First-order Gauss-Markov Process Research Articles

Thermospheric Density Estimation Method Using a First-Order Gauss–Markov Process

Low-Earth-orbit (LEO) spacecraft are significantly influenced by atmospheric drag. Accurately estimating thermospheric density is pivotal for the precise calculation of drag acceleration. However, thermospheric density along a specific orbit, computed using existing thermospheric models, has certain inaccuracies. In this work, a first-order Gauss–Markov process is used to model the deviation of atmospheric drag acceleration. With the Markov parameter of the initial state iteratively computed through sequential estimation and the smoothing method, the thermospheric density is derived from high-precision GPS measurements. In simulation scenarios, the root-mean-square error and relative error of the estimated thermospheric density reduce by about 45 and 50% relative to the prior density, respectively. Using the estimated density for orbit propagation, satellite trajectories’ one-day position and velocity error are, respectively, within 100 m and 0.1 m/s, and an average improvement in orbit precision is over 80%. The proposed method has been applied to the real Tsinghua Science Satellite (Q-SAT) GPS measurements for effectiveness verification. It shows strong adaptability under extreme space weather and during the occurrence of geomagnetic storms. Due to the estimated Markov parameter of the initial state obeying the Langevin dynamics properties, the proposed method also offers short-term thermospheric density forecasting potential.

UAV-Aided Vehicular Short-Packet Communication and Edge Computing System Under Time-Varying Channel

In this paper, a novel UAV-aided vehicular edge computing (VEC) network is proposed, where the vehicle and on-board UAV provide multi-access edge computing (MEC) service for the roadside Internet of Things (IoT) devices. In this system, considering the time-varying channel, we derive the lower bound of signal-to-noise ratio (SNR) based on the first-order Gauss-Markov process. Then, with the short-packet transmission, we maximize the total amount of computation by jointly optimizing the communication scheduling, the trajectories of the vehicle and on-board UAV, and the computing resource, subject to the mobility, connection and computation constraints. The formulated optimization problem is a mix-integer non-convex problem. To efficiently solve it, we propose an alternative algorithm based on the Lagrangian dual decomposition and successive convex approximation technique. Extensive simulation results are provided to show the performance gain of the proposed algorithm.

A POMDP-Based Approach to Joint Antenna Selection and User Scheduling for Multi-User Massive MIMO Communication

We devise a partially observable Markov decision process (POMDP) based joint antenna selection and user scheduling (JASUS) policy for a massive MIMO base station, equipped with only a small number of RF chains, that serves a large number of users. The users are served at different time slots within a frame. Relying on partial CSI obtained from training between the selected antennas and the users, at the beginning of each frame, the BS assigns each user to a time slot in the frame and selects a subset of antennas to serve the users scheduled in each time slot. Assuming that the channels evolve according to a Markov process and relying on zero-forcing beamforming, we formulate our JASUS problem using a POMDP framework to devise a real-time decision-making policy that maximizes the expected long-term sum-rate. We rigorously prove that for positively correlated two-state channel models, the myopic policy provides the optimal solution to our POMDP-based JASUS problem for any number of RF chains and for any number of users. Based on this, we model the Rayleigh fading channels as first-order Gauss-Markov processes and devise a low-complexity myopic policy-based JASUS algorithm for massive MU-MIMO systems that only relies on partial CSI.

Decoupled Planes’ Non-Singular Adaptive Integral Terminal Sliding Mode Trajectory Tracking Control for X-Rudder AUVs under Time-Varying Unknown Disturbances

This paper analyzes the trajectory tracking problem in decoupled planes for X-rudder AUVs under time-varying, unknown environmental interferences. The proposed scheme consists of the kinematic control law based on the compound line-of-sight guidance law and the dynamic control law based on a non-singular adaptive integral terminal sliding mode control (NAITSMC) to avoid the chattering problems, parameter perturbation, and time-varying disturbances. Meanwhile, we introduce a reduced-order extended state observer (RESO) to compensate for unknown ocean currents by the first-order Gauss–Markov process. We verify the whole system of the proposed scheme through global asymptotic stability, then present a set of numerical simulations revealing robustness and adaptability performances in decoupled planes.

Distributed robust power control in two-tier vehicle networks under uncertain channel environments

This paper proposes a novel optimization scheme to support stable and reliable vehicle-to-everything connections in two-tier networks, where the uplink channel of the cellular user is reused by underlay vehicle-to-vehicle communications. However, considering complex channel fading and high-speed vehicle movement, the certainty assumption is impractical and fails to maintain power control strategy in reality in the traditional statical vehicular networks. Rather than the perfect channel state information assumption, the first-order Gauss-Markov process which is a probabilistic model affected by vehicle speed and fading is introduced to describe imperfect channel gains. Moreover, interference management is a major challenge in reusing communications, especially in uncertain channel environments. Power control is an effective way to realize interference management, and optimal power allocation can ensure that interference of the user meets the communication requirements. In this study, the sum-rate-oriented power control scheme and minimum-rate-oriented power control scheme were implemented to manage interference and satisfy different design objectives. Since both of these schemes are non-convex and intractable, the Bernstein approximation and successive convex approximation methods were adopted to transform the original problems into convex ones. Furthermore, a novel distributed robust power control algorithm was developed to determine the optimal solutions. The performance of the algorithm was evaluated through numerical simulations, and the results indicate that the proposed algorithm is effective in vehicular communication networks with uncertain channel environments.

Globally Optimal Centralized and Sequential Fusion Filters for Uncertain Systems With Time-Correlated Measurement Noises

This paper is concerned with the fusion filtering problem for stochastic uncertain multi-sensor systems with time-correlated measurement noises, where the stochastic uncertainties are described by white multiplicative noises, and the additive measurement noises are first-order Gauss-Markov Processes. By introducing the recursive measurement noise estimators, the centralized fusion filter (CFF) based on the idea of batch process and sequential fusion filter (SFF) based on the idea of sequential process are designed in the linear minimum variance (LMV) sense by an innovation analysis approach, respectively. The proposed SFF can achieve the same estimation accuracy as the CFF. It is also globally optimal. The equivalence on estimation accuracy of the SFF and CFF is strictly proved by mathematical induction method. The stability and steady-state properties of the proposed fusion filters are analyzed. Two examples show the effectiveness of the proposed fusion algorithms.

Integrity Risk Under Temporal Correlation for Horizontal ARAIM

Integrity requirements for safety-critical global navigation satellite system applications, such as in civil aviation for the nonprecision approach through precision approach, are defined in a per hour or per approach (i.e., 150s) basis by the International Civil Aviation Organization. This article presents a novel methodology for mapping such operational requirements to the specific risk at an algorithmic level for advanced receiver autonomous integrity monitoring (ARAIM), in particular horizontal ARAIM (H-ARAIM). We thoroughly evaluated the actual risk over time by performing extensive first-order Gauss Markov Process Monte Carlo runs for the propagation of time-correlated position errors and test statistics over one hour exposure time and accounting for multiple events of loss of integrity over the time interval. A comparison of the risk over time and the risk for a single epoch leads to the number of effectively independent samples. The current integrity equation was modified using the number such that a specific risk requirement is allocated to a single sample for the determination of the protection level. This study also examined the impact of the modified risk allocation on the existing fault detection and exclusion algorithm by conducting H-ARAIM availability simulations and by comparing the results based on the newly proposed method with that obtained using the existing single sample-based risk allocation. In our preliminary assessment, little impact on the global availability (availability loss of approximately up to 1%) of the inflated terms of the integrity equation due to the number of valid samples was found.

Optimal linear recursive estimators for stochastic uncertain systems with time-correlated additive noises and packet dropout compensations

This paper is concerned with the state estimation problem over a packet-dropping network for stochastic uncertain systems with time-correlated additive noises. Additive process and measurement noises are both depicted by first-order Gauss-Markov processes. Stochastic parameter uncertainties are described by correlated white multiplicative noises. When a sensor measurement transmitted over networks is lost, its predictor is used for compensation. The optimal linear recursive full-order state filter, predictor and smoother are proposed under the linear minimum variance (LMV) criterion by an innovation analysis approach. They are calculated in terms of the filter of the product of the multiplicative noise and state, estimators of the process and measurement noises, and cross-covariance matrices for the state and/or noises. The steady-state estimators are also studied. A sufficient condition for convergence of optimal linear estimators is given. The simulation results verify the effectiveness of the proposed algorithms.

A Novel Adaptive Kalman Filtering Approach to Human Motion Tracking With Magnetic-Inertial Sensors

This article presents an adaptive Kalman filtering approach to estimate the orientation of human body segments by using magnetic-inertial measurement units (MIMUs) with three-axis gyroscope, accelerometer, and magnetometer. In order to mitigate the negative impact of the external accelerations and ferromagnetic disturbances, the disturbances are modeled by first-order Gauss–Markov processes, and two parallel adaptive Kalman filters containing disturbance models are implemented to eliminate the disturbances. An adaptive factor is introduced to adjust the process noise covariance matrix to compensate for modeling errors induced by unmodeled gyroscope biases and the erroneous process noise covariance matrices. Furthermore, the outliers are checked and discarded by hypothesis tests on the innovation, and the measurement is rejected when the innovation exceeds a given confidence interval. Then, the estimated gravity acceleration and geomagnetic field are used to calculate the orientation quaternion using triaxial attitude determination algorithm. Finally, experiments under different motion scenarios are carried out to evaluate the effectiveness of the proposed method, and the performance of the proposed method is discussed in comparison with existing ones. A forward kinematics three-dimensional (3-D) human motion reconstruction method is proposed to drive the human skeleton model to reproduce human motion with a visual interface based on ROS platform.

Real-time precise orbit determination of LEO satellites using a single-frequency GPS receiver: Preliminary results of Chinese SJ-9A satellite

Spaceborne Global Positioning System (GPS) receivers are widely used for orbit determination of low-Earth-orbiting (LEO) satellites. With the improvement of measurement accuracy, single-frequency receivers are recently considered for low-cost small satellite missions. In this paper, a Schmidt-Kalman filter which processes single-frequency GPS measurements and broadcast ephemerides is proposed for real-time precise orbit determination of LEO satellites. The C/A code and L1 phase are linearly combined to eliminate the first-order ionospheric effects. Systematic errors due to ionospheric delay residual, group delay variation, phase center variation, and broadcast ephemeris errors, are lumped together into a noise term, which is modeled as a first-order Gauss-Markov process. In order to reduce computational complexity, the colored noise is considered rather than estimated in the orbit determination process. This ensures that the covariance matrix accurately represents the distribution of estimation errors without increasing the dimension of the state vector. The orbit determination algorithm is tested with actual flight data from the single-frequency GPS receiver onboard China’s small satellite Shi Jian-9A (SJ-9A). Preliminary results using a 7-h data arc on October 25, 2012 show that the Schmidt-Kalman filter performs better than the standard Kalman filter in terms of accuracy.

Nonlinear Kalman Filtering for Improved Angles-Only Navigation Using Relative Orbital Elements

This paper addresses the design and validation of an accurate estimation architecture for autonomous angles-only navigation in orbits of arbitrary eccentricity. The proposed filtering strategy overcomes the major deficiencies of existing approaches in the literature, which mainly focus on applications in near-circular orbits and generally suffer from poor dynamical observability due to linearizing the filter dynamics and measurement models. Consequently, traditional angles-only navigation solutions require conducting known orbital maneuvers to reconcile the ambiguous range. In contrast, the algorithms developed in this work enable accurate maneuver-free reconstruction of the relative orbital motion. This is done through the full exploitation of nonlinearities in the measurement model using the unscented Kalman filter to improve dynamical observability and filter performance. The filter estimates mean relative orbit elements, adopting a state transition matrix subject to secular and long-period perturbation effects to decouple observable from unobservable parameters. The complete state is then reconciled with the angle measurements in the measurement model through a nonlinear transformation that includes the conversion from mean to osculating orbital elements. The resulting linear dynamics model is supplemented by either first-order Gauss–Markov processes (that is, differential empirical accelerations) or by a covariance-matching approach to online adaptive process noise tuning to increase performance at minimal computational complexity. Finally, the estimation architecture is completed by a novel deterministic algorithm for batch initial relative orbit determination to accurately initialize the sequential filter.

A New Technique for Integrating MEMS-Based Low-Cost IMU and GPS in Vehicular Navigation

In providing acceptable navigational solutions, Location-Based Services (LBS) in land navigation rely mostly on integration of Global Positioning System (GPS) and Inertial Navigation System (INS) measurements for accuracy and robustness. The GPS/INS integrated system can provide better land-navigation solutions than the ones any standalone system can provide. Low-cost Inertial Measurement Units (IMUs), based on Microelectromechanical Systems (MEMS) technology, revolutionized the land-navigation system by virtue of their low-cost miniaturization and widespread availability. However, their accuracy is strongly affected by their inherent systematic and stochastic errors, which depend mainly on environmental conditions. The environmental noise and nonlinearities prevent obtaining optimal localization estimates in Land Vehicular Navigation (LVN) while using traditional Kalman Filters (KF). The main goal of this paper is to effectively eliminate stochastic errors of MEMS-based IMUs. The proposed solution is divided into two main components: (1) improving noise cancellation, using advanced stochastic error models in MEMS-based IMUs based on combined Autoregressive Processes (ARP) and first-order Gauss-Markov Process (1GMP), and (2) modeling the low-cost GPS/INS integration, using a hybrid Fuzzy Inference System (FIS) and Second-Order Extended Kalman Filter (SOEKF). The results obtained show that the proposed methods perform better than the traditional techniques do in different stochastic and dynamic situations.

Observability Analysis and Filter Design for the Orion Earth–Moon Attitude Filter

The Orion attitude navigation design is presented, together with justification of the choice of states in the filter and an analysis of the observability of its states while processing star tracker measurements. The analysis shows that when the gyroscope biases and scale factors drift at different rates and are modeled as first-order Gauss–Markov processes, the states are observable so long as the time constants are not the same for both sets of states. In addition, the inertial-measurement-unit-to-star-tracker misalignments are modeled as first-order Gauss–Markov processes and these states are estimated. These results are used to finalize the design of the attitude estimation algorithm and the attitude calibration maneuvers.

Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it</sup> (D), for first-order Gauss-Markov processes. R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it</sup> (D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">op</sup> (D). We show that, for Gaussian sources, the latter can also be upper bounded as R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">op</sup> (D) ≤ R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it</sup> (D) + 0.5 log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (2πe) bits/sample. In order to analyze R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it</sup> (D) for arbitrary zero-mean Gaussian stationary sources, we introduce R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it̅</sup> (D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it̅</sup> (D), we derive three closed-form upper bounds to the additive rate loss defined as R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it̅</sup> (D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D ≤ σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , RU(D) can be realized by an additive white Gaussian noise channel surrounded by a unique set of causal pre-, post-, and feed- back niters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal niters and is guaranteed to converge to R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it̅</sup> (D). Finally, by establishing a connection to feedback quantization, we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves an operational rate lower than R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it̅</sup> (D) +0.254 and R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it̅</sup> (D) + 0.754 bits/sample, respectively. This implies that the OPTA among all zero-delay source codes, denoted by R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zd</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">op</sup> (D), is upper bounded as R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zd</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">op</sup> (D) <; R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">it̅</sup> (D) + 1-254 <; R(D) + 1.754 bits/sample.

Acoustic cardiac signals analysis: a Kalman filter&amp;ndash;based approach

Auscultation of the heart is accompanied by both electrical activity and sound. Heart auscultation provides clues to diagnose many cardiac abnormalities. Unfortunately, detection of relevant symptoms and diagnosis based on heart sound through a stethoscope is difficult. The reason GPs find this difficult is that the heart sounds are of short duration and separated from one another by less than 30 ms. In addition, the cost of false positives constitutes wasted time and emotional anxiety for both patient and GP. Many heart diseases cause changes in heart sound, waveform, and additional murmurs before other signs and symptoms appear. Heart-sound auscultation is the primary test conducted by GPs. These sounds are generated primarily by turbulent flow of blood in the heart. Analysis of heart sounds requires a quiet environment with minimum ambient noise. In order to address such issues, the technique of denoising and estimating the biomedical heart signal is proposed in this investigation. Normally, the performance of the filter naturally depends on prior information related to the statistical properties of the signal and the background noise. This paper proposes Kalman filtering for denoising statistical heart sound. The cycles of heart sounds are certain to follow first-order Gauss–Markov process. These cycles are observed with additional noise for the given measurement. The model is formulated into state-space form to enable use of a Kalman filter to estimate the clean cycles of heart sounds. The estimates obtained by Kalman filtering are optimal in mean squared sense.

Kalman Filter-Based Orbit Determination with Dynamic Model Compensation for a Maneuvered GEO Satellite

Orbit determination methods for a geostationary (GEO) satellite are introduced. In order to control or model the thrust force, a Kalman filter based on dynamic model compensation is proposed for the orbit determination of a maneuvered GEO satellite. The main idea is to use a first-order Gauss-Markov process to compensate the unmodeled or inaccurately modeled accelerations caused by orbital maneuver in Kalman filter-based orbit determination. Simulation with Chinese ground tracking network for a maneuvered GEO satellite was conducted to verify the performance of the proposed orbit determination technique. The results show that it can efficiently compensate the influence of orbital maneuver and achieve high orbit accuracy.

Bayesian Interpolation and Parameter Estimation in a Dynamic Sinusoidal Model

In this paper, we propose a method for restoring the missing or corrupted observations of nonstationary sinusoidal signals which are often encountered in music and speech applications. To model nonstationary signals, we use a time-varying sinusoidal model which is obtained by extending the static sinusoidal model into a dynamic sinusoidal model. In this model, the in-phase and quadrature components of the sinusoids are modeled as first-order Gauss-Markov processes. The inference scheme for the model parameters and missing observations is formulated in a Bayesian framework and is based on a Markov chain Monte Carlo method known as Gibbs sampler. We focus on the parameter estimation in the dynamic sinusoidal model since this constitutes the core of model-based interpolation. In the simulations, we first investigate the applicability of the model and then demonstrate the inference scheme by applying it to the restoration of lost audio packets on a packet-based network. The results show that the proposed method is a reasonable inference scheme for estimating unknown signal parameters and interpolating gaps consisting of missing/corrupted signal segments.

Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility

Stochastic modeling is a challenging task for low-cost sensors whose errors can have complex spectral structures. This makes the tuning process of the INS/GNSS Kalman filter often sensitive and difficult. For example, first-order Gauss–Markov processes are very often used in inertial sensor models. But the estimation of their parameters is a non-trivial task if the error structure is mixed with other types of noises. Such an estimation is often attempted by computing and analyzing Allan variance plots. This contribution demonstrates solving situations when the estimation of error parameters by graphical interpretation is rather difficult. The novel strategy performs direct estimation of these parameters by means of the expectation-maximization (EM) algorithm. The algorithm results are first analyzed with a critical and practical point of view using simulations with typically encountered error signals. These simulations show that the EM algorithm seems to perform better than the Allan variance and offers a procedure to estimate first-order Gauss–Markov processes mixed with other types of noises. At the same time, the conducted tests revealed limits of this approach that are related to the convergence and stability issues. Suggestions are given to circumvent or mitigate these problems when complexity of error structure is ‘reasonable’. This work also highlights the fact that the suggested approach via EM algorithm and the Allan variance may not be able to estimate the parameters of complex error models reasonably well and shows the need for new estimation procedures to be developed in this context. Finally, an empirical scenario is presented to support the former findings. There, the positive effect of using the more sophisticated EM-based error modeling on a filtered trajectory is highlighted.

Stochastic Approach to Optimal Guidance with Uncertain Intercept Time

The paper presents a stochastic approach to optimal guidance with significant uncertainty in time until intercept. The uncertain intercept time is modeled as a random variable with discrete probability density. An optimal guidance law (OGL) is derived by solving the appropriate Hamilton-Jacobi recursion under the following assumptions: 1) the target maneuver is modeled as a first-order Gauss-Markov process; 2) the missile's guidance commands are based on observing the line-of-sight (LOS) angle to the target in additive observation noise; 3) the missile acceleration response to the acceleration commands is well described by a linear first-order transfer function. Although the present problem is formulated in the linear quadratic Gaussian (LQG) framework, the certainty equivalence principle does not apply since the OGL depends on the discrete probability density of the time until intercept. A simple simulation example shows that when the interceptor has a large acceleration advantage over the target, the miss distances resulting from the use of the proposed law are essentially equivalent to those obtained when using the OGL, which requires full knowledge of the intercept time.

Assessing Probability of Correct Ambiguity Resolution in the Presence of Time-Correlated Errors

ABSTRACT: To meet their accuracy requirements, many applications require the resolution of the carrier phase ambiguities to their integer values. However, the process of ambiguity resolution is ultimately based on statistical values and therefore has an associated probability of being performed correctly. This paper develops a method of computing the probability of correctly fixing the ambiguities in the presence of time correlated errors. A new Kalman filter for use in the presence of time correlated observations is reviewed and adapted for carrier phase GPS applications. In terms of correlated errors, consideration is specifically given to ionosphere, zenith troposphere, and multipath effects; all modeled as first-order Gauss-Markov processes. Simulated results, based on the covariance matrix of the float ambiguities, are used to provide theoretical bounds on the probability of correct fix using several levels of observation error variances and time correlations. Results indicate that increased correlation of observations reduces the ability to resolve ambiguities suggesting that if observation correlation is ignored, overly optimistic probabilities of correct ambiguity resolution will be obtained.