Every sensor reports an estimate with a failure mode, and fusion trades one failure for another

Treating a sensor reading as a fact is a category error that surfaces later as a bug report. Kalman (1960) settled the alternative. A measurement yields an estimate of a state, and the estimate means nothing without the covariance that says how wrong it may be. Thrun, Burgard and Fox (2002) state the same premise for robotics.

The two units before it settled what to sense; this third of ten units turns to how well any single sensor can report it. The premise goes further here. A sensor does not merely report with noise. It fails in a characteristic way, and the failure belongs to the sensor, the mounting and the setting together. Fusing two sensors that fail differently improves robustness by trading one failure for another rather than deleting error. Sensor choice and fusion choice are therefore statements about which failures a product can tolerate. Those are design decisions rather than implementation details.

A reading is an estimate, and the estimate carries an interval

Kalman (1960) derived the optimal linear estimator recursively. As each measurement arrives, the filter updates both the state estimate and the covariance matrix of the estimation error. The filter applies to stationary and nonstationary statistics, and needs no whole measurement history. Two features matter for design. Optimality is conditional, since the filter is optimal for a linear system with Gaussian noise. A product that ignores the conditions inherits an error it cannot see.

The paper works the claim on two standard prediction problems rather than asserting it. The first recovers a signal from additive noise. In the second, a particle leaves the origin at an unknown constant velocity and only its position is measured, through correlated noise. The answer gives position, velocity and the covariance of the error, so the estimate can be watched firming up as samples arrive (Kalman, 1960).

A screen showing one number, whether a step count or a position dot, has discarded the interval. A designer who never sees the interval cannot know when the estimate is worthless.

The failure mode belongs to the sensor, and the mounting decides which one bites

The accelerometer is the cheapest sensor in this module and the one whose failure is easiest to overlook. Mathie and colleagues (2004) reviewed accelerometry for long-term ambulatory monitoring. They found that one waist-mounted sensor can serve many parameters. They include gait, sit-to-stand transfers, postural sway and falls. They also found that the method suits unsupervised monitoring of people going about their lives.

Yang and Hsu (2010) reviewed the motion detectors built on that sensor. The accuracy of an energy-expenditure estimate depends on the location and attachment of the accelerometer. It also depends on external vibration and gravitational artefact, and on the activities performed in a free-living environment. Loose attachment produces vibration and displacement that degrades the signal. The authors record why most studies choose the waist, near the centre of mass of the body. Two accelerometers of identical specification, mounted differently on the same person, report estimates that differ systematically. The review names no older body and no walking aid.

Where the failure lands is set by the setting as much as by the sensor

Inertial sensing is the clearest case of an error whose size is a function of time. Harle (2013) surveyed pedestrian dead reckoning. He covered step detection and characterisation, inertial navigation and map-aided particle filters. He also covered hybrid systems that use absolute position fixes to correct dead-reckoned output. His conclusion is a constraint rather than a result. Dead reckoning alone offers good short- to medium-term tracking under certain circumstances, but regular absolute position fixes are needed for long-term operation.

Foxlin (2005) shows what can be recovered without a second source. The NavShoe is a wireless inertial sensor small enough to sit in a shoelace and low-powered enough to run all day. Its selling point is negative: existing tracking technologies require an instrumented, marked or premapped environment, and this one does not. Outdoors, he reports, a user would barely notice its metre-level error, which suits augmenting distant objects and not close-range registration.

Where location is measured by radio, the environment supplies an even larger share of the variance. Hightower and Borriello (2001) built a taxonomy of location systems so developers could evaluate their options when choosing one. The taxonomy admits that no single system dominates. Liu and colleagues (2007) classify estimation into triangulation, scene analysis and proximity, and compare systems on accuracy, precision, complexity, scalability, robustness and cost. Brena and colleagues (2017) survey the evolution of indoor positioning across a wide range of technologies. Laoudias and colleagues (2018) find accuracy limited by the signal environment rather than the algorithm alone. Four surveys spanning seventeen years agree: the error budget of a location estimate is mostly a property of the building.

Fusion buys robustness by moving the failure, not by deleting it

Gravina and colleagues (2017) review multi-sensor fusion in body sensor networks. They note the shift to multi-device synchronous measurement, and observe that fusing heterogeneous sources is a non-trivial task that directly affects application performance.

Khaleghi and colleagues (2013) review the same field from the data side and are more cautionary. They locate the problems that make fusion hard in three places. The first is the data to be fused, the second the imperfection and diversity of the sensor technologies, and the third the application environment. Their crux is data imperfection. Sensor data always carries imprecision and uncertainty, and a fusion algorithm must express those imperfections rather than assume them away. The association and conflict problems that appear when two sensors disagree are not solved by adding a third.

Aziz and Koo (2025) reach the same position from the applied end. They review Bluetooth, WiFi, ultra-wideband, ZigBee and RFID localisation and find that hybrid solutions mitigate the individual drawbacks of each. Drawbacks are mitigated, not eliminated, and signal interference, energy consumption and limited scalability persist alongside cost and privacy concerns.

The same review supplies a deployed shape for that trade. A system built for firefighters and soldiers entering unknown buildings fuses four sources. One is GPS outdoors, and another is LoRa at 868 megahertz and 2.4 gigahertz. A third is ultra-wideband for short-range precision, and a fourth is altimeters for height (Aziz and Koo, 2025). Each source covers a failure the others have, which is the mechanism. The same review also records BLE beacons reaching centimetre accuracy in a hospital. It notes the security exposure such deployments carry.

The contested question: where does the error budget belong?

Three positions are held, differing over what to fix when a product misses its accuracy target. The first holds that the error belongs to the sensor and the estimator, and that better measurement and inference are the remedy. Kalman (1960) supplies the optimal estimator and Gravina and colleagues (2017) the fusion advantage: combine complementary sources and robustness improves. The test of success is a lower error on a benchmark.

The second holds that the error belongs to the setting. A benchmark number is a property of the test bed rather than the device. Hightower and Borriello (2001), Liu and colleagues (2007), Brena and colleagues (2017), Laoudias and colleagues (2018) and Aziz and Koo (2025) all report the same pattern. Performance depends on the environment and the infrastructure. The test of success is a system that works where a team installs it, and an accuracy figure without its setting is not evidence.

The third holds that the error belongs to the mounting and the body. Mathie and colleagues (2004) and Yang and Hsu (2010) review the same sensor class. In Yang and Hsu's synthesis, accuracy depends on where the sensor was worn and how it was attached, and on the activities performed. The test of success is whether a study reports its mounting, its population and its activity set so another team can reproduce the number.

The evidence that would settle the dispute is a factorial comparison. The same task, population and setting, with sensor count, mounting and environment each varied independently. The surveys reviewed here report no such comparison. The studies they aggregate change several of these factors at once. That is why the same technique can look accurate in one review and marginal in another.

Rated by kind, the three sides differ in evidence. The sensor-and-estimator side rests on Kalman's (1960) derivation, which is theory, and on Gravina and colleagues' (2017) fusion review. The setting side rests on survey after survey, from Hightower and Borriello (2001) to Aziz and Koo (2025), so it carries accumulated observation. The mounting side rests on two reviews of one sensor class (Mathie et al., 2004; Yang and Hsu, 2010). While the dispute is open, a designer reports accuracy with its setting, its mounting and its population. The strongest objection is that the unit's factorial comparison may never run, since no survey here varies the three factors independently.

Where this is heading

The direction of travel is more sensors, hybridisation and learning, and each step adds a failure mode as well as removing one. Aziz and Koo (2025) name three promising routes for indoor localisation. They are resilience to environmental change, edge computing for real-time processing and artificial intelligence for predictive modelling. Laoudias and colleagues (2018) set out a roadmap reaching beyond two-dimensional position towards height and indoor mapping. They also add security and privacy concerns to what a location system must get right. Jiang, Goncalves and Kostakos (2024) show the other half of the trend. Their systematic review of mobile near-infrared sensing follows prototypes, data collection and machine learning methods as the modality arrives on the phone. The sensor-choice decision therefore recurs with every sensor a phone acquires: which failures does this product tolerate?

Sources

• Kalman, R. E. (1960). A New Approach to Linear Filtering and Prediction Problems. Journal of Basic Engineering. doi:10.1115/1.3662552 Derived the optimal linear estimator recursively, updating both the state estimate and the covariance of the estimation error as each measurement arrives. Optimality is conditional on a linear system with Gaussian noise, so the design unit is an estimate with an interval.
• Thrun, S., Burgard, W. and Fox, D. (2002). Probabilistic robotics. Communications of the ACM. doi:10.1145/504729.504754 Set out probabilistic robotics, in which planning and navigation exploit statistics gleaned from uncertain, imperfect environments. It states the unit's premise for robotics.
• Mathie, M., Coster, A., Lovell, N. and Celler, B. (2004). Accelerometry: providing an integrated, practical method for long-term, ambulatory monitoring of human movement. Physiological Measurement. doi:10.1088/0967-3334/25/2/r01 Reviewed accelerometry for monitoring movement in free-living subjects, and described an integrated waist-mounted system measuring several parameters at once. It separates the sensor from the question it answers.
• Yang, C. C. and Hsu, Y. L. (2010). A Review of Accelerometry-Based Wearable Motion Detectors for Physical Activity Monitoring. Sensors. doi:10.3390/s100807772 Reviewed wearable accelerometry for activity monitoring. They report that accuracy depends on the location and attachment of the accelerometer, on external vibration and gravitational artefact and on the activities performed. The mounting, not the chip, decides the error.
• Harle, R. (2013). A Survey of Indoor Inertial Positioning Systems for Pedestrians. IEEE Communications Surveys and Tutorials. doi:10.1109/surv.2012.121912.00075 Surveyed pedestrian dead reckoning, covering step detection, inertial navigation and hybrid systems that correct dead reckoning with absolute fixes. He concluded that dead reckoning supports short- to medium-term tracking but needs regular fixes for long-term operation.
• Foxlin, E. (2005). Pedestrian tracking with shoe-mounted inertial sensors. IEEE Computer Graphics and Applications. doi:10.1109/mcg.2005.140 Described NavShoe, a shoe-mounted wireless inertial tracker, arguing that existing position-tracking technologies require an instrumented, marked or premapped environment and that this one does not. He reports metre-level error outdoors, so the design buys deployability by accepting error.
• Hightower, J. and Borriello, G. (2001). Location Systems for Ubiquitous Computing. Computer. doi:10.1109/2.940014 Built a taxonomy of location systems to help developers evaluate their options when choosing one, an implicit finding that the choice compares systems rather than selecting a best one. No location technology dominates.
• Liu, H., Darabi, H., Banerjee, P. and Liu, J. (2007). Survey of Wireless Indoor Positioning Techniques and Systems. IEEE Transactions on Systems, Man and Cybernetics Part C. doi:10.1109/tsmcc.2007.905750 Classified wireless indoor positioning into triangulation, scene analysis and proximity, examined fingerprinting, and compared systems on accuracy, precision, complexity, scalability, robustness and cost. The six-way comparison is itself the argument.
• Brena, R. F., Garcia-Vazquez, J. P., Galvan-Tejada, C. E., Munoz-Rodriguez, D., Vargas-Rosales, C. and Fangmeyer, J. (2017). Evolution of Indoor Positioning Technologies: A Survey. Journal of Sensors. doi:10.1155/2017/2630413 Surveyed and classified indoor positioning technologies, arguing that earlier surveys lacked a classification scheme able to map the field. The choice is setting-dependent and provisional.
• Laoudias, C., Moreira, A. J. C., Kim, S., Lee, S., Wirola, L. and Fischione, C. (2018). A Survey of Enabling Technologies for Network Localization, Tracking, and Navigation. IEEE Communications Surveys and Tutorials. doi:10.1109/comst.2018.2855063 Reviewed cellular and wireless local area network localisation and found accuracy limited by the signal environment rather than the algorithm alone. It adds security and privacy to location architecture.
• Khaleghi, B., Khamis, A., Karray, F. and Razavi, S. (2013). Multisensor data fusion: A review of the state-of-the-art. Information Fusion. doi:10.1016/j.inffus.2011.08.001 Reviewed data fusion, locating the obstacles in the data to be fused, in the imperfection and diversity of the sensor technologies and in the application environment. Measurements always carry imprecision and uncertainty, which fusion must express rather than assume away.
• Gravina, R., Alinia, P., Ghasemzadeh, H. and Fortino, G. (2017). Multi-sensor fusion in body sensor networks: State-of-the-art and research challenges. Information Fusion. doi:10.1016/j.inffus.2016.09.005 Surveyed multi-sensor fusion in body sensor networks and categorised fusion by its level, whether data, feature or decision. Fusion is non-trivial and affects application performance directly.
• Aziz, T. and Koo, I. (2025). A Comprehensive Review of Indoor Localization Techniques and Applications in Various Sectors. Applied Sciences. doi:10.3390/app15031544 Reviewed Bluetooth, WiFi, ultra-wideband, ZigBee and RFID localisation, reporting that combining technologies mitigates the individual drawbacks of each. Signal interference, energy consumption and limited scalability remain obstacles, so drawbacks are traded rather than abolished.
• Jiang, W., Goncalves, J. and Kostakos, V. (2024). Mobile near-infrared sensing: a systematic review of devices, data, modelling and applications. ACM Computing Surveys. doi:10.1145/3652596 Conducted a systematic review of mobile near-infrared sensing following PRISMA guidelines, covering prototypes, data collection and machine learning methods. It shows a new modality arriving on the phone.