Linear Combination Of Observations Research Articles

An integration scheme of simultaneous cycle slips determination combining improved geometry-free combination and TDCP model for undifferenced GNSS data

Fast and reliable cycle slip determination can ensure successive ambiguity resolution and precise positioning. Generally, it is not difficult to determine big cycle slips using the linear combination of observations, for instance, the geometry-free (GF) combination and the Hatch–Melbourne–Wübbena (HMW) combination. However, the participation of pseudorange observations may fail to identify small cycle slips. This contribution proposes an integration scheme combining the improved geometry-free (IGF) combination and time-difference carrier phase (TDCP) model to determine simultaneous cycle slips for undifferenced kinematic data. The IGF combination, which is improved from the modified geometry-free (MGF) combination and utilizes the Gauss floor function to take the decimal part of GF, can directly determine small cycle slips on a specific frequency. The TDCP model is used to estimate the differences of position and clock error between adjacent epochs by least-square adjustment using clean phase observations, and repair the remaining cycle slips by the predicted TDCP measurements obtained from the predetermined parameters. The proposed method is tested against 1 Hz kinematic dataset with simulation and highway dataset with real cycle slips. In the simulation test, all cycle slips can be correctly repaired by IGF for L1/L5, E1/E5 and E1/E5a. These combinations are unavailable for MGF. Compared to the HMW-GF method, the repair success rate of IGF improves from 96.80% to 99.16%, and the number of incorrect cases reduces from 9650 to 2535. The IGF-TDCP integration scheme can further improve the performance of IGF, whose repair success rate is more than 99.97% and incorrect cases are 38. The highway test shows that the proposed method effectively processes simultaneous cycle slips on more than half of the tracking satellites caused by the overpasses, even in the case of simultaneous 3 second data gaps on 5 satellites of 6 tracking satellites.

Characterization of the Geometric Distribution Via Linear Combinations of Observations and of Records

In a sequence of independent identically distributed geometric random variables, the sum of the first two record values is distributed as a simple linear combination of geometric variables. It is verified that this distributional property characterizes the geometric distribution. A related characterization conjecture is also discussed. Related discussion in the context of weak records is also provided.

A BDS-3 B1C/B2a dual-frequency joint tracking architecture based on adaptive Kalman filter and extended integration time

With the development of the third-generation BeiDou navigation satellite system (BDS-3), the availability of new civil B1C and B2a signals along with existing B1I and B3I signals will greatly benefit the design of BeiDou multi-frequency receivers. For instance, BDS-3 can provide signal observations at multiple frequencies to form flexible design strategies of advanced receiver baseband signal and a linear combination of observations used for different purposes. The B1C/B2a receivers have been proposed recently which, however, are limited by the integration time to improve the tracking sensitivity further. Also, the signal observations and characteristics of the dual-frequency tracking architecture have not been fully explored, which can be further designed to get mutual benefits and reach an optimal tracking performance. In order to improve the tracking performance, especially in challenging environments such as in the presence of a weak signal and selective frequency signal attenuation, a B1C/B2a joint tracking architecture for BDS-3 dual-frequency receivers is proposed based on an adaptive Kalman filter and an extended integration time. The experimental results show that compared to the modified traditional tracking architectures, the proposed joint tracking architecture can improve the receiver’s tracking sensitivity up to 3.29 dB and achieve an optimal availability, accuracy and robustness performance in both tracking and navigation solutions.

Performance analysis of dual-frequency receiver using combinations of GPS L1, L5, and L2 civil signals

Processing of GNSS signals from more than one frequency band enhances the accuracy and integrity of a position solution in both standalone and differential positioning. The modern GPS program and newly launched GNSS systems such as GALILEO, BeiDou allow civilians to access signals from multiple frequencies in the L-band spectrum. While there are some advantages in triple-frequency processing in carrier phase applications, in general most of the standalone kinematic receivers get benefit from dual-frequency signals for ionosphere error correction. In implementing a dual-frequency receiver, it is necessary to select a combination of frequencies leading to an optimum performance of the existing civilian signals. In the current research work, we have analyzed the performance of dual-frequency receiver in terms of combined signal observation noise, sensitivity and robustness using analytical models by taking the combination of GPS L1, L2C and L5 signals as an example. Further, we have investigated the benefits of common Doppler estimate-based two-frequency signal tracking to reduce the noise in linear combination of observations. Through analytical and experimental results, it is confirmed that the L1/L5 signal combination in GPS system has low observation noise, which is suitable to use in high accuracy and precise positioning applications using standalone dual-frequency receiver. Further, it is shown that common Doppler estimate-based dual-frequency signal tracking has improved receiver tracking loop performance in terms of observation noise and multipath in linear combination of observations and enhanced receiver sensitivity and robustness. In GPS system, L1/L5 signals processed using common Doppler estimate-aided two-frequency signal tracking architecture, it is possible to effectively mitigate ionosphere delay and other receiver observation errors, to achieve less than 1 m position accuracy using unambiguous code phase observations. Proposed analysis is applicable of finding an optimal two-frequency signal combination in multi-frequency GNSS system and suitable signal processing architecture to obtain high accuracy and precise ionosphere-free position solution using code phase observations in standalone dual-frequency receiver.

Optimal estimation of derivatives in nonparametric regression

We propose a simple framework for estimating derivatives without _tting the regression function in nonparametric regression. Unlike most existing methods that use the symmetric difference quotients, our method is constructed as a linear combination of observations. It is hence very exible and applicable to both interior and boundary points, including most existing methods as special cases of ours. Within this framework, we define the variance-minimizing estimators for any order derivative of the regression function with a fixed bias-reduction level. For the equidistant design, we derive the asymptotic variance and bias of these estimators. We also show that our new method will, for the first time, achieve the asymptotically optimal convergence rate for difference-based estimators. Finally, we provide an effective criterion for selection of tuning parameters and demonstrate the usefulness of the proposed method through extensive simulation studies of the first-and second-order derivative estimators.

Cluster-based cooperative spectrum sensing over correlated log-normal channels with noise uncertainty in cognitive radio networks

In this study, the authors consider the problem of cooperative spectrum sensing (CSS) based on linear combination of observations over correlated log-normal shadow-fading channels. To reduce the effects of imperfect reporting channels, a cluster-based CSS framework and a new cluster head selection algorithm are proposed. Using the received energies (as local observations) from different clusters, the fusion centre can make the final decision by linearly combining the noisy cluster observations. To calculate the combination weights, the authors come across the problem of joint distribution approximation of sum of the correlated log-normal random variables corresponding to different clusters. A joint moment generating function (MGF) matching algorithm is proposed in this study to estimate the summations by a single log-normal vector. Monte Carlo simulations confirm the accuracy of the proposed MGF-based approach in estimating the desired statistics and efficiency of the cluster-based spectrum-sensing algorithm in terms of primary signal detection.

Two-Stage Procedures for Multiple Comparisons with a Control

SYNOPTIC ABSTRACTGiven p + 1 populations πi which are distributed N(μi, σi2), comparisons are made between π0 and π1, …, πp by constructing joint confidence intervals, both one and two-sided, for the differences μi – μ0, based on two-stage sampling, the first stage being used to estimate the σi2. Such intervals are used to solve selection problems. It is shown that, for the case of symmetric two-sided intervals, procedures based on sample means are always preferred to those based on other linear combinations of observations, designed to control the confidence coefficient. For other intervals the P* requirement may not be met (using sample means), but an investigation of confidence conditional on first stage sample variances indicates that sample means may still be preferable. A hybrid procedure where sample means are used except for the control population has advantages for one sided intervals.

Polarization transfer in deuteron elastic scattering and the deuteron-nucleus tensor interaction

Abstract It is shown that the angular distributions of the polarization transfer coefficients contain new complementary information on the tensor part of the deuteron-nucleus interaction which cannot be obtained solely from tensor analyzing power measurements. Using a formalism where the polarization quantities carry definite spin-flip quantum numbers we derive the linear combinations of observables expected to be more sensitive to tensor force effects. The way they can help to distinguish between different types of tensor potentials is briefly discussed.

IV.—On Least Squares and Linear Combination of Observations

In a series of papers W. F. Sheppard (1912, 1914) has considered the approximate representation of equidistant, equally weighted, and uncorrelated observations under the following assumptions:–(i) The data beingu1, u2, …, un, the representation is to be given by linear combinations(ii) The linear combinations are to be such as would reproduce any set of values that were already values of a polynomial of degree not higher than thekth.(iii) The sum of squared coefficientswhich measures the mean square error ofyi, is to be a minimum for each value ofi.

Free functions and the ≫student≫-fisher theorem

Abstract The notion of Free Functions as conceived by Thiele in whose hands it has proved such a powerful instrument of research, is from the outset confined to linear combinations of observations, satisfying certain conditions. Thus, we read on p. 55 of the work quoted below.