Combined Navigation and Tracking with Applications to Low Earth Orbit Satellites ^†

Abstract

Low Earth Orbit (LEO) satellites complement classic GNSS by offering stronger signals, improved visibility, and system redundancy. Typical high speeds in LEO orbits generate rapid variations of the receiver-to-satellite geometry, which can improve the convergence of Precise Point Positioning (PPP) algorithms. However, high dynamics also induce strong Doppler rates at the receiver, which make the tracking procedures more difficult. In this paper, a loosely combined navigation and tracking architecture is applied to a Xona PULSAR™ Demonstration Signal in the L-Band such that the dynamic stress perceived by the receiver is mitigated. Other practical aspects of the Xona PULSAR™ receiver will be also discussed.

1. Introduction

Xona’s PULSAR™ constellation is a modern Low Earth Orbit (LEO) navigation system, which can provide several enhancements to legacy GNSS. Being closer to Earth, LEO satellites can broadcast stronger signals with better immunity to interference. The fast motion across the sky typical of LEO orbits (quick geometry change) gives much in the way of rapid convergence for Precise Point Positioning (PPP) as well favorable characteristics for multipath because signals change over shorter timescales. Another important aspect is related to security. New LEO signals are not bound by legacy, so there can be the inclusion of native encryption and data authentication [1,2,3,4,5].

When completed, the Xona LEO space segment will include about 260 satellites, with an average of 10–20 satellites in view, up to 170× stronger signals, and cm level target positioning accuracy. Finally, a commercial LEO layer can add capability and evolve quickly—on a 5-year timescale—to keep up with the pace of commercial demand. All these aspects are illustrated in Figure 1.

Combined navigation and tracking refers to a class of algorithms, where signal tracking and the navigation solution are jointly estimated—usually by a single Kalman filter [6]. When the dumped values (Is and Qs) and the Numerically Controlled Oscillator (NCO) commands are directly accessed by the navigation filter, the resulting structure is known as vector tracking and offers advantages in weak-signal, high-dynamics, and jamming scenarios [7]. Intermediate solutions between scalar and vector tracking retain all or part of the original control loops and inject deep aiding information such that outer feedback is created [8]. These structures present a cascaded configuration of control loops and Kalman filter, and their performances are expected to be sub-optimal with respect to a fully vectorized implementation [9]. Modular design and simplicity are the primary advantages of this kind of loop aiding—especially when a legacy scalar implementation is already available [10]. Inertial Navigation Systems (INSs) can be integrated with essentially any form of vector tracking or loop aiding [7].

This paper proposes a loosely combined navigation and tracking architecture to mitigate the effects of LEO orbits, which are perceived by the receiver tracking loops as high-dynamic stress. The legacy code and carrier control loops are retained, and deep aiding is realized through code-phase and frequency predictions as produced by the navigation engine.

Observable predictions are derived from the receiver-to-satellite relative kinematics, and LEO orbits must be accurately estimated before loop aiding can start. To solve this “chicken-and-egg” situation, LEO broadcast ephemeris should be either uploaded to the receiver at startup or downloaded from the navigation message while temporarily tracking and decoding in unaided mode. Both these solutions are valid and applicable.

A Xona PULSAR™ signal in the L-Band was used to simulate the LEO constellation. Special firmware was then developed to support the reception of this signal on the STMicroelectronics TeseoV multi-band GNSS chipset. Regular GPS L1 C/A signals were also simulated and synchronized with LEO. As part of the platform validation process, single-point solutions for Xona stand-alone and Xona + GPS have been generated. Other practical aspects of the Xona PULSAR™ receiver are also discussed, including assistance during acquisition, handling of navigation messages for large LEO constellations, and the usage of the LEO carrier phase with classic PPP algorithms.

The rest of the paper is organized as follows. Section 2 reviews the proposed deep aiding architecture—originally introduced in [10]—and adapts it for LEO combined navigation and tracking. Section 3 illustrates the Xona PULSAR™ demonstration platform, including aspects that showed up during software development. Section 4 contains the simulation results with the two-fold objective of validating the deep aiding concept and presenting the positioning performance of the TeseoV Xona receiver. The simulations are all open sky; however, the focus is kept on difficult land scenarios for automotive applications, where the proposed architecture is expected to provide most of the benefits in terms of increased availability and robustness. Finally, Section 5 concludes the paper.

2. Deep Aiding Architecture

The proposed architecture is illustrated in Figure 2. It combines navigation and tracking by feeding back observable predictions to the tracking control loops such that code and carrier NCO registers are steered according to the navigation solution [10]. For the LEO case, part of the dynamic stress originates from the satellites’ motion. INS/GNSS integration is reported in the block diagram for completeness; however, in the scope of this paper, INS is not strictly required and, therefore, will not be developed further. The navigation solution is essential for prediction calculation and can be supplied either by the embedded positioning engine or, alternatively, from an external host through proprietary sentences over UART. Both these configurations are supported by the TeseoV platform and reported in Figure 2.

2.1. Line of Sight (LOS) Predictions

At the receiver epoch $t_{REF}$, let ${\mathbf{x}}_m^p, {\dot{\mathbf{x}}}_m^p, {\ddot{\mathbf{x}}}_m^p$ be the relative ECEF position, velocity, and acceleration between the satellite p (at epoch of transmission) and the receiver m. The geometric range, range rate, and acceleration can be derived as follows, where ${\mathbf{e}}_m^p\triangleq {\mathbf{x}}_m^p/{\rho }_m^p$ is the line of sight (LOS) unit column vector [10,11].

$${\rho }_m^p=‖{\mathit{x}}_m^p‖ {\dot{\rho }}_m^p={\left({\mathbf{e}}_m^p\right)}^T{\dot{\mathbf{x}}}_m^p {\ddot{\rho }}_m^p={\left({\mathbf{e}}_m^p\right)}^T{\ddot{\mathbf{x}}}_m^p+{\displaystyle \frac{{‖{\dot{\mathbf{x}}}_m^p‖}^2-{\left({\dot{\rho }}_m^p\right)}^2}{{\rho }_m^p}}$$

(1)

Range rate and acceleration are converted into predictions and expressed in frequency units by dividing by carrier wavelength ${\lambda }^p$ and adding the receiver clock drift and drift rate: ${\dot{dt}}_m$ and ${\ddot{dt}}_m$, respectively. Code predictions are obtained from the range, correcting for both satellite and receiver clock biases, $d{t}^p$ and $d{t}_m$, and ionospheric and tropospheric errors: $I^p$ and $T^p$ [10].

$$\begin{array}{c}{\tau }_m^p\left(t_{REF}\right)={\rho }_m^p+cd{t}_m-cd{t}^p+I^p+T^p\\ F_m^p\left(t_{REF}\right)={\displaystyle \frac{1}{{\lambda }^p}}\left({\dot{\rho }}_m^p-c{\dot{dt}}_m\right) {\dot{F}}_m^p\left(t_{REF}\right)={\displaystyle \frac{1}{{\lambda }^p}}\left({\ddot{\rho }}_m^p-c{\ddot{dt}}_m\right)\end{array}$$

(2)

Typical Xona satellite profiles for frequency rates as from (1) and the corresponding elevations and frequencies are plotted in Figure 3.

The accuracy at which LOS geometry can be calculated is not sufficient to produce reliable predictions for the carrier phase. However, the aiding applied to frequency can indirectly benefit the estimation of the carrier phase through classic Frequency Locked Loop (FLL)-aided Phase Lock Loop (PLL) feedback or other equivalent open-loop schemes. For this reason, a general improvement is expected in the quality of the carrier phase observables and the ambiguity-fixing capability.

2.2. Carrier and Code Loops Aiding

The proposed loop-aiding model is based on a classic second-order FLL and an early-minus-late FLL-aided Delay Locked Loop (DLL) (Figure 4). The predicted quantities in (2) must be propagated at the epoch of loop update $t_U$ such that prediction errors can be obtained by the difference from the tracked values at the previous epoch. The state variables of the FLL are the estimated frequency $F_{NCO}$ and frequency rate $a$, whereas ${\tau }_R$ is the replica code phase. For small time steps ($\left|t_U-t_{REF}\right|<1 \mathrm{s}$, typical), a constant frequency rate can be assumed, resulting in the following expressions for the prediction errors:

$$\begin{array}{c}\dot{{\delta F}_m^p}={\dot{F}}_m^p\left(t_{REF}\right)-a\\ \delta F_m^p=F_m^p\left(t_{REF}\right)+{\dot{F}}_m^p\left(t_{REF}\right)\left(t_U-t_{REF}\right)-F_{NCO}\\ {\delta \tau }_m^p={\tau }_m^p\left(t_{REF}\right)-F_m^p\left(t_{REF}\right){\displaystyle \frac{r^p}{f^p}}\left(t_U-t_{REF}\right)-{\tau }_R\end{array}$$

(3)

The errors in (3) are smoothed by coefficients α < 1. The scaled frequency and code-phase errors are injected in the loops as “innovations” on top of discriminator outputs. The scaled frequency rate error is simply combined with the $a$ state variable.

An example of frequency and frequency rate prediction errors for a static receiver and CN0 ramp scenario are plotted and shown in Figure 5. Errors increase due to thermal noise as the CN0 is ramped (starting from 43 dBHz down to 15 dBHz) until signals are dismissed after ~550 s. Note that the CN0 of SV X103 is kept constant (at 43 dB Hz) for reference.

3. Xona PULSAR™ Demonstration Platform

The Xona PULSAR™ hardware demonstration platform (Figure 6) is based on the STMicroelectronics STA8135GA multi-band GNSS chipset and dedicated firmware. The STA8135GA is an automotive-grade Multi-Chip Module (MCM), combining in a single package one STA8100GA (TeseoV receiver with embedded RF tuner) and one STA5635A (additional RF tuner) [12]. The frequency plan was configured to receive the Xona demonstration satellite signal whose center frequency is 1260 MHz, referred to here as XL together with the legacy GNSS L1/L5 bands, such that MEO dual-band multi-constellation (GPS/Galileo/BeiDou) plus LEO Xona XL at the same time could be supported.

To enable integrated INS/GNSS positioning, the STA8135GA is connected through an I2C or SPI interface to the ASM330LHH module. The ASM330LHH is a system-in package featuring a 3D digital accelerometer and a 3D digital gyroscope designed to address automotive applications. The use of inertial sensors combined with loop aiding for MEO was introduced in [10].

The Xona observables are generated in a proprietary format based on legacy NMEA or RTCM3 MSM7 templates. External assistance commands have been extended to support the injection of Xona orbital parameters. For testing purposes, the receiver firmware can be configured also in autonomous Xona-only mode.

The TeseoV name identifies a family of mature GNSS receiver technologies and components from STMicroelectronics that evolved through several generations over the past few decades. Firmware development, after a quick check for frequency plan feasibility, took most effort in adding Xona support to this legacy platform. In general, the existing and consolidated software architecture could be adapted to include LEO. Few outstanding algorithms required a deeper review.

3.1. Approximate LEO Orbit Calculation

To be effective, aiding should be applied at every loop closure, typically with a period of 80–200 ms. This rate of calculation multiplied by the number of tracked signals represents a considerable amount of processing when satellite orbits are derived from Keplerian parameters. To reduce this load, the full ephemeris algorithm is computed only on a sparse time grid, roughly every 30 to 60 s. At these epochs ($t_0$ in Figure 7), the ephemeris errors are small and only determined by the accuracy of the orbital model.

For MEO, a simple constant acceleration hypothesis (4) can propagate the coordinates $x_0,v_0,a_0$ from $t_0$ to $t_{REF}$, efficiently and with good accuracy.

$$\begin{array}{c}{\mathit{x}}^p\left(t_{REF}\right)={\mathit{x}}^p\left(t_0\right)+{\dot{\mathit{x}}}^p\left(t_0\right)∆t+{\displaystyle \frac{1}{2}}{\ddot{\mathit{x}}}^p\left(t_0\right)∆t^2\\ ∆t=\left(t_{REF}-t_0\right)\end{array}$$

(4)

For LEO, due to higher orbit dynamics, satellite coordinates had to be integrated with steps of 3–5 s. At epochs $t_1\dots t_k$, accelerations were recomputed as from (5) (see [13] for notation). The constant acceleration model (4) was still used, but only for the remaining small $\Delta t$ until $t_{REF}$. This combined method was a good trade-off between accuracy and the computational load of a standard Keplerian model (like that employed in GPS).

$$\begin{array}{c}\ddot{x}=-{\displaystyle \frac{\mu x}{r^3}}+F\left(1-5{\left(z/r\right)}^2\right)\left(x/r\right)+2\dot{y}{\dot{\mathrm{\Omega }}}_e+x{\dot{\mathrm{\Omega }}}_e^2\\ \ddot{y}=-{\displaystyle \frac{\mu y}{r^3}}+F\left(1-5{\left(z/r\right)}^2\right)\left(y/r\right)-2\dot{x}{\dot{\mathrm{\Omega }}}_e+y{\dot{\mathrm{\Omega }}}_e^2\\ \ddot{z}=-{\displaystyle \frac{\mu z}{r^3}}+F\left(3-5{\left(z/r\right)}^2\right)\left(z/r\right)\end{array}$$

(5)

where $\mathrm{F}=-\left(3/2\right)J_2\left(\mu /r^2\right){\left(R_E/r\right)}^2$, $r=\sqrt{x^2+y^2+z^2}$, and $J_2,\mu ,R_E,{\dot{\mathrm{\Omega }}}_e$ are the WGS-84 parameters [13].

3.2. XL Signal Tracking Startup

The Xona XL is a modern dual-component signal (data + pilot) designed for the L-Band, with the carrier at 1260 MHz, a chip rate of 5Mcps, and a data rate of 500bps [1,3]. For the scenarios under test, Xona Space Systems provided both the simulated PULSAR™ demonstration signals and the full satellite orbit parameters. Simulated scenarios were generated using Safran’s GSG-8 simulator and Skydel simulation engine.

Under nominal steady-state conditions, the FLL is configured to track the pilot component with a 4-quadrant atan2() discriminator, a coherent period of 20 ms, and the number of incoherent accumulations in the range of 4–10 for a total dwell time of 80–200 ms. High dwell times are selected at low signal strengths (CN0) to guarantee good sensitivity. To reach this condition, a signal candidate must pass through a sequence of processing to reduce its code-phase and frequency uncertainties. This procedure is sometimes referred to as handover to emphasize the transfer of the signal candidate from acquisition to tracking specific hardware.

In cold start conditions, i.e., without any prior assistance information, the Xona XL signal is acquired using a dedicated time-domain correlation engine over a frequency range of 60 kHz. The acquired correlation peak is then passed to a tracking channel, which performs a code-phase and frequency grid refinement. Initial tracking is performed with a wide bandwidth, while at the same time, a pilot secondary code phase is acquired [14]. Finally, secondary code wipe-off is applied, tracking bandwidth is reduced, and additional correlation resources are allocated to the data component for navigation message decoding.

After handover completion, loop aiding can start. Orbit parameters and receiver coordinates are needed to compute LOS quantities as from (1). Satellite ephemerides are downloaded and extracted regularly from the decoded navigation bits, and, alternatively, they can be obtained offline and injected into the receiver through serial links.

In our demonstration receiver, all the described procedures did not change very much between MEO and LEO, especially when MEO modernized dual-component signals are compared. Clearly, LEO orbit dynamics had in proportion a bigger effect on the operation of the control loops and increased the signal search space.

4. Experimental Results

To validate the platform, the Xona team defined an XL open-sky simulator scenario with a constant CN0 of 43 dB Hz on all satellites (Figure 3b,c). The complete Xona ephemeris (orbital parameters) was simulated. For simplicity, both ionospheric and tropospheric errors were set to zero. GPS L1 C/A signals with the same CN0 were also simulated and synchronized with the Xona signal to serve as a reference.

Single-point position (SPP) and PPP algorithms were applied to verify the consistency of the Xona observables, for both the pseudo-range and carrier phase. The positioning results with loop assistance switched off are illustrated in Figure 8. The SPP horizontal error was obtained by a least-square, pseudo-range-based algorithm, whereas the PPP was a classic, single-band algorithm with float solution.

4.1. Loop-Aiding Results: CN0 Ramp

The same sky map of the reference scenario of Figure 3 was re-used to validate the loop-aiding concept. A decreasing CN0 ramp was applied to a few Xona satellites to simulate signal progressive obscuration. The reported CN0 at the receiver was plotted for the regular, unaided loops configuration and then compared with loop aiding. As expected, loop aiding improved the tracking sensitivity at low CN0, whereas the unaided configuration lost tracking (Figure 9a). Note that only the SV indicated in the legend of Figure 9b was aided. The number of aided channels was chosen to represent an average situation, where few satellites are obscured but the estimated receiver coordinates are still good enough to compute accurate predictions.

It was not straightforward to map the benefits of loop aiding from ranging to positioning domains. For simplicity, the simulated scenarios were short (~13 min) and open sky, with only a CN0 ramp applied. The tests were performed in cold-start conditions so that small random differences in the acquisition sequence could have minor effects on the results. With these assumptions, position and velocity Cumulative Distribution Functions (CDFs) were compared. The position results are plotted in Figure 9c and show an improvement in the positioning error when aiding is switched on. Velocity was basically unchanged, with marginal benefit on outliers.

4.2. Comparing LEO vs. Receiver Dynamics

The focus of this paper is on LEO dynamics; however, we found it of interest to compare the reference static case with a simple dynamic scenario: circle, duration = 500 s, radius = 50 m, constant speed = 50 km/h. Figure 10a illustrates the frequency rate for this circle scenario, where the user dynamic is visible like a perturbation on top of the LEO profile. The carrier phase jerk induced by the user motion and LEO orbits are shown in Figure 10b and Figure 10c, respectively.

5. Conclusions

A hardware Xona PULSAR™ receiver for the XL signal based on the STMicroelectronics STA815GA (TeseoV) chipset has been demonstrated. Autonomous Xona-only acquisition and data download and navigation were verified to prove practical system redundancy in case of MEO GNSS outage, with Xona+GNSS scenarios also shown to be effective. This shows not just PULSAR compatibility with existing GNSS but also interoperability. Furthermore, PULSAR LEO signals were shown to be effective in achieving high accuracy, with rapid convergence of Precise Point Positioning (PPP), achieving 11 cm, 68th percentile.

Combined navigation and tracking in the form of prediction aiding can be effective in reducing the stress on the receiver control loops induced by LEO high orbit dynamics. The proposed algorithms improved the tracking sensitivity and availability at low CN0. Observables quality and, eventually, positioning accuracy are also expected to benefit from loop aiding, especially under difficult signal conditions and automotive land scenarios.