Mastering TDoA-Based Geolocation with LoRaWAN and Fine Timestamping

“How accurate can LoRaWAN geolocation really get without GPS?”

When we think of geolocation, the first technology that usually comes to mind is GPS. While GPS is known for its accuracy, it comes at the cost of high-power consumption. In contrast, LoRaWAN offers a GPS-free geolocation solution that is more suitable for low-power applications. But how precise can LoRaWAN be? The answer lies in a technique called Time Difference of Arrival (TDoA), and it can be further enhanced by using a feature called Fine Timestamping.

Welcome to the third article of our LoRaWAN Geolocation series! This article goes beyond the basics to explore how TDoA-based geolocation works, introduces the concept of Fine Timestamping, and provides a step-by-step guide on implementing this advanced geolocation method. Let’s dive in and see how TDoA and Fine Timestamping can bring GPS-level precision to LoRaWAN geolocation!

The Science Behind TDoA-Based Geolocation: How it Works

?

Understanding TDoA: Theory and Mathematical Foundation

Time Difference of Arrival (TDoA) is a powerful method that uses the time it takes for a signal to reach multiple LoRaWAN gateways to estimate the position of a transmitting device. By measuring the Time of Arrival (ToA) at each gateway and calculating the time differences between these measurements, we can create hyperbolic equations to pinpoint the device’s location.

Let’s break down the process step-by-step:

?

Signal Transmission and Reception

When a LoRaWAN-enabled device transmits a signal, it is received by multiple gateways within range. The signal travels through the air at the speed of light, and each gateway records the exact time it receives the signal, known as the Time of Arrival (ToA).

The ToA values are recorded with nanosecond precision, thanks to Fine Timestamping, which we’ll discuss in more detail later. The precise ToA values are crucial for accurately determining the Time Difference of Arrival (TDoA).

?

Calculating Time Differences

Once the ToA values are recorded at each gateway, the Network Server calculates the Time Difference of Arrival (TDoA) between every pair of gateways. For example, if Gateway A receives the signal at Time 1 and Gateway B receives it at Time 2, the TDoA value is given by:

This TDoA value tells us how much longer the signal took to reach Gateway B compared to Gateway A. From this information, we can derive the relative distances between the device and each gateway.

?

Setting Up Hyperbolic Equations

Using the TDoA values, we set up a series of hyperbolic equations. Each TDoA value corresponds to a hyperbola on a 2D plane (or a hyperboloid in 3D space) that represents all possible locations of the device.

The equation for a hyperbola based on TDoA is:

Where:

• (x, y) are the unknown coordinates of the device.
• (xA, yA) & (xB, yB) are the known coordinates of the gateways (Gateway A & Gateway B respectively).
• c is the speed of light.

The left-hand side of the equation represents the difference in distances from the device to each gateway, and the right-hand side represents the product of the TDoA and the speed of light.

?

Finding the Intersection Points

The network server solves these hyperbolic equations to find the intersection point, which represents the estimated location of the device. The more gateways that receive the signal, the more hyperbolas we can form, and the more precise the solution will be.

Typically, at least three gateways are required for 2D positioning (latitude and longitude), and four or more are needed for 3D positioning (latitude, longitude, and altitude).

Pro Tip: Errors in TDoA calculations can arise due to factors such as clock drift, multipath effects, and environmental interference. These factors can lead to hyperbolas that don’t intersect perfectly, creating a region of uncertainty around the estimated position. Using more gateways helps reduce this uncertainty and improves accuracy.

Step-by-Step Implementation of TDoA-Based Geolocation

Implementing TDoA-based geolocation involves several steps, each with its own set of challenges and considerations. Let’s go through each step in detail:

?

Step 1: Time Synchronization Between Gateways

“Why do the gateways need to be synchronized?”

TDoA relies on measuring extremely small differences in time—often in the range of nanoseconds. Even a slight mismatch in gateway clocks can lead to significant errors in position estimation. There are two primary methods to ensure precise synchronization:

Using GPS Modules for Time Synchronization:

• The most accurate and reliable way to synchronize gateways is by equipping each with a high precision GPS module, which provides nanosecond-level accuracy. GPS synchronization is essential for outdoor environments, where clear line-of-sight to satellites can be maintained.
• GPS-based synchronization ensures that all gateways operate on a common, highly precise time reference, which is critical for minimizing TDoA errors. This involves attaching a GPS module to each gateway to provide a highly accurate and consistent time reference that synchronizes all gateways down to the nanosecond.
• This is the most common method for achieving time synchronization, as GPS modules are readily available and easy to integrate with LoRa gateways.

?

Using a Local High-Precision NTP Master Clock:

• If GPS is not feasible—such as in indoor environments where line-of-sight to satellites is restricted—a local high-precision NTP Master Clock can be used instead of relying on an internet-based NTP server. The local NTP server should ideally have a Pulse Per Second (PPS) signal source, providing greater accuracy by reducing time variation from network delays.
• A dedicated local NTP server minimizes round-trip latency and network jitter that would otherwise degrade synchronization accuracy if using a public NTP server. However, even with this setup, accuracy may still fall short of GPS-level nanosecond precision and may introduce timing variations on the order of microseconds to milliseconds.
• Important Note: When using a local NTP server, it is advisable to employ out-of-band messaging to factor out transmission delays, as even minimal discrepancies can impact TDoA calculations.

?

Custom Time Synchronization with PPS Signal Access:

• Another alternative for environments where GPS and high-precision NTP servers are not viable is to use a custom time synchronization approach. In this setup, each gateway is provided with a Pulse Per Second (PPS) signal, ideally synced to a high-precision clock, even if not directly linked to GPS.
• The PPS signal provides an accurate timing reference, allowing for precise alignment across gateways. Out-of-band messaging could further enhance this setup, enabling gateways to synchronize based on the PPS signal while minimizing the need for network-based timing adjustments.

?

Important Consideration:

The synchronization method used should match the accuracy required by the application. For the highest accuracy in TDoA calculations, GPS-based synchronization remains the gold standard. When using NTP or custom PPS methods, consider implementing robust error-correction techniques, such as Kalman filters, to compensate for timing discrepancies where possible.

Step 2: Collecting and Preprocessing ToA Data

Once the Gateways are synchronized, it’s time to collect and process Time of Arrival (ToA) data-

Record ToA Values at Each Gateway:

• When the device transmits a signal, each gateway records the Time of Arrival (ToA) down to the nanosecond level.
• Send the ToA values to the network server for processing.

Calculate TDoA Values:

• For each pair of gateways that received the signal, calculate the TDoA value:

• Store the calculated TDoA values along with the corresponding gateway pair IDs.

Filter Out Noisy Data:

Apply filtering techniques such as median filtering or Kalman Filtering to remove noisy ToA values that could distort the TDoA calculations.

Pro Tip: To reduce errors, exclude TDoA values from gateways with very low RSSI, as the signal quality may not be sufficient for precise ToA measurement.

Step 3: Constructing and Solving Hyperbolic Equations

Once the TDoA values are calculated, it’s time to set up and solve hyperbolic equations to estimate the device’s position.

Set Up Hyperbolic Equations:

For each pair of gateways, set up a hyperbolic equation representing the possible locations of the transmitter based on the TDoA value:

Where:

• (x, y) is the unknown position of the transmitter.
• (xA, yA) and (xB, yB) are the coordinates of the gateways.
• c is the speed of light.

Linearize the Equations:

Linearize the hyperbolic equations by substituting variables and rearranging terms to simplify them for solving.

Solve Using Least Squares Optimization:

Use a least squares optimization method or a numerical solver like the Gauss-Newton algorithm to solve for (X, Y)

The solution that minimizes the error between the estimated and actual TDoA values is the estimated position of the transmitter.

Step 4: Post-Processing and Refinement

After obtaining the initial position estimate, refine it further using post-processing techniques:

Apply Kalman Filtering:

• Kalman Filtering can help refine the estimated position by considering the previous position, velocity, and acceleration of the device. It’s especially useful for tracking moving devices.

Use Particle Filters:

• Particle Filters maintain a set of potential positions (particles) and update them based on the new TDoA measurements, providing a probabilistic estimate of the position.

Validate Against Known Positions:

• If possible, compare the estimated position with known reference points to validate the accuracy and make necessary adjustments.

Pro Tip: The refinement phase is crucial for minimizing error and ensuring stability in position estimates, especially in dynamic environments.

Testing and Validation: Ensuring TDoA-Based Geolocation Accuracy

Just like with RSSI-based geolocation, testing and validation are crucial to confirm that your TDoA system is working as expected. Here’s how to validate your implementation:

Controlled Testing in Open Spaces:

• Start by testing your system in an open area with minimal interference and obstacles.
• Deploy gateways at known positions and place the transmitter at various known locations.
• Record the ToA values at each gateway and validate the estimated positions against the known locations.

Testing in Real-World Scenarios:

• Deploy your system in the actual environment (e.g., factory, farm, or city area) where it will be used.
• Record data over several days to observe how environmental factors like humidity, temperature, or interference affect the accuracy.

Analyze Error Patterns:

• Calculate the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) to quantify the accuracy of your system.
• Use these metrics to identify areas or conditions that cause high error and apply corrective measures.

Validate Against GNSS (If Possible):

• Use GNSS as a reference to benchmark your TDoA system’s performance. Compare the results and note any deviations.

Pro Tip: For the highest accuracy, ensure that the gateways have clear line-of-sight to the transmitter, and avoid placing them in areas with heavy signal reflections or interference.

Improvement Suggestions for TDoA-Based Geolocation

Increase Gateway Density:

• Deploy more gateways to improve TDoA resolution and reduce error.

Use Higher Sampling Rates:

• Increase the sampling rate for recording ToA values to capture more accurate timing information.

Incorporate Machine Learning Models:

• Use machine learning models to predict and adjust for environmental impacts on ToA measurements.

Combine TDoA with Other Methods:

• Combine TDoA with RSSI or AoA for a hybrid geolocation system that leverages the strengths of each method.

TDoA-Based Geolocation Code Implementation

In this section, we present the complete code for implementing TDoA-based geolocation using LoRaWAN. Each function is designed to handle specific aspects of the system, from time synchronization to solving hyperbolic equations for position estimation. We'll break down the code into distinct segments, making it easier to follow and understand.

The code consists of five main functions:

1. Time Synchronization Check (check_time_sync): Ensures that the gateways are synchronized.
2. TDoA Calculation (calculate_tdoa): Calculates the Time Difference of Arrival between each pair of gateways.
3. Hyperbolic Position Calculation (solve_hyperbolic): Solves the hyperbolic equations to estimate the position.
4. Filtering Function (apply_kalman_filter): Applies a Kalman filter to refine the estimated position.
5. Main Function (main): Orchestrates the process, starting with time synchronization and ending with position estimation.

Let’s go through each function step-by-step.

Time Synchronization Check Function

This function checks if all gateways are synchronized within a specified tolerance. Without proper synchronization, the TDoA values will be inaccurate, leading to significant errors in position estimation.

Input Parameters:

• gateway_times: A dictionary with gateway IDs as keys and their time offsets as values.
• tolerance: The maximum allowable time difference between gateways for them to be considered synchronized.

Output:

Returns True if the maximum time difference between gateways is within the specified tolerance, otherwise returns False.

TDoA Calculation Function

This function calculates the Time Difference of Arrival (TDoA) between each pair of gateways based on the Time of Arrival (ToA) values.

Input Parameter:

• toa_values - A dictionary with gateway IDs as keys and their corresponding Time of Arrival (ToA) values.

Output:

• Returns a dictionary with each pair of gateways as keys and their TDoA values as values.

Hyperbolic Position Calculation Function

This function takes the TDoA values and solves the hyperbolic equations to estimate the position of the transmitting device.

Input Parameters:

• tdoa_values: Dictionary containing TDoA values for each pair of gateways.
• gateway_coords: Dictionary with gateway IDs as keys and their coordinates (x, y) as values.
• speed_of_light: Constant value for the speed of light (default is 3e8 m/s).

Output:

• Returns a tuple representing the estimated (x, y) coordinates of the transmitter.

Filtering Function

This function refines the estimated position using a Kalman filter, which is ideal for tracking moving devices.

?Input Parameters:

• estimated_positions: List of tuples with estimated (x, y) positions over time.
• process_variance: Variance of the process noise.
• measurement_variance: Variance of the measurement noise.

Output:

• Returns a list of smoothed positions after applying the Kalman filter.

Main Function

The main function orchestrates the entire process, from checking time synchronization to estimating the position using TDoA values and applying filtering for refinement.

Steps:

• Step 1: Check if the gateways are synchronized using check_time_sync.
• Step 2: Calculate TDoA values using calculate_tdoa.
• Step 3: Estimate position using hyperbolic equations with solve_hyperbolic.
• Step 4: (Optional) Apply Kalman filtering to refine the estimated positions.

Enhancing TDoA Accuracy with Fine Timestamping

In traditional TDoA-based geolocation, achieving high accuracy depends on precise time synchronization between gateways, usually down to the nanosecond level. This level of precision can be challenging to achieve with conventional timing methods. This is where fine timestamping comes in, significantly improving the geolocation accuracy without adding complexity or power consumption at the device level.

What is Fine Timestamping?

Fine timestamping involves using specialized hardware at the gateways to capture the Time of Arrival (ToA) of a signal with nanosecond resolution. When a LoRaWAN-enabled device sends a data packet, each gateway in range receives the signal and records the exact ToA, allowing the network server to calculate the Time Difference of Arrival (TDoA) between each pair of gateways.

To visualize this, think of a ripple effect. When you throw a stone into a pond, ripples spread out uniformly in all directions. If we place gateways at different locations along the shore, each gateway will experience the ripple at slightly different times based on its distance from the point of origin. Fine timestamping allows us to record these tiny time differences with extreme precision, helping us pinpoint the location of the stone—without needing a GPS module.

?

How Fine Timestamping Works in LoRaWAN

Device Transmission and Gateway Reception:

• A LoRa device transmits a data packet, which is received by multiple gateways in range.
• Each gateway, equipped with fine timestamping hardware, records the ToA down to the nanosecond.

TDoA Calculation:

• The network server collects these ToA values from each gateway and calculates the TDoA between pairs of gateways.
• The resulting TDoA values are used to set up hyperbolic equations that represent the potential location of the device.

Location Estimation:

• Using the TDoA values and the known positions of the gateways, the server estimates the location of the device by solving these hyperbolic equations.

The Fine Timestamp feature is available in advanced gateway processors like the Semtech SX1303, making it a practical solution for achieving precise geolocation without GPS dependency. This not only reduces power consumption at the device level but also lowers deployment costs.

Practical Implementation

Implementing fine timestamping requires gateways that support this feature, such as those using the SX1303 baseband processor. When a data packet is received, each gateway attaches a timestamp in nanoseconds and sends this data to the network and application servers. The cloud server then calculates the device's position based on the timestamps received from multiple gateways.

For applications like tracking delivery trucks, using gateways with fine timestamping means you can monitor the truck's location and environmental data (e.g., temperature) using a single LoRa-enabled device, enhancing the overall system's efficiency and reducing complexity.

Example Use Case: A logistics company could deploy a fleet of trucks equipped with LoRa devices to monitor both location and cargo temperature. As the trucks move, the LoRa devices send signals to nearby gateways, which use fine timestamping to track the truck's position with an accuracy of 75–150 meters, depending on conditions such as line-of-sight and the number of gateways in range.

Integrating Fine Timestamping in the Code Implementation

Function: record_fine_timestamp

We can introduce a new function that simulates recording fine timestamps at each gateway when a signal is received. This function would then be used to calculate precise ToA values, which are further processed to get TDoA values.

record_fine_timestamp: This function simulates recording fine timestamps at each gateway when a signal is received. The signal_time parameter represents the exact time when the signal was transmitted. The function adds a clock_drift parameter to simulate slight inaccuracies in gateway clocks.

Using this function, you can then update the TDoA calculation step to use these fine timestamps, improving the accuracy of the position estimation.

Integrating fine timestamping into the TDoA-based geolocation process can significantly boost accuracy and performance, making it a practical solution for applications where GNSS-level precision is required but power consumption must remain low.

Challenges in TDoA-Based Geolocation: Understanding the Limitations

Implementing TDoA-based geolocation is a promising solution for many IoT applications, but it comes with its own set of challenges. Understanding these limitations can help optimize deployments and improve system performance. The table below highlights the primary challenges, their impact on geolocation accuracy, and potential strategies to mitigate these issues.

Future Directions: Hybrid Methods and Advanced Technologies

The future of TDoA-based geolocation lies in hybrid methods and the integration of advanced technologies that can enhance accuracy, reliability, and ease of deployment. Let’s explore some of these exciting developments:

Hybrid Geolocation Methods

Combining TDoA, RSSI, and AoA: A hybrid approach that leverages multiple geolocation methods (e.g., TDoA, RSSI, and Angle of Arrival) can provide more robust position estimates by compensating for the limitations of each technique. For example, TDoA can be used for long-range accuracy, while RSSI provides quick estimations, and Angle of Attack (AoA) enhances precision in confined spaces.

Future Potential: Hybrid methods can also incorporate machine learning algorithms to dynamically switch between geolocation methods based on real-time conditions, providing the best accuracy possible for each scenario.

Emerging Technologies: LoRa Edge and LoRa Cloud Geolocation Services

LoRa Edge: Semtech’s LoRa Edge platform combines multiple geolocation technologies, including GNSS and Wi-Fi, with traditional LoRaWAN-based TDoA. This platform offers a unified solution that dynamically chooses the best method for location estimation based on power requirements and environmental conditions.

LoRa Cloud Geolocation Services: LoRa Cloud Geolocation Services simplify geolocation by offering a web-based API for estimating the location of LoRa-based devices using metadata such as RSSI, SNR, and ToA. This cloud service eliminates the need for on-premise infrastructure and complex gateway deployments, reducing costs and making geolocation more accessible.

Advanced Hardware and Firmware Integrations

Next-Generation Gateways: Newer gateway models, such as those using the Semtech SX1303 baseband processor, offer Fine Timestamping capabilities and higher ToA resolution, paving the way for more accurate TDoA implementations.

Firmware Updates for IoT Devices: Firmware that supports hybrid geolocation methods and integration with LoRa Cloud Geolocation Services can further enhance the geolocation accuracy of devices, making it possible to use a single device for multiple location methods.

Machine Learning and AI Integration

Integrating machine learning models can dynamically refine path loss parameters, predict ToA variations due to environmental changes, and filter out noisy data. AI-driven models can also help mitigate multipath effects and NLoS conditions, making geolocation more reliable even in challenging environments.

Conclusion

LoRaWAN-based geolocation has proven to be a game-changer, moving beyond basic connectivity to deliver a powerful, low-power alternative to traditional GPS. With techniques like TDoA and advancements in Fine Timestamping, LoRaWAN is bridging the gap between power efficiency and precision, making it a compelling choice for applications ranging from asset tracking to smart agriculture and industrial IoT.?

But this journey doesn’t end here.?

The evolution of geolocation continues, and we’re thrilled to announce that in Article 4—the final article of this series—we’ll be sharing a practical case study based on a real-world project executed by Oxit. This case study will illustrate how to utilize off the shelf HW, tools, and utilities to build a full-fledged LoRaWAN geolocation solution. Get ready to see these techniques in action and learn how to transform theory into a deployable, effective solution for your own IoT needs.

Ready to make geolocation work for your business? Connect with Oxit today, and let us help you build innovative, cost-effective IoT solutions that push the boundaries of what’s possible with LoRaWAN.

Follow us on LinkedIn for more insights and updates, and don’t miss the final chapter in our geolocation series!