Kalman Filter Design Strategies for Code Tracking Loop in Ultra-Tight GPS/INS/PL Integration

The integrated GPS/INS/PL system, with complementary characteristics to overcome the shortcomings of each individual part, can be achieved at different levels, namely loosely, tightly or ultra-tightly coupled. The next generation of integrated GPS/INS/PL navigation systems will be based on the ultra-tight coupled method. Ultratight coupled system offers numerous advantages, such as improved high-dynamic, anti-jamming and interference performance, due to its ability to maintain a narrow tracking loop bandwidth by employing unique integrated Kalman filter techniques. Under exposure to high dynamics, jamming or interference, the code tracking loop can sustain tracking with aiding Doppler derived from the ultra-tightly coupled Kalman filter. Hence, the code phase errors, i.e. the transmission time measeurement errors and therefore the pseudorange errors, will be correlated with the inaccuracy of the velocity estimates. If these correlations are not considered in the design of the Kalman filter, it is likely to result in the instability of code tracking loop and even loss of lock. This paper focuses on the Kalman filter design strategies for the code tracking loop considering the correlations between the pseudorange and velocity errors. Initially, the error model of code tracking loop was investigated to derive the relationship between the code tracking loop errors, i.e. pseudorange errors, and the estimated velocity errors. The performance of the ultra-tightly integrated system was evaluated via comprehensive simulation tests comparing the solutions with the correlations taken into account and without. Experimental test results indicate that the stability of the integrated Kalman filter was improved remarkably based on this correlation analysis. Hence, the optimally estimated velocity could be derived to enhance the code tracking performance, even under high dynamics, jamming or interference by generating more accurate pseudorange measurements. INTRODUCTION As an independent means of navigation, Global Positioning System (GPS) can provide position and velocity information via various measurements such as code and carrier based ranges and rates. While the precision of the information ascertained is independent of time, the performance becomes unreliable when the system is exposed to high dynamics, interference from communication equipment and jamming. Inertial Navigation Systems (INS) can be used to greatly enhance the navigation reliability under such conditions. INSs are completely autonomous and provide good short-term accuracy. Its usage as a stand-alone navigation system is limited due to the time-dependent growth of the inertial sensor biases. Additionally, pseudolites (ground based transmitters that can transmit GPS like signals) can also be implemented to improve the measurement geometry. Pseudolites have the advantages of high signal to noise ratios (SNR) and their location can be precisely known. However, pseudolites also suffer from many of the same weaknesses as GPS such as signal blockages and interference. Because of the aforementioned complementary characteristics, GPS, INS and pseudolites (PL) are commonly augmented to overcome the shortcomings of each individual system. System integration can be achieved at 3 different levels of coupling: loose, tight and ultra-tight. Loose and tight integration systems have been in existence for more than a decade. Though these two configurations were used in many applications, the main objective is always to improve the robustness of the navigation system. Ultra-tight integration will be the next generation of highly reliable and precise navigation systems, because it offers numerous advantages over the loose and tight coupling. Ultra-tight integration offers improved performance under exposure to high dynamics, jamming and interference. Other benefits of ultra-tight integration include minimization of the receiver clock error and it permits the effective use of a low cost IMU to maintain a narrow tracking loop bandwidth via mitigation of the system dynamics using the integrated Kalman filter. The raw GPS pseudorange measurement is obtained from the code tracking loop, in which the I and Q measurements from the correlators drive the loop filter to generate code phase errors to synchronise the local signal with the incoming signal. These code phase errors correspond to the timing measurement errors and hence the pseudorange measurement errors. In ultra-tight integration systems, the Doppler is derived from the velocity estimates of the integrated Kalman filter and is used to maintain tracking in the code tracking loop, even under high dynamics or heavy jamming. Therefore, the code tracking loop errors, i.e. code phase offset errors, transmitted time measurement errors and the pseudorange measurement errors will be correlated with the errors in the estimated velocity. If these correlations are not accounted for in the Kalman integration filter, they are likely to result in system instability and loss of lock. The purpose of this study is to determine optimal ultratight integration Kalman filter design strategies for the code tracking loop in consideration of the correlations between the inaccuracy of the estimated velocity and pseudorange measurement errors. Initially, based on a one-order Markov stochastic error model, the code tracking loop error model is investigated to derive the relation between pseudorange errors and the estimated velocity errors by theoretical analysis. Because, the errors of velocity and position are coupled, the relation between pseudorange errors and position errors has also been deduced. Secondly, Matlab based simulation tests are developed which include generating the flight maneuvers with high dynamics, simulating the GPS IF signal with relevant doppler information, generating the IMU data with gyro and accelerometer biases and drifts and implementation of the Kalman filter. The correlations of the estimated velocity errors and the pseudorange errors are taken into account by adding code loop errors as state variables of the Kalman filter. The raw data has been processed by a Matlab-based GPS receiver and Strapdown Inertial Navigation system (SdINS). Finally, the impacts of the correlations of the pseudorange measurement errors and estimated errors on the ultra-tight integration performance are analyzed through performance comparisons of when the correlations are ignored versus when they considered in the design of ultra-tight integration Kalman filter. Experimental test results indicate that elimination of these correlations improve the accuracy of the estimated velocity; minimize the code phase errors, thus avoiding the code tracking losing lock in severe dynamic application and deliver more accurate pseudorange measurements. Based on the analysis of the correlations, the integrated Kalman filter could be developed to embed itself in the GPS tracking loop and thus improve the stability and quality with respect to intentional or unintentional interference and provide a more precise navigation solution, even when using a low cost IMU. KALMAN FILTER-BASED STRUCTURE FOR ULTRA-TIGHT INTEGRATION An ultra-tight system derives its advantages primarily from the INS-derived Doppler feedback to the receiver tracking loops. This Doppler closely reflects frequency shift on the incoming GPS signals due to the relative motion between satellite and receiver, when integrated with the tracking loop removes the dynamics of the GPS signals, thereby facilitating a significant reduction in the tracking bandwidth to provide the more accurate navigation solutions. To achieve this purpose, many scenarios were developed as shown in Figure 1[1], where the ultra-tight integration blending algorithms combines either the I and Q samples from the GPS tracking loop, the pseudorange or Doppler measurement with the INS navigation parameters to provide the optimal Doppler estimate. Figure 1. GPS/INS System with Ultra-Tight Integration [1] In this paper, a practicable linear Kalman filter was developed to implement the GPS-Inertial Blending Algorithms. The nonlinear characteristics of the I & Q measurements could result in the divergence of the linear Kalman filter, thereby the pseudorange is feasible to be chosen as the measurement. The Kalman filter-based configuration for ultra-tight integration is given in Figure 2. Figure 2. Kalman Filter-Based Configuration for Ultra-Tight Integration Because of the intensive computations, the update rate of Doppler estimates derived from the Kalman filter typically is 1-10Hz. To synchronise the 1KHz-tracking loop, a federated Kalman filter approach with high dataoutput rate or the method to interpolate the lower Doppler rate to the required rate could be employed [2],[3]. For simplifying the system structure, here the interpolator was chosen. Basically GPS tracking loops are the accurate measuring systems of time and frequency, i.e. Time of Arrival (TOA) from satellite to the receiver and Doppler signal. In GPS receiver, the code tracking loop, i.e. Delay Lock Loop (DLL) generates the measurements of TOA. Furthermore the pseudorange is derived from TOA measurements. In the ultra-tight integration, the estimated Doppler aided DLL is shown in Figure 3. Because of the TOA, the replica code is misaligned, the early and late codes are unequal by an amount that is proportional to the TOA. The code tracking loop senses and measures this difference to provide the time measurements and then pseudoranges.