International Journal of Control, Automation, and Systems (2010) 8(5):1108-1122 DOI 10.1007/s12555-010-0520-1
http://www.springer.com/12555
Building a Robust Integrity Monitoring Algorithm for a Low Cost GPS-aided-INS System Tariq S. Abuhashim, Mamoun F. Abdel-Hafez*, and Mohammad Ameen Al-Jarrah Abstract: In this paper, the integrity of low cost GPS/INS systems is investigated to ensure the ability to obtain continuous high-integrity, high-accuracy vehicle state estimate under low-computational system requirement. The utilization of two fault detection and identification (FDI) techniques, the χ 2 (or sometimes referred to as chi-squared) gating function and the multiple model adaptive estimation (MMAE), is proposed to monitor the integrity of GPS measurements. A fault in GPS measurements is modeled with an increase in GPS measurements noise covariance matrix which may result from mistuning of filter’s noise parameters, interference, jamming, or multipath errors. These types of faults are covered by this work and are assumed to last for unconstrained period of time. χ 2 FDI systems are computationally very inexpensive, have good fault detection ability and require no a priori knowledge on system dynamics. However, they are sensitive to filter tuning and fail to detect faults when the filter converges to them rather than rejecting them. Model-based approaches provide outstanding FDI ability. However, they are computationally demanding, require a priori knowledge on system model, sensitive to mismodeling errors, have finite convergence time, and compromise filter optimality under no-failure conditions. The proposed fusion algorithm guarantees integrity and does not affect filter’s optimality under no-failure conditions. Simulated and experimental tests were conducted to verify the accuracy of the proposed techniques. Results are presented at the end of the paper to highlight the performance characteristics of the proposed FDI system implementation. Keywords: Fault detection, fault monitoring, GPS, IMU, low-cost.
1. INTRODUCTION As unmanned systems become more and more important, reliability and integrity issues become definite, specially when being implemented with low-cost (commercial of the shelf (COTS)) sensors while being designed to operate in harsh environments. As a result, fault detection and identification is a must, and is a crucial requirement for designing unmanned vehicles. There is an increasing demand on unmanned systems in different fields of applications, such as military, aerospace, transportation, and automation. Some of these systems are designed to operate in remote, hazardous, and harsh environments. Therefore, there is an increasing interest in the area of reliability, integrity and fault tolerance. Reliability is component dependent, i.e., a __________ Manuscript received April 15, 2009; revised December 13, 2009; accepted April 4, 2010. Recommended by Editorial Board member Chan Gook Park under the direction of Editor Jae-Bok Song. Tariq S. Abuhashim is with the Australian Centre for Field Robotics, The Rose St. Building JO4 The University of Sydney, Sydney, NSW 2006, Australia (e-mail:
[email protected]. edu.au). Mamoun F. Abdel-Hafez and Mohammad Ameen Al-Jarrah are with the School of Engineering, The American University of Sharjah, Sharjah, P. O. Box 26666, UAE (e-mails: {mabdelhafez, mjarrah}@aus.edu). * Corresponding author. © ICROS, KIEE and Springer 2010
navigation system is only reliable as its most unreliable component [1]. The probability that a component will fail is related to its rate of failure [2], and its reliability is measured by its mean time to failure (MTTF). Integrity implies the robustness of the system against failures and the ability of the the system to survive once a failure in one of its components (whether they are sensors, actuators, mathematical models or even computations) occurs. Without integrity, real time implementation of autonomous navigation systems is not safe and impractical. There are a number of issues that must be considered when designing a fault diagnosis system. Complexity of the implementation, overall system performance, and its robustness in the presence of mismodeling are important factors for a fault diagnosis design. Sensor characteristics along with its operational environment determine types of expected failures. In [3] failure modes and models of GPS-aided-INS systems were discussed. Modes were divided into groups based on their effect on the integration process and on each individual component of the integrated system. Complexity of the implementation increases the cost of the system in terms of hardware (for systems with hardware redundancy) and software (for systems with analytical redundancy). In fault diagnosis systems, it is more favorable for the detection algorithm to be as simple as possible and for the identification and/or isolation algorithm to be as efficient as possible. Fault
Building a Robust Integrity Monitoring Algorithm for a Low Cost GPS-aided-INS System
detection is implemented as a binary decision whether a fault has occurred or not. On the other hand, efficiency implies that there should be a trade-off between the level of complexity and performance. The more complex the system model and the more model-dependent the technique, the more susceptible the system to sensitivity issues. The robustness of the system is measured by its sensitivity to mismodeling errors. In [4], the mismodeling of Kalman filter system matrices was discussed in term of its effect on the mean and covariance of the residuals. Such mismodeling can result from mismodeling of the state transition matrix due to errors in state estimates, mismodeling of system matrices due to reduced order filter implementation, or mismodeling of system dynamics and can result in false alarms or miss alarms. In [4] expressions for the mean and covariance of the Kalman filter residuals in the presence of mismodeling in the input control matrix, output matrix, and state transition were derived. However, the effect of mismodeling in the process noise covariance matrix Q and the sensor noise covariance matrix R were neglected. This resulted into the conclusion that the conditional covariance matrix of the residuals is not dependent on the Kalman filter model, and it is only dependent on the covariance of the measurements. The motivation behind the assumption that Q and R represent the true model was to focus on system matrices variations because they commonly occur in failure detection applications considered by [4] where MMAE is used. The characterization of the Kalman filter residuals in the presence of mismodeling in the measurement covariance matrix R(k) is investigated in this work. The increase in the measurement noise covariance matrix R(k) models possible interference, jamming, or multipath errors. The overall performance of the system is measured by its tolerance to false alarms and how fast it detects and diagnoses failures. Therefore, a successful FDI system must have some essential characteristics. First, it should guarantees that all faults will be detected. Second, the system accuracy should not be affected during a no-fault condition. Thirdly, it should respond fast to faults. Finally, it should offer a trade-off between complexity, in terms of computational cost, and the FDI performance. FDI techniques were surveyed by [5] and [6]. In [5], Two different designs were introduced; failure sensitive filters, where a complete redesign of the filter is performed to include failures, and failure monitors, where an auxiliary system is designed to monitor the operation of the nominal filter. The later design has an advantage over the former since it does not affect the filter during no-fault mode of operation. In [6], the FDI problem was classified into two main categories based on their operational requirements. Model-based, where a priori knowledge of system dynamics is required, and data-driven, where a history of observations and system estimates are required to build up a data base. Examples of model-based approaches include the multiplehypothesis filters and parity space, while data-driven approaches may include statistical classifiers and
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Fig. 1. Stages of typical FDI systems with different implementations. artificial intelligence. The Ven diagram in Fig. 1 demonstrates the two basic FDI stages with their related techniques [7-18]. Among all other FDI techniques, the multiple model adaptive estimation (MMAE) [8] and the χ 2 [19,20] approaches are the most widely implemented filters. Innovation-based techniques have very simple implementation, require no a priori knowledge and do not affect system performance prior to the removal of failure. However, they are sensitive to filter tuning and fail to identify low frequency faults (due to inertial sensors biases and drifts) when the filter tracks the fault instead of rejecting it. On the other hand, the MMAE guarantees convergence of the estimator, it is insensitive to filter tuning, and covers a wide range of failures when implemented as a moving bank. However, it requires a priori knowledge on system dynamics and failure modes, requires time to converge, requires identical or similar failure parameters, affects performance during no-failure, and has a very expensive computational requirements. For GPS/INS systems, both FDI techniques are complements of each other. Therefore, a new FDI algorithm that is based on the fusion of both methods is proposed and is expected to overcome the weaknesses of both implementations weaknesses. This paper starts in Section 2, where the mechanization equations for the implemented strapdown inertial navigation algorithm are described. In Section 3 a brief discussion on the Kalman filter equations and implementation issues is presented. Section 4 discusses the χ 2 innovation-based and the MMAE model-based algorithms. A sequential FDI implementation is proposed in Section 5. Section 6 presents simulated results of the two FDI techniques along with the proposed sequential implementation for two different failure scenarios. Actual inertial and GPS data is processed in Section 7, where experimental results are presented. Finally, we conclude our work in Section 8. 2. STRAPDOWN INERTIAL NAVIGATION Inertial sensors, such as accelerometers and gyroscopes, measure acceleration and rotational rate, respectively, with respect to the inertial reference frame. Accelerations measured by three (not-necessary orthogonal) accelerometers, fixed such that their sensitive axes are oriented with one along vehicle’s longitudinal axis, one transverse to the vehicle
Tariq S. Abuhashim, Mamoun F. Abdel-Hafez, and Mohammad Ameen Al-Jarrah
1110
much lower rates than the body rotations, it can be implemented at the lower rate l computer cycle. The two rotations are described by (2) and (3)
Cbn((lk)+1) = Cbn((lk)) Cbb(( kk )+1) ,
(2)
Cbn((lk++1)1) = Cnn((ll )+1) Cbn((kl )+1) ,
(3)
where Cbb (( kk )+1) the DCM which transforms vectors from Fig. 2. Typical Inertial Navigation System (INS) using the Direction Cosine Matrix (DCM) approach utilized in this paper. longitudinal axis, and one vertical, are integrated once to compute vehicle’s velocity. The computed velocity is then integrated to compute vehicle’s position. Gyroscopes are utilized for coordinate system transformations, attitude representation, and removal of undesired components such as the gravity component measured by the accelerometers and misalignments. The mechanization equations presented in this section are employed to free measurements from undesired components and calculate vehicle’s position, velocity and attitude [27,28]. Fig. 2 shows the mechanization process utilized to implement a strapdown inertial navigation system (SDINS). 2.1. Attitude computations Attitude computation is the most critical part in the whole INS mechanization process, specially in high dynamic applications. The ability of the strapdown algorithm to keep track of body attitude accurately determines its performance. The conventional approach for attitude computation is to compute the direction cosine matrix Cbn , relating the vehicle body frame to the local navigation frame. When navigating with respect to the local geographic frame, it is required to solve the matrix differential equation of the form: n C b
=
Cbn Ωbib
Ωbib
n n − Ωin Cb ,
(1)
is the angular velocity of the body frame where relative to the inertial frame represented in the body n frame, Ωin is the angular velocity of the navigation frame relative to the inertial frame represented in the navigation frame. The first term of (1), Cbn Ωbib , is required to update the DCM for vehicle body motion. It is a function of the body rates sensed by the strapdown n n gyroscopes. While the second term, −Ωin Cb , takes into account updating the DCM for navigation frame rotations. This includes the rotation of the navigational frame with respect to the earth frame, which is referred to as the transport rate, and the Earth’s rate of rotation. The computation of (1) is carried out using two steps of direction cosine rotations, the first takes care of body rotations and the second takes care of local navigation frame rotations. Since local navigation frame rotates at
Cbn((lk))
body frame coordinates at the k +1 cycle to body frame coordinates at the k cycle, the DCM which transforms vectors from
Cbn((kl )+1)
body frame coordinates at the k cycle to navigation frame coordinates at the l cycle, the DCM which transforms vectors from
Cnn ((ll )+1)
body frame coordinates at the k +1 cycle to navigation frame coordinates at the l cycle, the DCM which transforms vectors from
Cbn((kl ++1)1)
navigation frame coordinates at the l cycle to navigation frame coordinates at the l +1 cycle, the DCM which transforms vectors from
body frame coordinates at the k +1 cycle to navigation frame coordinates at the l +1 cycle. In (2) and (3), the terms Cbb (( kk )+1) and Cnn ((ll )+1) update the DCM for the rotations of body and navigation frames respectively. To compute Cbb (( kk )+1) , equation (4) is used 2
Cbb (( kk )+1) = I + f1 (σ ) [σ ×] + f 2 (σ )[σ ×] ,
f1 (σ ) = f 2 (σ ) =
σ = ω +
sin σ , σ 1 − cos σ σ2
(4) (5)
,
1 1 ×ω + σ ×σ ×ω, σ 12
(6) (7)
where σ is a rotation vector with direction and magnitude such that a rotation of the body frame about σ , through an angle equal to the magnitude of σ and assuming that the direction of the rate-vector ωibb is unchanging, will rotate the body frame from its orientation at the computer cycle k to its orientation at the computer cycle k +1. This angular vector is computed by (8)-(10) [27] σ = α k +1 + δα k +1 , t
α k +1 = ∫ ωibb dt , tk
δα k +1 = ∫
tk +1 tk
α k +1 × ωibb dt ,
(8) (9) (10)
where α represents the sum of the incremental angle outputs provided by the gyroscopes from tk to tk +1. Equations (7)-(10) can be rewritten as in (11)
Building a Robust Integrity Monitoring Algorithm for a Low Cost GPS-aided-INS System
1 2 σ x = ωibb x(tk +1 − tk ) + ωibb x(tk +1 − tk ) 2 , 2 1 2 σ y =ωibb (tk +1 −tk )+ ωibb (tk +1 −tk )2 , y 2 y 1 2 σ z =ωibb (tk +1 −tk )+ ωibb (tk +1 −tk )2 , z 2 z
(11)
n
V = (vN
is its magnitude, which is given in (12) σ = σ x2 + σ y2 + σ z2 .
(12)
Finally, the skew matrix [σ ×] in 4 is computed by (13) 0 [σ ×] = σ z −σ y
−σ z 0 σx
σy −σ x . 0
(13)
Similar algorithm is used to compute Cnn ((ll )+1) . Equation (4) is replaced by (14) Cnn((ll )+1) = I +
sin θ 1 − cos θ [θ ×] + [θ ×]2, 2 θ θ
(14)
where θ is an angle vector with direction and magnitude such that a rotation of the navigation frame about θ , through an angle equal to the magnitude of θ , will rotate the navigation frame from its orientation at the computer cycle l to its position at the computer cycle l + 1. θ is computed by (15) θ =∫
tl +1 tl
ωinn dt.
(15)
An alternative approach carries the computation of both rotations at the moderate k − cycle computer rate. In this approach equation (1) is replace by the differential equation given in (16) n = Cn Ω b , C b b nb
2.2. Velocity computations The navigation equation expressed in the n frame can be written as (ignoring effects of Coriolis and rotation of navigation frame relative to earth frame) n = Cn f b + g n , V b
where (σ x , σ y , σ z ) are the components of σ and σ
(16)
b n ω nb = ωibb − Cbn ωien + ωen .
(17)
To solve (16), equations (4)-(13) are used. However, the b rotation rate ωibb must be replaced by ω nb which is the angular rate of the b frame relative to n frame and it is given by b ω nb
φ −ψ sin θ = θ cos φ + ψ cos θ sin φ . ψ cos θ cos φ − θ sin φ
(18)
(19) T
vE
vD ) ,
(20)
where vN, vE, and vD are velocity components in the north, east, and down directions respectively, and fb is composed of the three accelerations measured in the the body frame. The descritization of this equation [28] leads us into
V n (k + 1) = V n (k ) + Cbn (k )∆Vsfn (k + 1) + ∆Vgn (k + 1), (21) where ∆Vsfn (k + 1) is the change in velocity due to specific force acceleration, represented as 2 ∆Vsfn (k + 1) = I + f 2 (σ ) [σ ×] + f3 (σ )[σ ×] ν ,
where f1 (σ ) and respectively, and f3 (σ ) =
ν =∫
1 σ2
tk +1 tk
f 2 (σ )
(22)
are as in (5) and (6),
(1 − f1 (σ ) ) ,
f b dt.
(23) (24)
∆Vgn (k + 1) is the change in velocity due to gravity ∆Vgn (k + 1) = ∫
tk +1 tk
gln dt.
(25)
2.3. Position computations Once the vehicle’s velocity is calculated, its position can also be calculated as P n = V n
(26)
and the descritization of this equation leads into P n (k + 1) = P n (k ) + V n (k )∆tk + Cbn (k )∆Psfn (k + 1)
b , and where Ωbnb is the skew symmetric matrix of ω nb b ω nb is the rotation rate of the body frame with respect to the navigation frame measured in the body frame, which is given by
1111
+ ∆Pgn (k + 1),
(27)
where ∆Psfn (k + 1) is the change in position due to specific force acceleration, represented as 2 ∆Psfn ( k + 1) = I + 2 f3 (σ ) [σ ×] + 2 f 4 (σ )[σ ×] Sν , (28)
where f 2 (σ ) and respectively, and f 4 (σ ) =
Sν = ∫
1 1 − f 2 (σ ) , 22 σ
tk +1 tk
f3 (σ ) are as in (6) and (23),
ν .dt.
(29) (30)
∆Pgn (k + 1) is the change in position due to gravity,
Tariq S. Abuhashim, Mamoun F. Abdel-Hafez, and Mohammad Ameen Al-Jarrah
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represented as ∆Pgn (k + 1) = ∫
tk +1 tk
∆Vgn (k + 1)dt.
(31)
The algorithms used for attitude, velocity and position computations in (4), (21) and (27), respectively, hold for the assumption of piece-wise constant angular rate ωibb and specific force fb. For this case of constant inputs, the algorithm input is the direct integral of angular rate/specific force vector components provided by gyroscopes and accelerometers. However, for general motion (non-constant inputs) the algorithms should be modified. Integrated angular rates and specific forces are replaced by rotation and velocity/position translation vectors. For more details on the unified approach in case of general motion refer to [28]. 3. GPS/INS SENSOR FUSION FILTER The strap-down inertial measurement unit (IMU) and the GPS position and velocity measurements are fused using an extended Kalman filter (EKF). For the purpose of low-cost GPS/IMU applications, a loosely-coupled filter is implemented. Nevertheless, the algorithms developed are applicable to tightly-coupled GPS/IMU measurements fusion. The linearized continuous time system kinematic equation is represented as: x = Ax + Bw ,
(32)
where x is the error state which is composed of the position error in the navigation frame, the velocity error in the navigation frame, the body to navigation frame attitude error, the accelerometer bias, and the gyroscope bias. w is the additive process noise, B is the noise matrix, and A is the state dynamics matrix. These matrices are defined as: A=
A ins 0
Acoupled Abiases
15×15,
(33)
where Ains
I 0 0 n n b = 0 −2ω ie × (Cb f ) × 0 −ω ien × 9×9, 0
A coupled =
0 n Cb 0
Abiases = 06×6
(34)
0
0 −Cbn 9×6,
(35)
(36)
in the above equations, I is the 3 × 3 identity matrix, ω ien is the angular velocity of earth relative to the
inertial system represented in the navigation frame, Cbn is the direction cosine matrix from the body frame to the navigation frame, and f b is the specific force of the vehicle in the body frame. The latter is measured by the
inertial measurement unit. Also measured by the IMU is, ω ibb , the angular velocity of the body frame relative to the inertial frame represented in the body frame. This angular velocity does not appear in the linearized dynamics equations but it is used to integrate the nonlinear dynamics to produce the a priori attitude of the vehicle. The process noise transition matrix B is represented by B
B =
ins
0
0
Bbiases 15×12,
(37)
where Bins =
0 n Cb 0
0
0 −Cbn 9×6,
Bbiases = I 6×6 .
(38)
(39)
Equation (32) is discretized to produce: x(k ) = F (k − 1)x(k − 1) + G (k − 1)w (k − 1),
(40)
where F(k − 1) is the state transition matrix at time k − 1, calculated as F (k − 1) = I − Adt ,
(41)
where dt is the sampling time, and G (k − 1) is the noise transition matrix at time k − 1, calculated as G (k − 1) = B.
(42)
The linearized measurement equation at time k is represented as: z (k ) = H (k )x(k ) + v (k ),
(43)
where z(k) is the linearized measurement at time k, x(k ) is the error state at time k, H(k) is the observation matrix, calculated as I 0 0 0 0 H= 0 I 0 0 0 6×15
(44)
and v(k ) is the observation noise. A loosely-coupled GPS/IMU filter is implemented in this study and therefore the linearized GPS measurements are the error in the position measurement and the error in the velocity measurements. Both, w (k ) and v(k ) are assumed to be Gaussian, uncorrelated and zero mean white noise processes, i.e., E [ w (k ) ] = E [ v (k ) ] = 0, ∀k
(45)
and with corresponding covariances Q(k ) i = j = k E w (i )wT ( j ) = i≠ j 0
and
(46)
Building a Robust Integrity Monitoring Algorithm for a Low Cost GPS-aided-INS System
R (k ) i = j = k E v(i ) vT ( j ) = i≠ j 0
(47)
and being uncorrelated gives: E w (i ) vT ( j ) = 0, ∀i, j.
(48)
Given the system dynamics model and the measurement equations, the EKF state estimate is obtained from the following equation: xˆ (k | k ) = xˆ (k | k − 1) + W (k )ν (k ),
(49)
where x(k | k − 1) is the estimate of the error state at time k using the measurements up to time k − 1, W(k ) is the Kalman gain obtained from: T
−1
W (k ) = P (k | k − 1)H (k )S (k )
(50)
and ν (k ) is the innovation vector, given by ν (k ) = z (k ) − H (k )xˆ (k | k − 1),
(51)
where P(k | k − 1) is the covariance of the error state estimate at time k given the measurements up to time k − 1 and S(k ) is the covariance of the innovation sequence ν (k ). The a priori state estimate, xˆ (k | k − 1), is given as: xˆ (k | k − 1) = F(k − 1)xˆ (k − 1 | k − 1) .
(52)
The updated state covariance is given as: P(k | k ) = (I − W(k )H(k ))P(k − 1 | k − 1)(I − W (k )H (k ))T + W (k )R (k ) WT (k )
+ Q(k − 1).
(54)
The innovation convariance is given by the following equation: T
S(k ) = H (k )P (k | k − 1)H (k ) + R (k ).
(55)
If the system model is accurate and the covariance of the dynamics noise and the measurement noise represents their actual uncertainties, the innovation sequence should be zero-mean and with the covariance given by the above S(k ) [20]. The process and sensor noise covariance matrices are represented by
Q( k ) =
2 σ f b 0 0 0
0
0
σ 2b
0
ωib
0
σ2
0
0
∆f
0 , 0 σ 2 b ∆ω
0
b
, 2 σ v gps
0
(57)
where Q(k ) represents the covariances of the dynamics noise in inertial sensor measurements (f b and ω ibb ), and in inertial sensor biases (∆f b and ∆ω ibb ). These values are determined based on sensor specifications in manufacturer datasheets and by manual tuning [21]. R (k ) is the measurements covariance matrix, where σ r2gps and σ v2gps represent uncertainties in GPS position
and velocity measurements, respectively. 4. FAULT DETECTION AND IDENTIFICATION (FDI): INNOVATION-BASED AND MODELBASED APPROACHES From the surveyed FDI methods, the multiple hypothesis techniques yield the best performance for the widest class of failures. However, they are the most computationally-complex ones. When combined with innovation-based techniques, they offer tradeoffs between system complexity (in term of computations time) and performance. This proposed FDI implementation is suited for low-cost GPS/INS systems. Innovation-based techniques, such as the χ 2 and the Generalized Likelihood Ratio (GLR), provide a good fault detection performance, have a simple implementation and cause no performance degradation prior to failure onset [5].
(53)
and the a priori state covariance is given as: P(k | k − 1) = F(k − 1)P(k − 1 | k − 1)FT (k − 1)
R (k ) =
2 σ rgps 0
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(56)
4.1. Innovation-based χ 2 fault detection Innovation-based techniques detect abrupt changes (jumps) in sensor measurements by monitoring the innovation sequence, represented by (51), and its corresponding covariance, represented by (55). Fault detection is based on statistical consistency testing (SCT) of the innovation and its covariance [20]: q(k ) = ν (k )T S(k ) −1ν (k ),
(58)
if the normalized innovation squared, represented by the left hand side of (58), exceeds the preselected threshold γ , a fault is declared. Given a confidence level (percentage probability) of detection and the number of degrees of freedoms, the value of γ is determined from the χ 2 probability distribution tables prior to the fusion process and represents the probability that a particular observation lies within an ellipsoid [20]. Therefore, given a hypothesis H1 of a fault being detected, and considering a probability of false detection of 5% (that is a 95% level of confidence), then
γ = χ m2 ( P {q (k ) > γ | H1 } ) = 12.59, where in the case of loosely coupled implementation
(59)
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m = dim(z (k )) = 6.
Tariq S. Abuhashim, Mamoun F. Abdel-Hafez, and Mohammad Ameen Al-Jarrah
(60)
Once a fault occurs, sensors measurements are discarded and the filter remains in the correction stage. This rule may also be applied at the observation level and then observations are validated individually. Such algorithms include Receiver Autonomous Integrity Monitoring (RAIM) [29]. Although such an implementation may increase the consistency level of the filter, attention must be taken when noisy environments are considered since continuous rejection of GPS observation can result into the INS missing most of the GPS fixes. Therefore, system level FDI algorithms, such as the one proposed by this paper, aim not only to detectthen-reject faulty observations, but also to manipulate these observations, based on their accuracy, in order to improve the quality of the filter estimates [22]. 4.2. Multiple Model Adaptive Estimation (MMAE) MMAE utilizes a bank of Kalman filters, each with a different internal model, as shown in Fig. 3. The probability of each filter model is sequentially updated in the filter as new measurements are processed. All the elemental filters are provided with the same measurement vector z (k ) and since they have different internal models, each filter produces its own state estimate xˆ i (k ), residuals ri (k ) and uncertainty Pi (k | k ). When implemented for fault diagnosis purposes, each elemental filter represents a failure mode (discussed in next section) with one filter representing the normal mode (no failure). Residuals behavior is used as an indication of how adequately each filter represents the actual operational mode. A hypothesis conditional probability generator is weighting each elemental filter’s estimate based on the behavior of the residuals and an adaptive estimate is provided.
The weighting process is based on the fact that under normal conditions the residuals are Gaussian, zero-mean and white with covariance Sk. Therefore, Gaussian probability distribution function is utilized in the calculation of the hypotheses conditional probabilities pi (k ). First, each elemental filter is initialized based on its hypothesis, while initial hypotheses probabilities are selected based on the implementation of the bank and on the application [22]. Second, for each elemental filter the conditional density function of the measurement, given the filter model and the measurement history, is described by a multivariate gaussian distribution calculated as: f (z (k ) | ai , Z k −1 )
(61)
= βi (k ) exp{−αν iT (k )Si−1 (k )ν i (k )}, βi (k ) =
1
( 2π )
m 2
Si (k )
1 2
,
(62) 1 , 2
where α is a scalar penalty usually selected as
and m is the dimension of the measurement vector. Then, the conditional probabilities of the various hypotheses are updated as follows pi (k ) =
f (z (k ) | ai , Z k −1 ) pi (k − 1)
K
∑ j =1 f (z (k ) | a j , Z k −1 ) p j (k − 1)
,
(63)
where K is the number of elemental filters in the bank, and K
∑ pi (k ) = 1.
(64)
i =1
Finally, the adaptive state estimate is formed as follows K
xˆ (k | k ) = ∑ xˆ i(k | k ) pi (k ).
(65)
i =1
The state estimate covariance is calculated as P(k | k ) T
= E [ x(k ) − xˆ (k ) ][ x(k ) − xˆ (k )] | Z(k ) = Z k
(66)
K
{
T
}
= ∑ pi (k ) Pi (k | k ) + [ xˆ i(k ) − xˆ (k )][ xˆ i (k ) − xˆ (k )] . i =1
The optimal hypothesis may also be computed along with its uncertainty as follows K
aˆ (k ) = ∑ ai (k ) pi (k ),
(67)
i =1 K
Pa (k ) = ∑ pi (k ){[ai (k ) − aˆ T (k )][ai (k ) − aˆ T (k )]T }, (68) i =1
Fig. 3. In MMAE, a bank of Kalman filters is utilized and outputs are weighted in probabilistic manner.
where ai (k ) represents elemental filter hypothesis parameter(s). In [8] performance enhancements to this method were proposed. They include stripping the β term of (62),
Building a Robust Integrity Monitoring Algorithm for a Low Cost GPS-aided-INS System
scalar penalty increase, probability smoothing, increased residual propagation, Kalman filter tuning, and bounded conditional probabilities. Only the last three, which are residuals propagation, filter tuning, and bounded probabilities, are utilized in this work, particularly in the implementation of the sequential algorithm discussed in Section 5. The number of elemental filters (hypotheses) in the bank and the size of the bank depend on the number of expected failures and the number of hypothesis parameters. For example, if 5 failure modes are expected with each hypothesis formed by varying 2 parameters, then 32 elemental filters are required. To avoid the potentially large number of elemental filters needed for an MMAE bank, a moving bank MMAE is implemented [23,24]. In the moving-bank implementation, the number of elemental filters in the bank is fixed and predetermined by the designer. In the previous example, one might choose to build the system with 3 filters per parameter which reduces the number of filters in the bank to 9. In the INS/GPS case, GPS position and velocity observations are fed into the filter bank through the measurements vector z (k ), and the dimensionality of the multivariate gaussian described in (61) is six. Hypotheses vector a(k ) are used to model different values of measurement noise covariance tuning parameters represented by diagonal matrix R (k ), discussed later in 5 and each block is treated as a separate filter implemented using vehicle’s inertial model error states and covariance matrix. After each update step, filters state estimates, uncertainties and hypotheses, represented by R (k ), are summed to form an optimal estimate as presented by (65), (66) and (67). States estimates and uncertainties are used as estimates of means and uncertainties or errors and biases in the the inertial mechanization computation. The estimated optimal hypothesis presented by (67) is then used to update the central filter hypotheses, and then the whole filters bank. Unlike the χ 2 innovation-based test presented by the previous section, the MMAE aims to utilize the faulty observations as much as possible based on their accuracy. The overall performance depends on the range of hypotheses covered which depends basically on the number of elemental filters in the bank. This is the span of filters hypotheses which depends on the bandwidth of the bank. The filter performance is also characterized by the convergence time which determines how fast the algorithm is able to identify fault parameters (measurements noise covariance in this case) and therefore how efficient the implementation is. In other words, while the χ 2 innovation-based method provides fault detection and isolation ability to the navigation algorithm, MMAE provides the system with the ability to adaptively tune for the appropriate value of measurement noise covariance R. However, it doesn’t provide criteria to quarantine filter consistency in real time and during both conditions of non-faulty and faulty measurements.
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4.3. Failure modes and models In this section, modes and models of sensor failures in MMAE are discussed. In [3] failure modes were classified into groups with each group representing a single component of a GPS-aided-INS system utilizing MEMS inertial sensors. In this work, only sensor (i.e., GPS) failures are considered. Failure modes are divided into two groups, based on their effect on the performance of the GPS; hard failures and soft failures. A hard failure results into total sensor failure (i.e., the sensor reads nothing but noise, stop reading at all or stuck at a constant value) [25,26]. A soft failure results into degradation in sensor accuracy, such as incorrect modeling of orbital parameters, jamming, interference, atmospheric errors, multipath and low satellites availability. A Hard failure is modeled by zeroing the corresponding row of the output matrix H(k ). For example, if a failure affects the j th observation of the measurements vector, then the failure mode is modeled by zeroing the j th row of H (k ). The corresponding j th element of the innovation sequence becomes ν j (k ) = z j (k ).
(69)
The corresponding elements of the innovation covariance are S j , j (k ) = R j , j (k ),
(70)
S j ,k (k ) = 0 ∀k ≠ j, k = 1,… , m,
(71)
S k , j (k ) = 0 ∀k ≠ j, k = 1,… , m
(72)
and its contribution in the normalized innovation squared is
q j (k ) = zTj (k )R −j,1j (k ) z j (k ),
(73)
which should be minimal if the filter was properly pretuned. Then, the hypothesis is correct and will have higher probability. Soft failures are modeled by varying the measurement error noise covariance matrix R (k ). In a MMAE filters bank, all elemental filters will have similar innovation, and the only difference is in the value of the measurements noise covariance R (k ). The hypothesis that satisfies the true fault condition will have minimum normalized innovation squared (NIS) and will therefore have the higher probability assigned to it. 5. SEQUENTIAL FDI ALGORITHM A single Kalman filter is required for fault detection, while fault identification requires a bank of Kalman filters. The sequential FDI algorithm implemented for low-cost GPS/INS systems integrates two different FDI techniques. A simple and fast one is used for detection and consistency testing, while an efficient and more
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complex one is used for identification and states and/or parameters estimation. The first detection algorithm is based on thresholding, such as statistical consistency tests (SCT), while the second scheme used for identification is based on the multiple model-based approach. The consistency of the identification stage estimates may also be checked using a similar SCT. The proposed sequential algorithms is the χ 2 -MMAE, where the χ 2 is used for detection while the MMAE is used for identification and state estimation. The implementation of this scheme is represented in Fig. 4. Advantages of such implementation include low computational requirements since the filters bank is only allowed to operate on segments of time when faults were detected. Also, the effect of the filters bank idle-time on the estimation filter consistency is eliminated since the consistency of the algorithm’s estimates is checked at all time. Furthermore, the effect of mistuning is reduced since an adaptive algorithm is employed to tune for filter parameters, which is the measurement noise covariance matrix R in this case. When implemented in real time, a single (nominal) filter monitors the consistency of the innovation sequences. When an inconsistent sequence is detected, a fault is declared and a bank of Kalman filters starts tuning for the appropriate value of sensor noise covariance matrix through the utilization of the Gaussian probability density function, as follows: K
a MMAE (k ) = ∑ pi (k )ai ,
(74)
R MMAE (k ) = a MMAE (k )R MMAE (k − 1),
(75)
i =1
where qi (k ) represents the ith elemental filter calculated NIS, qMMAE (k ) represents the filter bank calculated NIS. A similar algorithm such as that implemented in Section 4.1 is used to test the consistency of the algorithm’s estimates as follows qMMAE (k ) ≤ γ ,
(77)
where γ is selected as in Section 4.1. An interaction step similar to the one implemented in the interactive multiple model algorithm [30,31] can be added to this sequential algorithm. In such a case, fixed or dynamic transition probability matrix Pij (a j (k + 1) | ai (k )) provides the probability of failure j occurring
at time k + 1 if failure i exist at time k. This transition matrix is used to calculate the mixing probability μi| j (k | k ) that defines the weights with which the estimates from previous cycle are given to each filter hypothesis at the beginning of the current cycle. The implementation of such a step will require a realization of the physical environment of the system using vision sensors or other sensors that will help identify possible transition in the measurement accuracy. Alternatively, a fixed transition probability matrix giving more probability in staying at the current hypothesis or transitioning to neighboring hypotheses can be used. The next two sections aim to verify all the developed algorithms in both simulated and experimental environments. 6. SIMULATED RESULTS
where pi (k)
represents the ith elemental filter’s hypothesis probability at time k, ai represents the ith elemental filter’s hypothesis parameter, aMMAE represents the filters bank optimal estimated failure parameter at time k, R MMAE (k ) represents the filters bank optimal estimated failed sensor noise covariance at time k, and the bank is centered at R MMAE . The filter bank residuals utilized for consistency test are generated as follows K
qMMAE (k ) = ∑ pi (k )qi (k ),
To validate the performance of the proposed algorithms, a path was simulated using the AEROSONDE model in MATLAB SIMULINK. The simulated path contained a series of five rotations all towards right with short straight line segments as shown in Fig. 5. Two failure scenarios, of 45 seconds-length each, were simulated by introducing random noise to the
(76)
i =1
Fig. 4. The χ 2 -MMAE sequential FDI Implementation.
Fig. 5. Simulated trajectory (solid line) against inertial solution alone (dashed line). The drift rate of the inertial solution depends mainly on the grade of utilized sensors.
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simulated GPS signal. First while the simulated aircraft was traveling in straight line (522-567 sec) and then while rotating (875-920 sec). This is also indicated by the interval between points A and B in the trajectory plots (applied for both simulated and experimental results). The added noise was zero-mean with standard deviation of 15m and 0.75m/s for simulated GPS position and velocity observations, respectively [24,32]. When the moving bank MMAE was used, five elemental filers were used with hypotheses a = [0.01, 0.1,1,10,100] . A sixth filter was added when the sequential algorithm was employed. It had a fixed (stationary) hypothesis a6=1. Figs. 6, 7, 8 and 9, show the resulted trajectory where noise was introduced while the vehicle was moving in straight-line for different filter implementations. Figs. 10, 11, 12, and 13 show the portion of trajectory where noise was introduced to the simulated GPS signal while the simulated aircraft was turning. In these figures, the noisy GPS observations are represented by the small circles, the truth is represented by the dotted line, and the estimated position is in the solid dark line. When no FDI technique is implemented and the filter assumes the nominal, no-fault, GPS measurements, Fig. 6 shows that the estimated position jumps to follow the faulty GPS observations. These jumps depend on how the filter was initially tuned and on the magnitude of the noise introduced to the GPS signal. In Fig. 7, the χ 2 gating function is applied alone. As a result, when faulty
GPS observations are rejected, the filter remains in the prediction stage which causes the estimate to drift and the estimation error to grow in time. Once the observations are validated, the filter enters the update stage and the estimated position jumps towards the GPS fix according to how the filter was initially tuned. Fig. 8 shows the position estimate when a movingbank MMAE is used to identify the true R(k), the filter will always consider the GPS observations and weight them according to their estimated accuracy. Therefore, the estimated trajectory became continuous and closer to truth. Nevertheless, in this case, the filter might be putting small probability on incorrect hypotheses when the GPS measurements do not have a fault. This might degrade the optimality of the estimation filter. In Fig. 9, the sequential χ 2 -MMAE FDI filter implementation is used and the moving-bank MMAE is activated on segments where faults were detected. This sequential scheme estimated a trajectory close to that in Fig. 8. Figs. 10, 11, 12 and 13, show the resulted trajectory where noise was introduced while the vehicle was turning for the same filter implementations that were used in the straight-line motion case. The figures show similar performance to those obtained in the straight-line motion case for the different FDI filter implementations. Results show that the estimated trajectory is continuous and closer to truth when both the moving bank MMAE and the sequential scheme were employed. Fig. 14 presents the computational complexity of the
Fig. 6. Straight-line motion with no FDI filter implementation.
Fig. 8. Straight-line motion with a moving-bank MMAE FDI filter implementation.
Fig. 7. Straight-line motion with χ 2 gating function implementation.
Fig. 9. Straight-line motion with sequential MMAE FDI filter implementation.
χ2 -
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Fig. 10. While turning without any FDI ability, the estimator behaves similarly to the straight line case.
Fig. 13. Similar to the MMAE, the sequential scheme shows a good result at corners by giving the GPS observations the appropriate weight based on their accuracy.
Fig. 11. Applying the χ 2 gating function results into a trajectory with segments where the estimator runs on prediction only. During these segments and due to sensor biases, estimates drift over time resulting into jumps in the navigational solution.
Fig. 14. As expected from the sequential scheme, in this failure alarm plot, a 1 represents detection of fault, and the filters bank was only activated during segments of time when a failure was detected. implementation only when a fault is detected. This implies a significant reduction in computations while achieving a near optimal performance. In MMAE implementation, 6 extended Kalman filters will be operating to obtain the state estimate and its associated covariance for each assumed failure hypothesis. Also, the probability for each hypothesis is calculated to weigh the estimates of the different hypotheses and produce the final estimate and final covariance of the state estimate. This represents a considerable computational burden. In the sequential χ 2 -MMAE FDI filter implementation,
Fig. 12. Implemented with MMAE, the estimator shows a good performance even while cornering. χ 2 -MMAE implementation. When a fault is detected, a 1 is assigned to represent a faulty GPS measurement. During this stage, the sequential χ 2 -MMAE FDI filter implementation starts to calculate the probability of the existence of each hypothesis in our hypotheses bank. When no fault is detected, the figure shows that the computational requirements are reduced to those required by the stand alone χ 2 implementation, and becomes similar to the requirements of the MMAE
this is only done when a fault is detected by the χ 2 method. And once the MMAE filter converges, the estimator goes back into only monitoring for an onset of a fault using χ 2 method. Fig. 14 shows that time when the MMAE filter is activated is very short compared to the total time of the filter operation. Tables 1, 2, and 3, present statistics of the estimation errors, including the mean-square-error (MSE) and the variance (between parenthesis), during the three 45seconds-length segments; including when the simulated vehicle underwent GPS errors while in straight-line motion and while turning, and during no-fault or normal mode of operation. These results show that the proposed
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Table 1. MSE and variance of estimation errors with different filter implementations for the 45 seconds segment when the vehicle underwent a failure in GPS signal while traveling in straight line. No FDI North Pos. East Pos. Down Pos.
53.30 (51.42) 94.14 (42.96) 34.98 (26.86)
χ2 158.29 (50.63) 79.96 (76.27) 44.78 (38.21)
MMAE 1.168 (0.92) 29.52 (9.64) 12.11 (5.24)
χ 2 -MMAE 3.27 (0.75) 30.47 (9.69) 13.78 (4.99)
Fig. 15. The platform and the utility used in the test.
Table 2. MSE and variance of estimation errors with different filter implementations for the 45 seconds segment when the vehicle underwent a failure in GPS signal while cornering. No FDI North Pos. East Pos. Down Pos.
55.71 (37.80) 22.66 (20.44) 62.95 (60.61)
χ2 138.50 (104.99) 80.02 (78.84) 131.98 (119.08)
MMAE 9.17 (2.91) 2.93 (0.46) 28.68 (5.75)
χ 2 -MMAE 3.95 (3.86) 0.47 (0.39) 8.59 (5.36)
Table 3. MSE and variance of estimation errors with different filter implementations for 45 seconds segment when the vehicle was traveling at normal-mode of operation, no applied faults. No FDI North Pos. East Pos. Down Pos.
0.1586 (0.1135) 0.1207 (0.0965) 0.0789 (0.0659)
χ2 0.16 (0.11) 0.11 (0.09) 0.08 (0.07)
MMAE 0.21 (0.17) 0.14 (0.13) 0.09 (0.09)
χ 2 -MMAE 0.16 (0.11) 0.11 (0.09) 0.08 (0.07)
sequential scheme has similar and sometimes better performance compared to that of the MMAE algorithm, specially while turning or while at the normal mode of operation. It can be seen from the tables that the MSE and the variance are considerably less when implementing the proposed FDI algorithms than with no FDI implementation. Also, it is seen that the χ 2 test does not improve the performance of the state estimator because, once a fault is detected, the filter completely depends on the propagated state coming from the IMU measurements integration. 7. EXPERIMENTAL RESULTS In this section, an experimental test was conducted and actual IMU and GPS data is processed. The test was conducted in Sheikh-Zayed seaport in Abu Dhabi, United Arab Emirates. Fig. 15 shows the platform and the land vehicle used in the test. The platform contains the 6DoF “Crossbow” IMU, “Novatel smart antenna” GPS receiver, and "Honeywell" digital compass, which is used to provide the initial guess of the vehicle attitude
Fig. 16. Testing area with trajectory. Table 4. Sensors specifications. Sensor
Specifications Angular rate range: ±100 /sec
Crossbow IMU
Novatel GPS
Angular rate bias: < ±1 /sec Gyros bandwidth: > 25Hz Acceleration range: ±4 g Acceleration bias: < ±12 mg Accelerometers bandwidth: > 75 Hz Sample rate: 133 Hz Update rate: 5Hz Position accuracy: 5m RMS Velocity accuracy: 0.05m/s RMS Heading accuracy: < 0.5 RMS
Honeywell compass
Pitch accuracy: ±0.4 RMS Roll accuracy: ±0.4 RMS Pitch and roll ranges: ±40 (both)
and for filter initialization. The uncertainty in this initial estimate is due to misalignment between the body frame and the sensor frame and due to external effects such as hard and soft iron effects on magnetic field measurements. Table 4 summarizes the specification of the sensors used. The test area with the trajectory are shown on the map in Fig. 16. Figs. 17, 18, 19, 20 and 21 show the east versus north vehicle position when going around the trajectory. The different curves show the path of the vehicle during the test. To test the effect of GPS interference or jamming which results in an increase in the GPS covariance matrix, noise is introduced to GPS data during part of the vehicle’s trajectory. In this part of the vehicle’s trajectory, the noisy GPS data are represented with bold circles. In Fig. 17 the filter was implemented with no FDI
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Fig. 17. When no FDI scheme being used, all GPS fixes are validated and the resulted path starts to jump following the GPS.
Fig. 20. When a bank of filters is used to tune R(k), GPS observations are given the appropriate weight and the effect of jumps is efficiently reduced.
Fig. 18. When jumps are detected using the χ 2 SCT, GPS observations are rejected and the filter remains in the prediction stage. Once observations are validated, the filter enters the update stage and GPS observations are weighted based on their uncertainties.
Fig. 21. Resulted path when χ 2 SCT and MMAE are used in sequential scheme. Once faulty GPS data is detected a bank of filters is used to identify fault parameters and tune the filter.
Fig. 19. Tuned to reject jumps, the filter puts less weight on GPS observations. However, this implementation scarifies filter optimality in all its modes of operation. ability. Therefore, GPS observations are always used for navigation based on how the filter was originally tuned. In this case, the GPS observables were given a constant weight throughout the vehicle’s trajectory. As shown in Fig. 17, the noise in the GPS data is transmitted to the filter estimates and they become noisy as well. Fig. 18 shows part of the path when the gating function in (58) is
used to detect jumps in the GPS. As a result of inconsistent innovations, GPS observations are rejected and the filter works on predictions. Once observations are validated, the filter enters the update stage. If the filter is properly pre-tuned, observations are weighted based on their accuracy and filter estimates should be closer to the truth. As shown in Fig. 18, the updated position is closer to the actual position. To reduce the effect of jumps in the estimates and to prevent the filter from relying on predictions, the filter is tuned as suboptimal. This can be done by increasing the observation noise covariance matrix R(k). The resulted trajectory when a suboptimal filter is implemented is represented by Fig. 19. However, changing R(k) affects filter performance in other places where no faults are detected. Therefore, the estimation filter should be adaptive to the existing GPS measurement noise magnitude in each stage of motion. Fig. 20 shows the results when a bank of filters is used to continuously tune the observation noise covariance matrix. Since the uncertainty of the GPS is changing, the value of R(k) will be changing as well, and the resulted path will be better than that when a suboptimal filter is used. However, for the filter to be tuned for R(k) accurately, the bank hypothesis should match the actual
Building a Robust Integrity Monitoring Algorithm for a Low Cost GPS-aided-INS System
[3]
[4]
[5] Fig. 22. The solid and dashed lines present the estimated trajectory when the sequential and MMAE schemes are used respectively. condition otherwise the filter will lose its optimality. To reduce the effect of mismodeling error in R(k), the bank is only operated when a fault is detected. In doing so, the MMAE should be integrated with a detection method. In Fig. 21, a χ 2 -MMAE sequential algorithm is used to tune the filter. As shown in the figure, during GPS sensor faults, the estimated trajectory is similar to that in Fig. 20 where MMAE was used alone. On the other hand, Fig. 22 shows a different part of the test trajectory with no faults. In this figure, the estimated trajectory using MMAE alone (dashed bold line) drifts from the actual fault-free one (solid thin line). This is because the MMAE algorithm provides no guarantee that it will converge to exact no-fault value. This is not the case for the sequential method (solid bold line), since the nominal filter it not affected by the performance of the bank. 8. CONCLUSIONS This paper has presented a method for monitoring the performance of the GPS for a low-cost INS/GPS integrated navigation system. The motivation was to increase the level of reliability and integrity of the navigation system. In doing so, two GPS fault detection and identification (FDI) techniques were discussed; the χ 2 gating function and the multiple model adaptive estimation (MMAE). A sequential FDI scheme was proposed to integrate both methods in order to obtain a high-integrity, high-accuracy state estimate from a filter structure with low-computational requirement. Simulated as well as actual GPS and inertial data were processed and results were introduced for different FDI implementations. Results showed that the new algorithm provides similar identification ability as the MMAE with reduced computational requirement and without affecting filter’s optimality at normal, no-fault, modes of operation.
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tech House, 2006. [30] Y. Bar-Shalom, K. C. Changk, and H. A. P. Blom, “Tracking a maneuvering target using input estimation versus the interacting multiple model algorithm,” IEEE Trans. on Aerospace and Electronic Systems, vol. 25, no. 2, pp. 296-300, October 1989. [31] E. Mazor, A. Averbuch, Y. Bar-Shalom, and J. Dayan, “Interacting multiple model methods in target tracking: a survey,” IEEE Trans. on Aerospace and Electronic Systems, vol. 34, no. 1, pp. 103-123, October 1998. [32] A. Brown, D. Nguyen, Y. Lu, and C. Wang, “Testing of ultra-tightly-coupled GPS operation using a precision GPS/inertial simulator,” Proc. of the Institute of Navigation, 18th International Technical Meeting of Satellite Division, pp. 439-447, September 2005. Tariq Abuhashim is a Ph.D. research student at the Australia Centre for Field Robotics. His research interests include multi-sensor fusion for localization and mapping. He obtained his B.S. degree in Electrical Engineering from the University of Jordan in 2003, and his M.S. degree in Mechatronics Engineering from the American University of Sharjah in 2008. Mamoun F. Abdel-Hafez is an Assistant Professor in the Department of Mechanical Engineering at the American University of Sharjah. He received his B.S. in Mechanical Engineering from Jordan University of Science and Technology in 1997, an M.S. in Mechanical Engineering from the University of Wisconsin, Milwaukee in 1999, and a Ph.D. degree in Mechanical Engineering from the University of California, Los Angeles (UCLA) in 2003. Dr. Abdel-Hafez served as a Post Doctoral Research Associate in the Department of Mechanical and Aerospace Engineering at UCLA from June 2003 to December 2003, where he was involved in a research project on fault-tolerant autonomous multiple aircraft landing. His research interests are in stochastic estimation, control systems, and algorithms and applications of GPS/INS systems. Mohammad Ameen Al-Jarrah received Diploma Engineer in Machine design and Manufacturing in 1980 from the Byelorussian Polytechnic in USSR, M.S. in Applied Mechanics from Yarmouk University in 1983, and M.S. and Ph.D. in Aeronautical Engineering from Stanford University in 1985 and 1989, respectively. He joined the Department of Mechanical Engineering at the American University of Sharjah in 2000, where he is presently a full professor. He has served as the founding director of the AUS mechatronics graduate program since it was founded in 2001 until August of 2007. He is currently the head of the Mechanical Engineering Department at AUS. He has also authored or coauthored more than 80 papers that have appeared in various journals and conference proceedings. His research spans autonomous vehicles with emphasis on UAVs, Mechatronics systems design, modeling and simulation of physical systems, and applied aerodynamics.
