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I. Introduction: Strategic Changes at the Data Layer under the Critical Infrastructure Legislation

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HONGKE SOLUTIONS] The Effect of Gaussian Noise on Positioning Effect in GNSS Simulation

The Physical Definition and Necessity of Gaussian Noise in GNSS Simulation

In an ideal mathematical model, satellite signals are perfectly modulated BPSK sequences at a specific frequency. However, in the real world, satellite signals arrive at the ground with extremely low power (approximately -130 dBm) and are typically drowned out by thermal noise at the receiver’s front end. GNSS simulators introduce Gaussian noise primarily based on the necessity of the following two factors:

1. Accurate Recreation of the Physical Environment

By adding AWGN and precisely controlling the carrier-to-noise ratio (C/No), the simulator bridges the gap between “digital simulation” and “physical RF.”

2. The “Pressure Chamber” in the Receiver Algorithm

When no noise is added, the test evaluates the receiver’s “logical correctness” (code logic); when noise is added, the test evaluates the receiver’s “signal processing performance” (sensitivity, tracking accuracy, and loop bandwidth design) under strong noise interference.

Experimental Analysis: Nonlinear Effects of Gaussian Noise Under Two Special Operating Conditions

In actual testing, there is a complex nonlinear relationship between noise and localization performance, which is primarily evident in the following two extreme scenarios.

Special Case 1: Without Gaussian noise testing, the positioning performance is actually worse.

At standard signal power, with the simulator noise turned off, the receiver achieves a higher signal-to-noise ratio, but the positioning performance isConvergence is extremely slow (500 s), there is a clearSystematic error (altitude error of up to 10 m), with only the trajectory appearing extremely smooth.

GNSS 模擬器未加高斯噪聲時的衛星 C/N0 信噪比觀測界面 (48-51 dBc)
GNSS 模擬器未加高斯噪聲時的定位偏差曲線：高度誤差達10m且收斂極慢

Analysis of the Reasons Why Physical Limits Are the Dominant Factor:

1. The “deadlock” effect of the Kalman filter (KF)

KF relies on the observed noise covariance matrix (R) and the covariance matrix of the prediction errors (P) Calculate the Kalman gain (K). When the input signal is completely noise-free, the residuals of the observed values are extremely small or even zero, causing the filter to assume that the system has reached a perfect state. As a result, it excessively reduces the gain, rejects new observation updates, and ultimately becomes insensitive to system bias, significantly prolonging the convergence time.

2. “Dead Zone” and Quantization Error in Relays

A moderate amount of noise acts as dithering in signal processing, and through statistical averaging, the resolution can be improved beyond the quantization bit. Without noise, minute system errors (such as slight timing discrepancies between the simulator and the receiver) would fall within the phase detector’s “dead zone” and remain uncorrected, thereby accumulating as a fixed positional error.

Special Case 2: In low-power environments, the addition of noise causes positioning errors to increase.

When simulating obstructions or indoor environments (with an additional 30 dB attenuation applied externally, reducing the output power to approximately -140 dBm), the addition of Gaussian noise causes a significant drop in the signal-to-noise ratio, resulting in azimuth and elevation errors of up to 3 m, altitude errors of up to 5 m, and severe jitter. If the power is reduced further, it may even cause the receiver to lose lock.

GNSS 模擬器添加高斯噪聲後的衛星 C/N0 信噪比觀測界面 (24-29 dBc)
GNSS 模擬器添加高斯噪聲後的定位偏差曲線：經緯高誤差保持在1m內快速收斂

Analysis of the Reasons Why Physical Limits Are the Dominant Factor:

1. Fall below the detection threshold

When the signal itself is extremely weak, the superimposed Gaussian noise directly raises the noise floor, causing the C/No to fall below the receiver’s minimum detection signal-to-noise ratio, and the correlation peak cannot stand out from the noise.

2. Periodic Jumps in the Phase-Locked Loop (PLL)

At low carrier-to-noise ratios, the variance in phase jitter caused by Gaussian noise exceeds the linear tracking range of the phase detector, resulting in frequent cycle slips that render the carrier phase measurements completely unusable.

Comprehensive Comparison Matrix of the Effects of Gaussian Noise

To visually demonstrate the impact of Gaussian noise under different operating conditions, the overall performance under these conditions is summarized as follows:

GNSS 模擬器高斯噪聲對比矩陣：信號功率、C/N0與定位表現核心機制

Deste Practical Guide: How to Scientifically Configure GNSS Simulation Noise?

When conducting test projects using Tesight GNSS simulators (such as the Skydel engine), it is recommended to follow the "tiered testing" principle:

1. Algorithm Verification Level (Logic Verification)

  • Settings: Turn off Gaussian noise.

  • goal: Check whether the code logic, ephemeris calculations, and coordinate system conversions are correct, focusing on whether the position can be calculated.

2. Performance Benchmark

  • Settings: Enable Gaussian noise and calibrate C/No to the standard value (recommended C/No = 44 dB-Hz, which corresponds to -174 dBm/Hz in the Skydel interface).

  • goal: Most closely simulates real-world outdoor conditions, using RMS, CEP, and TTFF as acceptance criteria for receiver performance.

  • Compliance Notes: In standardized tests such as GB/T-45086.1, a direct connection using RF cable is typically used. Unless otherwise specified in the standard, Gaussian noise is not enabled to prevent the superimposed noise power spectral density from altering the total power at the antenna port and interfering with the accuracy of the power meter measurements.

3. Stress Testing

  • Settings: Keep the noise floor constant while reducing the signal power, or increase the noise density.

  • goal: Plot the C/No versus positioning error curve to determine the sensitivity threshold at which the receiver completely loses lock.

Frequently Asked Questions

Q1: Why does enabling Gaussian noise at standard power result in faster localization convergence than when noise is disabled?

A1: Modern GNSS receivers rely on Kalman filters for state estimation. A completely noise-free signal would cause the filter residuals to approach zero, leading to a gain “deadlock” and preventing the timely correction of initial errors; the dithering effect provided by an appropriate amount of noise helps the Kalman filter continuously update its state, thereby significantly reducing the convergence time.

Q2: When conducting conducted emission tests in accordance with national automotive standards (such as GB/T-45086.1), is it necessary to enable the simulator’s Gaussian noise?

A2:It is generally not recommended to enable this feature. National standard test requirements call for precise control of the signal power reaching the receiver antenna port. If the simulator’s Gaussian noise is enabled, the superposition of the noise power spectral density will alter the total power at the port, affecting the accuracy of the power meter and the test results.

Want to learn more about how you can continuously optimize your high-precision positioning devices and provide a rigorous, repeatable simulation environment using Deste's full-stack GNSS testing solutions? Visit us nowGNSS Main PageLearn more.

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