Application of RTS optimal smoothing algorithm in satellite attitude determination

Application of ARIMA-RTS optimal smoothing algorithm in gas well production prediction

The finite impulse response (FIR) approach is known to be more robust than the Kalman approach. In this paper, we derive a batch q-lag maximum likelihood (ML) FIR smoother for full covariance matrices and represent it with an iterative algorithm using recursions for diagonal covariance matrices. It is shown that, under ideal conditions of fully known model, the ML FIR smoother occupies an intermediate place between the more accurate Rauch-Tung-Striebel (RTS) smoother and the less accurate unbiased FIR smoother. With uncertainties and errors in noise covariances, ML FIR smoothing is significantly superior to RTS smoothing. It is also shown experimentally that ML FIR smoothing is more robust than RTS smoothing against measurement outliers.

Passive target tracking deals with nonlinear filtering in which dynamics of the system are considered to be linear, while the target state is built on nonlinear measurements. In this paper, a comparative study is conducted for accurate state estimation of an underwater far-field moving target by exploiting the strength of well known nonlinear variant of Bayesian filter, i.e., extended Kalman filter (EKF) with discrete-time Kalman smoother, called Rauch–Tung–Striebel (RTS) smoother. Analysis is performed with two key parameters in target tracking by mean of variation in the number of sensors and different standard deviations of measured noise in the context of underwater bearings-only tracking technology. Exhaustive experiments are performed for finding the least root-mean square error between true and estimated position of target movement in the trajectory at every time instant. Relatively accurate estimation of the target state is observed from noisy measurements of sensors in case of RTS smoother than that of EKF for each scenario.

When satellite is running, it may be influenced by external factors, and the measurement models of gyro and star sensor are changing with time uncertainly. This situation may lead extended Kalman filter(EKF) divergent. So new adaptive filter can be used in this situation, and it can estimate process noise and measuring noise on-time. This paper has applied Sage-Husa adaptive filter in satellite attitude determination. This adaptive filter algorithm can estimate satellite attitude parameters and gyro drift on-time with high accuracy reaching 10-3 level, and stability of the algorithm is also very good.

A localization and tracking algorithm for an early-warning tracking system based on the information fusion of Infrared (IR) sensor and Laser Detection and Ranging (LADAR) is proposed. The proposed Kalman filter scheme incorporates Out-of-Sequence Measurements (OOSMs) to address long-range, high-speed incoming targets to be tracked by networked Remote Observation Sites (ROS) in cluttered environments. The Rauch–Tung–Striebel (RTS) fixed lag smoothing algorithm is employed in the proposed technique to further improve tracking accuracy, which, in turn, is used for target profiling and efficient filter initialization at the targeted platform. This efficient initialization increases the probability of target engagement by increasing the distance at which it can be effectively engaged. The increased target engagement range also reduces risk of any damage from debris of the engaged target. Performance of the proposed target localization algorithm with OOSM and RTS smoothing is evaluated in terms of root mean square error (RMSE) for both position and velocity, which accurately depicts the improved performance of the proposed algorithm in comparison with existing retrodiction-based OOSM filtering algorithms. The effects of assisted target state initialization at the targeted platform are also evaluated in terms of Time to Impact (TTI) and true track retention, which also depict the advantage of the proposed strategy.

The celestial navigation system is one of the important autonomous navigation system for spacecraft. The basic principle of it is using the extended Kalman filter (EKF) and the measurement of angle between celestial bodies estimate the position and velocity of spacecraft. But the EKF may not converge because of the inaccurate initial state. In this paper, a new Bayesian bootstrap filtering approach is used at the initial stage of the filtering interval to provide EKF with an accurate initial state to overcome the divergence problem. Simulation results demonstrated the high precision of orbit determination even in the presence of large initial states errors.

This paper presents an innovative application of the particle filtering techniques to the vertical gyro problem, which is a highly nonlinear and non Gaussian recursive state estimation problem. The classical approach to recursive state estimation problem of nonlinear and/or non Gaussian systems is based on the extended Kalman filter (EKF), which is a heuristic method based on the linearization of the state dynamics and observations near a nominal path. Depending on the amount of nonlinearities and non Gaussian noise, the EKF often provides a solution far from acceptable. The vertical gyro is an instrument adopted to measure the tilt angles (pitch and roll) of an aircraft with respect to local vertical. It is composed by three orthogonal gyros that are used as process sensors and by three orthogonal accelerometers that are used as aiding sensors. The output of accelerometers is filtered using a proper low-pass filter to allow for the estimation of the local direction of the gravity vector that is assumed the same of the local vertical. In the application to the vertical gyro, Gordon's version of the particle filter was used. The relevant dynamical model is based on non-linear attitude rate equation using Euler angles rather than quaternions. The algorithm, developed in Matlab environment, was first calibrated and tested in simulations, obtaining very appealing performances. Subsequently, it was implemented using real data, acquired by means of an inertial unit produced by Crossbow <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> (model DMU-HDX <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TM</sup> ), and its results were compared to those provided by the proprietary EKF embedded in the unit. First of all, stationary tests were performed. Sensor data were input to the particle filter that outputs the tilt angles (roll and pitch) with respect to the local geodetic reference. The results were compared to those provided by the internal EKF. Subsequently, the same operation was done using data that were acquired with moving platform. The accuracy of the filter was tested also for degraded operating conditions (lower data rates) and large initial errors. The main advantage of the methodology is that, while the internal filter works with 7 states (quaternions, biases and temperature), the particle filter ensures the convergence with 3 states, and provides acceptable performances with 1000 particles only, appearing promising for a real time application.

PPP-based UAV modeling using Galileo HAS orbit/clock products and RTS smoother

Strictly nonwhite measurement noise (NMN) is observed in many industrial processes. Therefore, effective smoothing is often required to extract useful information about the process state with maximum accuracy. This article proposes a batch <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> -lag optimal finite impulse response (OFIR) smoother, operating under NMN with full block covariance matrices. It is shown that the OFIR smoother significantly outperforms the Rauch–Tung–Striebel (RTS) smoother and the unbiased FIR (UFIR) smoother. Testing is provided based on object tracking. The results are validated by a practical example of a three degree-of-freedom helicopter system, which confirms that OFIR smoothing provides better noise reduction than UFIR smoothing, RTS smoothing, and modified RTS smoothing using state augmentation and measurement differencing.

MEMS (micro-electro-mechanical-system) based gyroscopes are commonly used for satellite's attitude determination and control system in recent years. They are packaged in a small form factor and have lower power consumption. They provide a low-cost solution to the emerging new space industry. MEMS gyroscopes exhibit some time-zero null bias with variation over temperature. To overcome this problem, this paper proposes a novel on-orbit gyroscope bias compensation technique based on the model predictive control approach. The proposed method can estimate the gyroscope bias instantly which is not feasible with the typical method. Furthermore, the proposed method has a low computational requirement as compared to the typical EKF (Extended Kalman Filter) method. While the proposed method allows on-orbit compensation of gyroscope bias, the satellite's attitude is required to be nearly at steady state. This limitation will be addressed in detail.

In this paper we consider the transmission of stored video from a server to a client for medical applications such as, Telemonitoring, to optimize medical quality of service (m-QoS) and to examine how the client buffer space can be used efficiently and effectively towards reducing the rate variability of the compressed variable bit rate (VBR) video. Three basic results are presented. First, we show how to obtain the greatest possible reduction in rate variability when sending stored video to client with a given buffer size. Second, how to reduce high peak data rate of compressed VBR video when a patient is moving/walking very fast in hospital. Third, we evaluate the impact of optimal smoothing algorithm on the network parameters such as, peak-to-mean ratio, standard deviation, delay, jitter, average delay and average jitter to optimize the m-QoS. To resolve these all problems we used optimal smoothing algorithm and show its performance over a set of long MPEG-4 encoded video traces. Simulation results show that m-QoS is optimized by minimizing network metrics.

Recently, Lainiotia (1971 c), using the so-called ‘ partition theorem ’, has obtained an optimal linear smoothing algorithm in explicit, closed-form expressions that are attractive, both from a computational and an analysis point of view. Lainiotis (1971c( ‘partition smoothing’ algorithm is re-examined herein, and its computational and analytical advantages studied. It is compared to the previously established two-filter smoothing algorithm of Mayne (1966), Fraser (1967), and Mehra (1968), as well as to the ‘ innovation smoothing ’ algorithm of Kailath and Frost (1968) Subsequently, the so-called ‘ iterative ’ or ‘ reprocessed ’ smoothing scheme, used extensively as a data reduction process in the Apollo Space Programme, is studied using the ‘ partition smoothing ’ algorithm. The resulting explicit and closed-form expressions are readily amenable to interpretation and optimization, and are, moreover, both theoretically interesting as well as practically useful. The statistical and limiting properties of t...

The Extended Kalman Filter (EKF) is a widely used estimator for nonlinear systems. The stability characteristics of the EKF have been examined, but have not been rigorously proven for realistic assumptions on the initial error and noise disturbances. The existing stability analysis methods were first implemented in order to obtain a baseline calculation of the requirements on the system’s initial error and noise disturbances. Since these requirements were determined to be too strict for realistic application, modifications were applied to the stability analysis in order to relax these assumptions and prove the stability with more realistic assumptions. Significant improvements in the initial error and noise bounds were achieved. Using a case study of low-cost attitude estimation, experimental flight data was utilized to reinforce and demonstrate the theoretically derived results. While the stability characteristics were examined in the context of a specific problem, the derived methods can be applied to any EKF application.

A new method for dynamic measurement of deflections of the vertical (DOV) is proposed in this paper. The integration of an inertial navigation system (INS) and global navigation satellite system (GNSS) is constructed to measure the body's attitude with respect to the astronomical coordinates. Simultaneously, the attitude with respect to the geodetic coordinates is initially measured by a star sensor under quasi-static condition and then maintained by the laser gyroscope unit (LGU), which is composed of three gyroscopes in the INS, when the vehicle travels along survey lines. Deflections of the vertical are calculated by using the difference between the attitudes with respect to the geodetic coordinates and astronomical coordinates. Moreover, an algorithm for removing the trend error of the vertical deflections is developed with the aid of Earth Gravitational Model 2008 (EGM2008). In comparison with traditional methods, the new method required less accurate GNSS, because the dynamic acceleration calculation is avoided. The errors of inertial sensors are well resolved in the INS/GNSS integration, which is implemented by a Rauch–Tung–Striebel (RTS) smoother. In addition, a single-axis indexed INS is adopted to improve the observability of the system errors and to restrain the inertial sensor errors. The proposed method is validated by Monte Carlo simulations. The results show that deflections of the vertical can achieve a precision of better than 1″ for a single survey line. The proposed method can be applied to a gravimetry system based on a ground vehicle or ship with a speed lower than 25 m/s.

A novel set-membership-based smoothing method for state estimation using the optimal bounding ellipsoid (OBE) algorithms is presented. OBE filters have been proven to be effective in state estimation problems with unknown but bounded errors. Compared with filtering methods, smoothing methods provide a much more accurate and reliable state estimate because observations beyond the current estimation time are used. The new method is a Rauch-Tung-Striebel (RTS)-type smoother which employs both forward and backward passes to estimate the system state. The forward pass is performed using the OBE filter, while the backward pass maintains the fundamental spirit of OBE algorithm in the backward direction. The minimum-volume and minimum-trace bounding ellipsoids containing the feasible state set are derived from this algorithm. Simulation results show the performance of the proposed smoother is superior to both the traditional OBE filter and Kalman filter for state estimation.