. The game moddel (Section III) investigates the player conflictions. III. PURSUIT-EVASION GAME MOD DEL A. Space object states and dynamics In this paper, we assume both observer (purrsuer) and evader (space object being tracked) apply the continnuous low-thrust such as the Ion thrust [31] as shown in Figure 2. Ion thrusters tend to produce low thrust, which results in low acceleration. For example, a NASA Solar Technoloogy Application Readiness (NSTAR) thruster producing a thrrust (force) of 92 mN will accelerate a satellite with a mass of 1,000 kg by 0.092 N / 1,000 kg = 0.000092 m/s2. The magnitudde of the thrust is assumed to be fixed and small. The controols of the thrust commands are the directions of these thrusts.

Fig. 3. system states r, v, Ȗ, ȗ, ȟ (longitude) and ij(latitude). Į, ȕ are the pointing angles of the thrust T.

Given a local direction (Į, ȕ) and a ¨t, we can propagate the system state by following the flowchart (Fig. 4): System states (in ECI) at Timee to

Convert the statess to local coordinate sysstem

Using numerical integrattion method to compute the local staates at t0+¨t Convert the new w local states to EC CI

Fig. 2. NASA’s 2.3kw NSTAR Ion Thrust for the D Deep Space 1 [31]

We use the following states (Fig. 3) to describbe the kinematics and dynamics of the spacecraft’s with continuoous low-thrust.

r = v sin γ

Fig. 4. Flow chart for system state propagattion with local thrust controls.

(19)

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Fig. 6 illustrates the block diagram m of the PE game approach for space-based sensor maneuver strategies. To solve the game problem, a fictitious play (FP) concept is exploited. It ning algorithms. At each refers to a family of iterative learn iteration, each player is able to obseerve the actions of all other players and computes the best ressponse strategy. It can be shown that for some special types of o games such as zero-sum games, fictitious play always conveerges to a Nash equilibrium [32]. Several recent contributions have also proposed many orithms [33, 34, 35]. enhancements to fictitious play algo

The conversion between Earth-centered ineertial (ECI) and local coordinate system (East-North-Up, or ENU) is illustrated in Fig. 5 and the following equationns.

ª de º ª − sin ξ « dn » = « − sin φ cos ξ « » « «¬ du »¼ «¬ cos φ cos ξ ª dx º ª − sin ξ « dy » = « cos ξ « » « «¬ dz »¼ «¬ 0

cos ξ − sin φ sin ξ cos φ sin ξ

− sin φ cos ξ − sin φ sin ξ cos φ

0 º ª dx º cos φ »» «« dy »» (25) sin φ »¼ «¬ dz »¼

cos φ cos ξ º ª de º cos φ siin ξ »» «« dn »» (26) sin φ »¼ «¬ du »¼

Control optimization to maximize eq. e 17 (Iteration mode until convergence or maximum itteration number met)

where (dx, dy, dz) is a vector in ECI and ((de, dn, du) is a vector in ENU coordinate system. System Dynamics Eq. 27, 29,31 of pursuer System Dynamics Eq. 28, 30,32 of evader

Trackin ng algorithm with ment measurem model based on o states of pursuer and a evadeer

Production of Eigenvalues of P matrix

Control optimization to minimize eq. e 17 (Iteration mode until convergence or maximum itteration number met) Fig. 6. The block diagram off PE game solution

IV. SIMULATION AND DISCUSSION A. Orbital Propagators s osition (x,y,z) and velocity The spacecraft states include the po (vx, vy, vz) in the Earth-Centered Inertial (ECI) coordinate system. We cannot use NASA Geneeral Mission Analysis Tool (GMAT) [36] as our propagatorr because our PE game approach needs to dynamically peerform satellite maneuvers based on Nash equilibrium. In this section, we used the simplified perturbations models (SDP4 and SGP4) [37] as a baseline propagator and added add ditional terms to model the maneuver effects.

Fig. 5. ECI and local ENU coordinate sysstems.

B. PE Game Setup In our dynamic PE game model, each playerr P (purser) or E (evader) has its own system states and state traansitions:

We implemented the NORAD SG GP4 and SDP4 algorithms drafted in [37]. The orbital modelss include SGP4, for "nearearth" objects, and SDP4 for "deeep space" objects. These models are widely used in satelllite tracking software and support the current NORAD two-lin ne element (TLE) data. To verify our codes, we compared the results with the benchmark data in [37] (page 81) as well as thee GMAT and other software tool results as shown in Fig.7.

(27) (28) (29) (30)

In Fig.7, the gravity only model is based on the dynamic ఓ equation ࢘ሷ ൌ െ య ࢘ , where ߤ is the standard gravitational ௥ e propagator” uses 6 parameter of Earth. The “orbital element orbital elements [1]: Eccentricity (e), semimajor axis (a), Inclination (i), Longitude of thee ascending node ( ¡ ), Argument of periapsis (ω), and Meean anomaly at epoch (M). Under ideal conditions of a perfectly y spherical central body and zero perturbations, all orbital elemeents, with the exception of

(31) (32) Eq. (27-28) are the augmented vectors of E Eq. (19-24). The cost function is defined in Eq. (17), which w will be minimized by the purser and maximized by the evader.

98

the Mean anomaly (M), are constants. Mean anomaly changes linearly with time, scaled by the Mean motion ݊ ൌ ඥߤȀܽଷ . Hence, if at any instant to the orbital parameters are [eo, ao, io, ȍo, ωo, Mo], then the elements at time to+¨t is given by [eo, ao, io, ȍo, ωo, Mo+n¨t]. The TLE Analyzer [38] is a two lines elements analysis and satellite tracking tool (freeware).

and GEO (evader). Their orbits are shown in Fig. 9. The maneuver commands are from the PE game solutions. The red line indicates the direction of sun light. We used a spacebased visible (SBV) sensor model. The field of view of the SBV sensor is 1.4 degree by 1.4 degree for each Charge Coupled Device (CCD). The total field of view of all four CCDs is 6.6 degree by 1.4 degree. We can see the first several steps, no measurements can be obtained.

Position Errors: SGP4 Benchmark Dataset

Δx (km)

4000 2000 0 -2000

0

Δ y (km)

5000

SGP4 Gravity only model 500 orbital element propagator TLE Analyser GMAT

1000

1500

1000

1500

1000

1500

0

-5000

0

500

-5000 0

500

Δz (km)

10000 5000 0

time (mins)

Fig. 7. Comparison among various propagators ఓ

From the comparison, we can see that i) the ࢘ሷ ൌ െ య ࢘ ௥ method has the largest errors, ii) the SGP4 and the GMAT codes are correct, and iii) the TLE Analyzer software obtain similar results as using SGP4 propagator.

Fig. 9. The orbits of SBSS and GEO under the game theoretic maneuver strategies

The tracking results are shown in Fig. 10. The tracking uncertainties are increasing during the no-measurement period. The game controls are shown in Fig. 11 and in Fig. 12 separates the parameters.

Based on Eq. (19-26), we can compute the maneuvering effects as the difference between the t0 and t0+¨t. This difference can be added to the SGP4 baseline propagator. In this way, ground truth data for the dynamic PE game approach for information uncertainty conflicts can be generated.

Error in x axis

Tracking Performance

Error in z axis

Error in y axis

B. Research Scenario In this research scenario (Fig. 8), a Space-Based Space Surveillance (SBSS) satellite [39] is used to track a GEO object. The GEO object trajectory is denoted by the green line. The trajectory of the SBSSs is denoted by the red line.

1000 EKF-Consensus information based filter (CIF) CKF-Consensus information based filter (CIF)

500

0

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800 1000 1200 time (k) x 10s

1400

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0 300 200 100 0

Fig. 10. The tracking performance with PE game theoretic maneuver strategies

We can see two intervals ([0,274] and [1274, 1385]) when the satellites keep their controls constants. In the first interval, there are no measurements, so both players will use the thrust to increase their velocities (Į=0, ȕ=0). In the second interval, the measurement uncertainties are very small (from the tracking errors in Fig. 10), then both players have no desire to

Fig. 8. A space tracking scenario displayed in GMAT

C. Numerical Simulations and Results We tested our PE game approach for informational uncertainties with a scenario of two satellites: SBSS (pursuer)

99

change their controls because the players cannot (or chose not to) mislead the opponents.

ቀ

ଶ

௫ ξ଻Ǥ଼ଵହఙೣ

ቁ ൅൬

ଶ

௬ ξ଻Ǥ଼ଵହఙ೤

൰ ൅ቀ

ଶ

௭ ξ଻Ǥ଼ଵହఙ೥

ቁ ൌͳ

(34)

Satellite Thrust Controls (α , β) Based on Nash Equlibrium

200

α (degree)

100 0 -100 -200

0

200 400 600 Pursuer (SBSS) Evader (GEO)

800

1000

1200

1400

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0

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800 1000 1200 time (k) x 10s

1400

1600

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200

β (degree)

100 0 -100 -200

400

600

Fig. 11. The satellite maneuver directional controls based PE game solutions.

Fig. 13. The error ellipsoid of error covariance matrix.

From Fig. 12, we can see some jumps from -180o to 180o or 180o to -180o. It is because we set the control angle to [-180o, 180o] for both angles.

Since the eigenvectors of the covariance matrix P are the directional vectors of the ellipsoid, and eigenvalues of the covariance matrix P represents how large the spread is in the directions, the axis-aligned error ellipsoid equation is:

GEO βo

SBSS βo

GEO α o

SBSS α o

controls of SBSS and GEO based on PE game solution 200

ቀ

0 -200 1800 1820 1840 200

1860 1880 1900

1920 1940 1960

1980 2000

1860 1880 1900

1920 1940 1960

1980 2000

1860 1880 1900

1920 1940 1960

1980 2000

1860 1880 1900 1920 1940 1960 time (k) x 10s

1980 2000

0 -200 1800 1820 1840

௬ ξ଻Ǥ଼ଵହఒమ

ଶ

ቁ ൅ቀ

௭ ξ଻Ǥ଼ଵହఒయ

ଶ

ቁ ൌͳ

Fig. 12. The satellite maneuver directional controls in zoomed view.

To illustrate the uncertainties in tracking, Fig. 13 shows the error ellipsoid of P matrix in (position error only). In the plot, the blue diamond represents the tracking result position (x,y,z) and the red ellipsoid shows the 95% confidence level. That is Prob{the true object position located in the ellipsoid} = 95%. For a general axis-aligned error ellipsoid in 3D space, the equation is ௫

ଶ

௬

ଶ

௭

ଶ

ቀ ቁ ൅൬ ൰ ൅ቀ ቁ ൌ‫ݏ‬ ఙೣ

ఙ೤

ఙ೥

(35)

Figure 14 shows all the error ellipsoids along the filtered positions. The blue dots are for the filtered positions and red ellipsoids are the 95% confidence ellipsoid. We can see the first several steps have increasing error covariance due to the no-measurement situations.

0 -200 1800 1820 1840 200

ଶ

ቁ ൅ቀ

where (λ1, λ2, λ3) are the eigenvalues of the error covariance matrix P. Then we can rotate it according to the associated eigenvectors and move the ellipsoid to the filtered position (‫ݔ‬ො௞ȁ௞ ).

0 -200 1800 1820 1840 200

௫ ξ଻Ǥ଼ଵହఒభ

(33)

where s is chosen to represent a desired confidence level. Since he sum of squared standard normal data points is known to be distributed according to a so called ߯ ଶ Chi-Square distribution. For a 95% confidence level, s should be 7.815. Then eq. (33) can be rewritten as

Fig. 14. Position error ellipsoid of tracking results (x, P).

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V. CONCLUSION In this paper, a pursuit-evasion (PE) game approach has been presented to deal with the uncertainties in the space object tracking. In the game setup, the evader (the space object to be tracked) performs maneuvers to maximize the uncertainties while the pursuer (the observer) will control the low-thrust to minimize the tracking uncertainties. The uncertainties are modeled based on the entropy. For the consensus-based filters, the entropy is simplified as the product of eigenvalues of error covariance matrices. The fictitious play framework has been exploited to solve the non-linear PE games. A space situational awareness scenario of one space based space surveillance (SBSS) satellite observing one GEO satellite has been simulated to demonstrate the PE game theoretic approach. Numerical results show the proposed PE game modeling is a promising approach to track elusive and smart space objects.

[17] [18]

[19]

[20] [21]

[22]

[23]

Future work includes communications assessment [40, 41], cloud technology [42], and resource management [43].

[24]

ACKNOWLEDGMENT

[25]

IFT was supported under contract FA9453-14-M-0161. Erik Blasch was supported in part by a grant from the AFOSR DDDAS program.

[26]

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