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The Flight Path Reconstruction (FPR) techniques are performed to verify the data compatibility check and post-flight. This is often achieved by calibrating the onboard sensors such as inertial and airdata sensors. In this paper, the limitations of FPR techniques in terms of Maximum Likelihood Estimation (MLE) and Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) have been reported. To demonstrate the FPR and sensor calibration, kinematic trajectory simulations with wind box type maneuvers have been performed. It is also shown as how a kinematic simulation is valid for the studies carried out in this work.

Agile, high performance aircraft are based more and more on flight mechanical unstable airframes with control laws stabilizing the air vehicle. This requires an accurate knowledge of the center of gravity position, particularly during agile maneuvering. This theoretical investigation is intended to serve a systematic framework in form of a fuel system which tries to cover all aspects of defueling during flight. Measurement and process noise as well as biases are accounted for in the simulated performance characteristics of fuel pumps and fuel probes. A simple simulation delivers the rates and accelerations exerted on the tanks which are typical for agile maneuvering. Various approaches such as an output and filter error approach are compared with the simulated fuel probe measurement with respect to their fuel state prediction capability. Main outcome is that the fuel probe measurements fail to predict fuel states during agile maneuvering whereas their accuracy is acceptable during gentle course changing maneuvers. The integration of pump rates in the output error approach shows significant deviations in the fuel states during simulation since it fails to cope with the process and measurement noise. Only the filter error approach which fuses in an optimal manner probe data during gentle course changing maneuvering and integration of pump rates during agile maneuvering produces a significantly improved fuel state prediction capability which translates into an accurate cg calculation. I. Nomenclature= center of gravity f, f  = system state function F = process noise distribution matrix FF T = covariance matrix of process noise T F Fˆ = modelled covariance matrix of process noise FE = filter error approach FS = fuel stage g, g  = system observation function G = measurement noise distribution matrix GG T = covariance matrix of measurement noise T G Gˆ = modelled covariance matrix of measurement noise I = identity matrix I y = inertia around y-axis k 1 = measurement noise parameter K k = Kalman gain at k-th time sample L EngLH = left engine power lever r N = distance wing to horizontal stabilizer CG Tank Tank R R   , = empty tank cg position CG AC R  = aircraft cg position S = reference area S  = acceleration rate at tank t,t = time, time step T 2 = time to double u = control input vector v, v  = measurement noise with variance 1 V 0 , V  = freestream velocity w, w  = process noise with variance 1 x, x  = fuel content in tank/fuel state x max = maximum fuel content in tank x CG = x-position of c.g.  k x = predicted fuel state at k-th time sample k x = corrected fuel state at k-th time sample y, y  = simulated observation vector y CG = y-position of c.g. z, z  = measured observation vector Z  = normal force derivative  = angle of attack  = angle of sideslip § Professor in Aeronautics, Esplanade 10, 85049 Ingolstadt, Germany, and AIAA Senior Member. Downloaded by UNIVERSITY OF ILLINOIS on October 1, 2015 | http://arc.aiaa.org | L EngRH = right engine power lever L L ,L W = length and width of tank m = ma...

Flight test data of an unstable feedback controlled aircraft (Eurofighter) is artificially generated with added linear and nonlinear (de-)stabilizing error on the deri vati ves comprising also process and measurement noise that is analyzed with three estimators: equation error, output error, and wi th the new combi ned equati on/ output error methods estimati ng linear deri vati ves. The investigati on focuses on the estimation performance in the equation and output error domains when the estimators are applied on nonlinear errors wi th a linear error model. Main outcome is that when the error becomes nonlinear , the matching performance degrades and the s pread in the estimates of the various estimators increases considerabl y where underestimati on of the l ocal characteristics such as the stability characteristics occurs. Measurement and process noise influences particularl y the estimates of the secondary deri vati ves. If the error destabilizes the aircraft consi derabl y even small deviations in the estimates may produces very different maneuver responses in the output error domain which makes pure equation error estimation unrel iable in this respect. Moreover, the matching performance of the estimator is best in its own domain but compromising the other domain whereas the combi ned esti mator produces a g ood balance in matching performance for both equation and output error domains . Nomenclatureforce coefficient c l = rolling mo ment coefficient c m = pitching mo ment coefficient c n = yawing mo ment coefficient f = system state function F = process noise distribution matrix g = system observation function G = measurement noise distribution matrix I = inertia matrix J = cost function K = maximu m nu mber of time samp les l  = reference cord m = size of unknown parameter vector RMSE(x) = root mean square error o f x M  = mo ment vector N = maximu m nu mber of time samp les N = order of polynomial p = size of observation vector p,q,r = roll, p itch, and yaw rate S = reference area t = time t 0 = initial t ime u = control input vector v = measurement noise V = freestream velocity w = process noise w pi = diagonal elements of W W = normalizat ion matrix x = state vector x 0 = initial condit ion of state vector x 1,2,3 = input signals 1,2,3 y = simu lated observation vector z = measured observation vector  = angle of attack  = angle of sideslip  = flaperon deflection  = weighting between equation/output error  = normalizat ion factor  = unknown parameters to be estimated  = leading edge sweep   = angular rate vector  = aileron deflection  = rudder deflection § Professor in Aeronautics, Esplanade 10, 85049 Ingolstadt, Germany, and AIAA Senio r Member.Downloaded by MONASH UNIVERSITY on November 26, 2014 | http://arc.aiaa.org | q dyn = dynamic pressure s = half span Subscripts/Superscripts 0 = static offset ADM = aerodynamic model ctrl = control surface deflections Engine = engine related FT = flight test related G = gravity related i,j,n = i-th, j-th, n -th sample  = angle of attack derivative  ...