GPS is a satellite-based navigation system that is able to determine the exact position of objects on the Earth, sky, or space. By increasing the velocity of a moving object, the accuracy of positioning decreases; meanwhile, the calculation of the exact position in the movement by high velocities like airplane movement or very high velocities like satellite movement is so important. In this paper, seven methods for solving navigation equations in very high velocities using least squares method and its combination with the variance estimation methods for weighting observations based on their qualities are studied. Simulations on different data with different velocities from 100 m/s to 7000 m/s show that proposed method can improve the accuracy of positioning more than 50%.

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Accurate Solution of Navigation Equations in GPS Receivers for Very High Velocities Using Pseudorange Measurements

Today Global Positioning System (GPS) is the most important system of positioning in the world and is used in different industries. Basic positioning methods in GPS receivers are based on pseudo-range and carrier phase measurements types whilst each of which has its own advantages and disadvantages. Pseudo-range method is not very much accurate. Carrier phase has a substantial accuracy, but its main problem is that it is an indirect measurement which only computes the displacement. Carrier phase measurement can include some whole cycles plus a fraction of carrier phase. The number of whole cycles may change through time however this change is unknown for us. Code measurements (based on pseudo-range) and carrier phase are corrupted with the same error sources, but with main differences. Basically, code tracking with low accuracy makes unambiguous pseudo-ranges. Carrier phase measurements are highly accurate, but get limited with integer ambiguity. Integer is fixed until the time that carrier tracking loop is saved. Every kind of gap in tracking, no matter how short it is, changes the amount of integer which is the biggest problem in carrier phase utilization. In this paper, the corporation of pseudo-range capability and carrier phase in single-frequency GPS receivers will be discussed which makes a substitute for the pure pseudo-range observations and provides a high level of positioning accuracy. To achieve this aim, Kalman filter will be used.

Position Estimation in Single-Frequency GPS Receivers Using Kalman Filter with Pseudo-Range and Carrier Phase Measurements

A novel direct identification using the residual model of Kalman filter (KF) is proposed for multiple-input and multiple-output Box–Jenkins model of the system formed of the signal and disturbance models using the residual model relating the input and output of the system without any a priori knowledge of the statistics of the disturbance and measurement noise corrupting the output. To avoid a non-linear optimisation, the auto-regressive and moving average (MA) residual model is approximated by a high-order MA model, so that the unknown parameters of the KF enter the residual model linearly. A key property of the KF is established, namely that the transfer matrix of the signal model is the matrix fraction description (MFD) model relating the residual and the system input and output. A two-stage identification method is developed here. In stage 1, a high-order KF of the system is identified using the robust, and computationally efficient least-squares method to capture completely both the signal and disturbance models. In stage 2, the KF for the signal is derived using the balanced model reduction technique. The signal model is derived using the key MFD property. The performance of the proposed scheme is successfully evaluated on both simulated and physical systems.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-cta.2017.0829

Robust Kalman filter-based least squares identification of a multivariable system

For autonomous vehicles, navigation systems must be accurate enough to provide lane-level localization. Highaccuracy sensors are available but not cost-effective for production use. Although prone to significant error in poor circumstances, even low-cost GPS systems are able to correct Inertial Navigation Systems (INS) to limit the effects of dead reckoning error over short periods between sufficiently accurate GPS updates. Kalman filters (KF) are a standard approach for GPS/INS integration, but require careful tuning in order to achieve quality results. This creates a motivation for a KF which is able to adapt to different sensors and circumstances on its own. Typically for adaptive filters, either the process (Q) or measurement (R) noise covariance matrix is adapted, and the other is fixed to values estimated a priori. We show that by adapting Q based on the state-correction sequence and R based on GPS receiver-reported standard deviation, our filter reduces GPS root-mean-squared error by 23% in comparison to raw GPS, with 15% from only adapting R.

/pdf/adaptive-kalman-filtering-methods-for-low-cost-gps-ins-4vt1rc4irg.pdf

Adaptive Kalman Filtering Methods for Low-Cost GPS/INS Localization for Autonomous Vehicles

A Cascaded Approach for Quadrotor's Attitude Estimation

Navigation technology plays an important role in the designing of advanced robot. An advanced robot navigation system based on GPS/INS is modeled in this paper. According to the model, the causes of the errors in measurement equation are analyzed, concluding that HDOP (Horizontal Dilution of Precision) and VDOP (Vertical Dilution of Precision) provided by GPS receiver are the crucial factors for the change of measurement noise in the mathematical model. Based on the above conclusion, this paper proposes a novel second order fuzzy self-adaptive filter design. Choosing the differences of location and velocity information provided by GPS receiver and INS device as the inputs, this filter modifies the regulation factor based on the residual sequence statistical information and PDOP (Position Dilution of Precision) provided by GPS receiver to correct the outputs of INS device using fuzzy logic. The experimental results demonstrate that the improved adaptive Kalman filtering algorithm proposed in this paper has a strong adaptability to time-varying measurement noises, which improves precision of the advanced robot navigation.

Min Zhang

Papers

An improved adaptive Kalman filtering algorithm for advanced robot navigation system based on GPS/INS