Least-squares, cascaded, centralized, and federated architectures. Integration of all sensor types.
No single navigation system works well in all environments. GNSS fails indoors. INS drifts. Odometers only work on land. Radar altimeters need terrain. By integrating multiple sensors, we get a system that is more accurate, more robust, and available in more environments than any individual sensor.
Benefits of multisensor integration:
• Accuracy: Each sensor's strengths compensate for the others' weaknesses
• Availability: When one sensor fails or becomes unavailable, others maintain the solution
• Robustness: Redundancy enables fault detection and isolation
• Completeness: Different sensors provide different state information (position, velocity, attitude, height)
Example: Urban land vehicle navigation. A system might integrate:
| Sensor | Provides | Works When |
|---|---|---|
| GNSS | Absolute position, velocity | Open sky |
| IMU | Attitude, dead reckoning | Always (but drifts) |
| Odometer | Speed, yaw rate | Wheels on ground |
| Barometer | Height | Always (with calibration) |
| Magnetometer | Heading | Away from magnetic interference |
| Map matching | Cross-track position | On known roads |
The simplest form of multisensor integration is least-squares position fixing. Multiple independent position or range measurements are combined in a single least-squares solution, weighted by their respective accuracies.
If multiple radio navigation systems each provide a range measurement, a weighted least-squares solution gives:
where W = R−1 is the inverse of the measurement noise covariance matrix, H is the geometry matrix, and δz is the measurement innovation vector.
Advantages:
• Simple and computationally cheap
• No system model needed (no prediction step)
• Good for combining position fixes from different systems
Disadvantages:
• No time filtering — each epoch is independent, so measurement noise passes through
• Cannot estimate sensor error states (biases, scale factors)
• Cannot propagate a solution between measurement epochs
Least-squares integration is used when the sensors provide only occasional fixes (not continuous measurements) and when the error characteristics do not need to be modeled.
In cascaded integration, each navigation subsystem has its own Kalman filter, and the output of one filter becomes the input (measurement) to the next. The filters are arranged in a chain.
Example: An AHRS Kalman filter (gyros + accelerometers + magnetometer) produces an attitude solution. This attitude feeds into an odometry dead-reckoning filter. The DR solution feeds into a GNSS/DR integration filter.
Advantages:
• Modularity: Each subsystem is self-contained with a clean interface. Subsystems can be developed and tested independently.
• COTS-friendly: Commercial sensor packages often have built-in filters. Cascaded integration uses their outputs directly.
• Robustness: If one subsystem fails, the others continue.
Disadvantages:
• Suboptimal: Each subsystem discards information (by producing a single estimate instead of passing the full probability distribution). The downstream filter does not know the upstream filter's internal state or how its estimate was formed.
• Double-counting: If two subsystems use the same sensor (e.g., both use gyro data), cascading can double-count that information, leading to overconfident estimates.
• Feedback problems: If the downstream filter corrects the upstream filter's reference navigation system, this creates a feedback loop that the upstream filter does not model, potentially causing instability.
Centralized integration uses a single, large Kalman filter that processes all sensor measurements directly. The state vector includes error states for every sensor and the navigation solution.
Architecture: All raw sensor measurements feed into one Kalman filter. The filter's state vector includes the navigation error states plus error models for every sensor (biases, scale factors, alignment errors). This gives the theoretically optimal solution because all correlations between sensor errors are captured.
Typical state vector for an urban land vehicle:
| States | Count | Source |
|---|---|---|
| Attitude error | 3 | INS |
| Velocity error | 3 | INS |
| Position error | 3 | INS |
| Accel/gyro biases | 6 | IMU |
| Clock offset & drift | 2 | GNSS receiver |
| Baro bias | 1 | Barometer |
| Odometer scale factor | 1 | Odometer |
| Mag heading bias | 1 | Magnetometer |
| Total | 20 |
Advantages: Theoretically optimal; all correlations captured; all sensor errors estimated jointly.
Disadvantages: Large state vector (20–50+ states); high computational cost (O(n³) in the number of states); single point of failure; requires detailed error models for every sensor; numerical stability challenges.
Federated integration is a middle ground between cascaded and centralized. Multiple local filters each process a subset of the sensors, and a master filter combines their outputs.
Architecture:
• Each local filter integrates one sensor type with a common reference (typically the INS)
• The master filter combines the local filter outputs, accounting for the common INS reference
• The common information (INS state and covariance) is distributed to the local filters with a scaling factor to prevent double-counting
Information sharing: The key design parameter is the information-sharing factor. Each local filter receives a fraction (1/N for N local filters) of the common-state information. This prevents the common information from being counted N times.
Fusion methods:
• No-reset: Local filters run independently; master fuses at each epoch. Simple but suboptimal.
• Fusion-reset: After each master fusion, the local filters are reset with the fused state and covariance. Better performance but requires information sharing.
• Zero-reset: Local filter states are zeroed after each fusion, with only the covariance shared. Most robust to local filter failures.
Advantages: Modular, fault-tolerant (failed local filter can be isolated), parallelizable, near-optimal with fusion-reset. Disadvantages: More complex than cascaded; information sharing can be tricky; not as optimal as truly centralized.
Terrestrial radio navigation systems (Chapter 9) are integrated using the same principles as GNSS integration.
Loosely coupled: The radio navigation system computes its own position solution, which is compared with the reference navigation solution (INS or DR). This requires enough transmitters for a standalone solution.
Tightly coupled: Raw range or time-difference measurements are input directly to the integration filter. This allows operation with fewer transmitters and enables per-transmitter quality control. The measurement model is similar to tightly coupled GNSS, with the line-of-sight vectors computed from the estimated position and known transmitter locations.
Common receiver clock: In tightly coupled systems, the receiver clock can be shared between different radio navigation systems. If the same receiver processes both GNSS and Loran signals, a single clock offset state serves both, reducing the state count.
Range biases: Terrestrial radio signals are affected by propagation delays that vary with terrain and atmospheric conditions. These range biases are often estimated as additional Kalman filter states, modeled as slowly varying random processes.
Dead-reckoning sensors (Chapter 10) can be integrated as either the reference or aiding navigation system. When an INS is present, it should always be the reference, with DR sensors providing aiding measurements.
Attitude integration: Magnetometer heading and accelerometer leveling measurements from an AHRS can be input to the integration filter as direct observations of the attitude error states. The measurement model is:
Height integration: Barometric and radar altimeter measurements provide height observations. The baro bias should be estimated as a Kalman filter state (slowly drifting). The baro and INS should always be integrated as separate sensors, not through a baro-inertial loop, because the loop behavior is difficult to model in the integration filter.
Odometer integration: Odometer speed measurements constrain the body-frame forward velocity. The odometer scale factor error (due to tire radius uncertainty) should be estimated. The non-holonomic constraint (zero lateral velocity) provides an additional measurement that aids heading observability.
Pedestrian DR: Step length, step heading, and ZUPT measurements (Chapter 13) are integrated. The step length model parameters may be estimated as additional states.
Doppler radar/sonar: Body-frame velocity measurements from the Janus configuration are integrated, with the Doppler scale factor and alignment errors estimated.
Feature-matching systems (Chapter 11) provide position fixes that are integrated differently depending on whether they give a position fix, a line fix, or an ambiguous measurement.
Position fixes: TRN (terrain-referenced navigation), image matching, and similar systems provide position corrections in latitude and longitude. These are integrated as straightforward position measurements, similar to loosely coupled GNSS. The measurement innovation is the difference between the feature-matching position fix and the INS/DR position estimate.
Line fixes: Map matching constrains the position to a road or rail line. This is a one-dimensional measurement (cross-track position). The measurement matrix projects the 2D position error onto the direction perpendicular to the road:
where ψroad is the road heading. This corrects only the cross-track error; the along-track position is uncorrected.
Ambiguous measurements: Some feature-matching systems produce multiple candidate positions (e.g., TERCOM in complex terrain). The integration filter must determine which candidate is correct. Options include selecting the candidate with the smallest innovation, running parallel filters for each candidate (MMAE), or using a probabilistic data association filter.
This simulation compares navigation with different sensor combinations. Watch how adding sensors improves the position estimate.