Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

scholarly journals Performance Evaluation of GPS Auto-Surveying Techniques

Sensors ◽  
2021 ◽  
Vol 21 (21) ◽  
pp. 7374
Author(s):  
João Manito ◽  
José Sanguino
Keyword(s):  
Kalman Filter ◽  
Least Squares ◽  
Unscented Kalman Filter ◽  
Weighted Least Squares ◽  
Base Station ◽  
Global Navigation Satellite Systems ◽  
Precise Position ◽  
Satellite Systems ◽  
Global Navigation Satellite ◽  
Position Estimate

With the increase in the widespread use of Global Navigation Satellite Systems (GNSS), increasing numbers of applications require precise position data. Of all the GNSS positioning methods, the most precise are those that are based in differential systems, such as Differential GNSS (DGNSS) and Real-Time Kinematics (RTK). However, for absolute positioning, the precision of these methods is tied to their reference position estimates. With the goal of quickly auto-surveying the position of a base station receiver, four positioning methods are analyzed and compared, namely Least Squares (LS), Weighted Least Squares (WLS), Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), using only pseudorange measurements, as well as the Hatch Filter and position thresholding. The research results show that the EKF and UKF present much better mean errors than LS and WLS, with an attained precision below 1 m after about 4 h of auto-surveying. The methods that presented the best results are then tested against existing implementations, showing them to be very competitive, especially considering the differences between the used receivers. Finally, these results are used in a DGNSS test, which verifies a significant improvement in the position estimate as the base station position estimate improves.

Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains

2009 ◽  
Author(s):  
James R. McCusker ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Time Scale ◽  
Prediction Error ◽  
Nonlinear Least Squares ◽  
Integrated Approach ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Single Model ◽  
Iterative Estimation

A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.

scholarly journals Performance Analyses of a RAIM Algorithm for Kalman Filter with GPS and NavIC Constellations

Sensors ◽  
2021 ◽  
Vol 21 (24) ◽  
pp. 8441
Author(s):  
Susmita Bhattacharyya
Keyword(s):  
Kalman Filter ◽  
Measurement Errors ◽  
Weighted Least Squares ◽  
Temporal Variations ◽  
Global Navigation Satellite Systems ◽  
Model Parameters ◽  
Integrity Monitoring ◽  
Satellite Systems ◽  
Performance Analyses ◽  
Global Navigation Satellite

This paper evaluates the performance of an integrity monitoring algorithm of global navigation satellite systems (GNSS) for the Kalman filter (KF), termed KF receiver autonomous integrity monitoring (RAIM). The algorithm checks measurement inconsistencies in the range domain and requires Schmidt KF (SKF) as the navigation processor. First, realistic carrier-smoothed pseudorange measurement error models of GNSS are integrated into KF RAIM, overcoming an important limitation of prior work. More precisely, the error covariance matrix for fault detection is modified to capture the temporal variations of individual errors with different time constants. Uncertainties of the model parameters are also taken into account. Performance of the modified KF RAIM is then analyzed with the simulated signals of the global positioning system and navigation with Indian constellation for different phases of aircraft flight. Weighted least squares (WLS) RAIM used for comparison purposes is shown to have lower protection levels. This work, however, is important because KF-based integrity monitors are required to ensure the reliability of advanced navigation methods, such as multi-sensor integration and vector receivers. A key finding of the performance analyses is as follows. Innovation-based tests with an extended KF navigation processor confuse slow ramp faults with residual measurement errors that the filter estimates, leading to missed detection. RAIM with SKF, on the other hand, can successfully detect such faults. Thus, it offers a promising solution to developing KF integrity monitoring algorithms in the range domain. The modified KF RAIM completes processing in time on a low-end computer. Some salient features are also studied to gain insights into its working principles.

Composite distribution inversion applied to crosshole tomography

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1283-1294 ◽  
Author(s):  
James D. Clippard ◽  
Douglas H. Christensen ◽  
Richard D. Rechtien
Keyword(s):  
Least Squares ◽  
Reference Model ◽  
A Priori ◽  
Ideal Point ◽  
Stable Solution ◽  
Parameter Estimates ◽  
Point Spread Functions ◽  
Priori Information ◽  
Damped Least Squares ◽  
Composite Distribution

Crosshole tomography requires solution of a mixed‐determined inverse problem and addition of a priori information in the form of auxiliary constraints to achieve a stable solution. Composite distribution inversion (CDI) constraints are developed by assuming parameters are drawn from a composite distribution consisting of both normally and uniformly distributed parameters. Nonanomalous parameter estimates are assumed to be Gaussian while anomalous parameters are assumed uniform. The resulting constraints are sensitive to anomaly volume and are an alternative to the usual constraints of minimizing [Formula: see text] solution length or some measure of roughness. Damped least‐squares inversion, which minimizes solution length, distributes anomalous signal through poorly resolved areas to produce in attenuated and smoothed anomalies. Similar regularization methods, such as smoothness or flatness constraints, also degrade small spatial wavelength features and produce diffuse images of distinct anomalies. CDI constraints preserve small spatial wavelength features by encouraging small amplitude anomalies to assume the value of the reference model and by allowing truly anomalous parameter estimates to assume whatever value minimizes prediction error without incurring additional penalty. CDI tomograms are characterized by nearly ideal point‐spread functions, suggesting the possibility of better quantitative parameter estimates than are produced using most existing methods. CDI tomograms of both synthetic and field data are shown to produce less diffuse images with more accurate anomaly amplitude estimates than damped least‐squares methods. The CDI algorithm is potentially applicable to nontomographic inversion problems.

Multi-Sensor Integrated Navigation in Urban and Indoor Environments

2018 ◽  
pp. 397-442 ◽  
Author(s):  
Mohamed Atia
Keyword(s):  
Sensor Fusion ◽  
Global Navigation Satellite Systems ◽  
Measurement Unit ◽  
Indoor Environments ◽  
Integrated Navigation ◽  
Satellite Systems ◽  
Tightly Coupled ◽  
Sensor Processing ◽  
Global Navigation Satellite ◽  
Dense Urban Environment

The art of multi-sensor processing, or “sensor-fusion,” is the ability to optimally infer state information from multiple noisy streams of data. One major application area where sensor fusion is commonly used is navigation technology. While global navigation satellite systems (GNSS) can provide centimeter-level location accuracy worldwide, they suffer from signal availability problems in dense urban environment and they hardly work indoors. While several alternative backups have been proposed, so far, no single sensor or technology can provide the desirable precise localization in such environments under reasonable costs and affordable infrastructures. Therefore, to navigate through these complex areas, combining sensors is beneficial. Common sensors used to augment/replace GNSS in complex environments include inertial measurement unit (IMU), range sensors, and vision sensors. This chapter discusses the design and implementation of tightly coupled sensor fusion of GNSS, IMU, and light detection and ranging (LiDAR) measurements to navigate in complex urban and indoor environments.

scholarly journals EXPLICIT FORMULAE FOR PARAMETERS OF STOCHASTIC MODELS OF A DISCOUNTED EQUITY INDEX USING MAXIMUM LIKELIHOOD ESTIMATION WITH APPLICATIONS

2017 ◽  
Vol 12 (02) ◽  
pp. 1750010 ◽  
Author(s):  
K. FERGUSSON
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Models ◽  
Likelihood Estimation ◽  
Market Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
No Arbitrage ◽  
Explicit Formulae ◽  
Equity Index

A discounted equity index is computed as the ratio of an equity index to the accumulated savings account denominated in the same currency. In this way, discounting provides a natural way of separating the modeling of the short rate from the market price of risk component of the equity index. In this vein, we investigate the applicability of maximum likelihood estimation to stochastic models of a discounted equity index, providing explicit formulae for parameter estimates. We restrict our consideration to two important index models, namely the Black–Scholes model and the minimal market model of Platen, each having an explicit formula for the transition density function. Explicit formulae for estimates of the model parameters and their standard errors are derived and are used in fitting the two models to US data. Further, we demonstrate the effect of the model choice on the no-arbitrage assumption employed in risk neutral pricing.

scholarly journals Seamless Indoor-Outdoor Navigation based on GNSS, INS and Terrestrial Ranging Techniques

2017 ◽  
Vol 70 (6) ◽  
pp. 1183-1204 ◽  
Author(s):  
Wei Jiang ◽  
Yong Li ◽  
Chris Rizos ◽  
Baigen Cai ◽  
Wei Shangguan
Keyword(s):  
Navigation System ◽  
Global Navigation Satellite Systems ◽  
Indoor Environments ◽  
Integrated Navigation ◽  
Satellite Systems ◽  
Integrated Navigation System ◽  
Outdoor Environments ◽  
Federated Kalman Filter ◽  
Indoor And Outdoor Environments ◽  
Global Navigation Satellite

We describe an integrated navigation system based on Global Navigation Satellite Systems (GNSS), an Inertial Navigation System (INS) and terrestrial ranging technologies that can support accurate and seamless indoor-outdoor positioning. To overcome severe multipath disturbance in indoor environments, Locata technology is used in this navigation system. Such a “Locata-augmented” navigation system can operate in different positioning modes in both indoor and outdoor environments. In environments where GNSS is unavailable, e.g. indoors, the proposed system is designed to operate in the Locata/INS “loosely-integrated” mode. On the other hand, in outdoor environments, all GNSS, Locata and INS measurements are available, and all useful information can be fused via a decentralised Federated Kalman filter. To evaluate the proposed system for seamless indoor-outdoor positioning, an indoor-outdoor test was conducted at a metal-clad warehouse. The test results confirmed that the proposed navigation system can provide continuous and reliable position and attitude solutions, with the positioning accuracy being better than five centimetres.

scholarly journals Performance assessment of a low-complexity autoregressive Kalman filter for GNSS carrier tracking using real scintillation time series

GPS Solutions ◽  
2021 ◽  
Vol 26 (1) ◽  
Author(s):  
Sergi Locubiche-Serra ◽  
Gonzalo Seco-Granados ◽  
José A. López-Salcedo
Keyword(s):  
Kalman Filter ◽  
A Priori ◽  
Gaussian Function ◽  
Real Data ◽  
Autoregressive Process ◽  
Low Complexity ◽  
Global Navigation Satellite Systems ◽  
Ionospheric Scintillation ◽  
Satellite Systems ◽  
Phase Dynamics

AbstractIonospheric scintillation is one of the most challenging sources of errors in global navigation satellite systems (GNSS). It is an effect of space weather that introduces rapid amplitude and phase fluctuations to transionospheric signals and, as a result, it severely degrades the tracking performance of receivers, particularly carrier tracking. It can occur anywhere on the earth during intense solar activity, but the problem aggravates in equatorial and high-latitude regions, thus posing serious concerns to the widespread deployment of GNSS in those areas. One of the most promising approaches to address this problem is the use of Kalman filter-based techniques at the carrier tracking level, incorporating some a priori knowledge about the statistics of the scintillation to be dealt with. These techniques aim at dissociating the carrier phase dynamics of interest from phase scintillation by modeling the latter through some correlated Gaussian function, such as the case of autoregressive processes. However, besides the fact that the optimality of these techniques is still to be reached, their applicability for dealing with scintillation in real-world environments also remains to be confirmed. We carry out an extensive analysis and experimentation campaign on the suitability of these techniques by processing real data captures of scintillation at low and high latitudes. We first evaluate how well phase scintillation can be modeled through an autoregressive process. Then, we propose a novel adaptive, low-complexity autoregressive Kalman filter intended to facilitate the implementation of the approach in practice. Last, we provide an analysis of the operational region of the proposed technique and the limits at which a performance gain over conventional tracking architectures is obtained. The results validate the excellence of the proposed approach for GNSS carrier tracking under scintillation conditions.

Dynamically Adjusting Filter Gain Method for Suppressing GNSS Observation Outliers in Integrated Navigation

2018 ◽  
Vol 71 (6) ◽  
pp. 1396-1412 ◽  
Author(s):  
Lihui Wang ◽  
Kangyi Zhi ◽  
Bin Li ◽  
Yuexin Zhang
Keyword(s):  
Inertial Navigation System ◽  
Normal Values ◽  
External Environment ◽  
Processing Method ◽  
Global Navigation Satellite Systems ◽  
Integrated Navigation ◽  
Satellite Systems ◽  
Loosely Coupled ◽  
Global Navigation Satellite ◽  
The Impact

Global Navigation Satellite Systems (GNSSs) are easily influenced by the external environment. Signals may be lost or become abnormal thereby causing outliers. The filter gain of the standard Kalman filter of a loosely coupled GNSS/inertial navigation system cannot change with the outliers of the GNSS, causing large deviations in the filtering results. In this paper, a method based on a χ2-test and a dynamically adjusting filter gain method are proposed to detect and separately to suppress GNSS observation outliers in integrated navigation. An indicator of an innovation vector is constructed, and a χ2-test is performed for this indicator. If it fails the test, the corresponding observation value is considered as an outlier. A scale factor is constructed according to this outlier, which is then used to lower the filter gain dynamically to decrease the influence of outliers. The simulation results demonstrate that the observation outlier processing method does not affect the normal values under normal circumstances; it can also discriminate between single and continuous outliers without errors or omissions. The impact time of outliers is greatly reduced, and the system performance is improved by more than 90%. Experimental results indicate that the proposed methods are effective in suppressing GNSS observation outliers in integrated navigation.

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