I am a bit confused, are these metal objects producing the magnetic field you mentioned and that is disrupting your measurments? If so, could you parhaps remove them and then detemrine their magnetic signature for subtraction from your readings. Or are they permenent objects?

The default sensor fusion solution for me usually involved Kalman filters, have You looked into those?

If your device is in open sky environment, GPS signals (pseudoranges and Doppler) will do the job in a differential mode. Depending on the quality of your inertial sensors, different fusion scheme via Kalman filter will also achieve accurate positioning. Finally even perturbed, magnetic fields can be used to calibrate gyros errors. You can read more about it in the paper "Magnetic perturbations detection and heading estimation using magnetometers" (http://www.mdpi.com/1424-8220/11/12/11390). One correction has been published after this publication. It is available on the same page. This will improve the estimation of your motion using your inertial navigation system.

@Robin: Unfortunately I cannot rely on magnetometer as we use it for magnetic disturbance detection so its readings will be inaccurate (we are detecting the magnetic field around metal objects – building area –like magnetic signature of the object).

@Valerie, Paavo thanks for hints I have read about Kalman filters but I have not found direct example of fusing acc+gyro in order to detect (open field) accurate positioning – What I am looking for is an algorithm or just a brief description of a method to experiment with. One more question DO You know any papers which verify the accuracy of smartphone sensors against the external ones?

Correction I meant the paper "Use of Earth’s Magnetic Field for Mitigating Gyroscope Errors Regardless of Magnetic Perturbation". I don't know any paper that compares the accuracy of smartphone sensors against the external ones ? Do you want to fuse acc+gyro only or GPS signals too? If GPS sinals too, positions only or raw GPS data?

Gerd Boedecker:

The problem mentioned is not clearly defined yet: Is it a short term movement? Or a slow long term movement? Within a lab or outside? What is the distance, characteristics of the movement? You mentioned "precise device ORIENTATION", but later "1 cm accurate". Is the direction finding critical or the position? In principle, the sensors mentioned are o.k., but for the layout of a procedure, more details have to be known.

What Paavo Heiskanen said.

The critical question is, is the GPS carrier phase? Only then may you expect cm level precision. GPS will help maintain orientation of the accelerometer axes, while the accelerometer will help to average the GPS-derived positions over time.

Moving around a square, if you do it quick enough, is just what the Kalman filter needs. And remember to start from, and close on, a known (or: the same) location. I'm afraid there is no shortcut to doing your own mechanization, i.e., read up further on Kalman and inertial. A good book is Jekeli "Inertial Navigation Systems with Geodetic Applications", 2001, with a section on GPS/INS integration.

You mention the need to discern orientation yet give accuracy requirements for position changes - can you be more specific?

In terms of detecting changes in position using GPS/GNSS, you will need to process carrier phase (pseudorange will not be good enough), this should give sub-cm position change accuracy .These will be biased due to propagation-induced errors and orbital errors, so if you need absolute position accuracy (not just relative), you will need a nearby reference receiver.

As for heading, if you can use two receivers, you may be able to get sub degree accuracy with a baseline of half a metre. Gyroscopes and accelerometers will only help with differential attitude, and cannot help with absolute attitude, so unless this is a dynamic problem, they likely won't help.

I would think that such precise positioning is possible with current technology. The problem you may run into is in getting the high-quality inertial components.

Carrier phase in GPS kinematic positioning can give accuracies on the order of a millimeter or so. To have that hold up requires high-quality inertial sensors. The USAF at Holloman has been looking into ultra-precise inertial systems. The best commercially available gyros out there are fiber-optic made by Honeywell. But these may be out of your price range and my have ITAR or other such restrictions.

To make sure what you have for sensors will suffice for the job, I recommend you write a covariance analysis code with Kalman filter for integrating in the measurements. You may also need an Allan variance code to generate inertial sensor noise models if you don't have good models of inertial sensor performance from the manufacturers. To go that route you will need to measure the noise sources.

Even if your existing sensors are not up to the job, you could use the covariance code to apportion requirements as to what sensors you would need to pull it off. You can find good GPS noise models in the GPS books by Kaplan & Hegarty and by Parkinson et Al.

If you're looking at industrial application, you may want to consider local radio transmitters rather than GPS. Multipath ought to be a major concern in such an application.

Thank You all in advance fr the fruitful discussion. I must clear things out concerning the proposed topic: I am working on a mobile system (smartphone based) which is using magnetometer as magnetic field disturbance sensor. We are experimenting with pattern recognition of object's magnetic signatures. Up till now I was manually ensuring the correct readouts of the sensor within the area but I would like to have some kind of a guiding system for that. That is why I'm trying to develop a method of positioning the sensor within the inspected area.

The user will be moving the sensor slowly scanning the area below the device and the algorithm will identify the position of the device performing two tasks: first guiding the user through correct scanning procedure (warning about incorrect speed and orientation of the device) and secondly marking discrete positions in the area with the magnetic sensor readout.

Is it a magnetic vector sensor, or just strength?

I only want to consider static device (sensors) orientation aligned to the surface which is being scanned. I always collect 3 values and merge them to obtain vectors length (the strength of magnetic field).

The accuracy you can get from IMU+GPS really depends on the movement you wanna study. Any motion constraints? like being a planar motion or a cyclic one?

It is impossible to detect precision (1 cm accurate) using GPS+GYRO and Accelerometer.The differential GPS can achieve the precision. The position error of inertial system is accumulation over time due to drift error.

I am trying to rely only on smartphone built-in sensors which means minor accuracy. I am trying to reuse also external sensor but I would like to find some real-world examples and comparison of accuracy – for smartphone and off-the shelf sensors.

To be honest, the rest of the answers are too long so I didn't read them. However, maybe the information shown here is useful for you:

http://www.uc3m.es/portal/page/portal/news_repository/general_news/A%20system%20that%20improves%20the%20precision%20of%20GPS%20in%20cities%20by%2090?_template=/SHARED/pl_noticias_detalle_pub_ingles

One of the best (inexpensive) inertial navigation sensor on the market is: http://invensense.com/mems/gyro/mpu6150.html Obviously, this solution would require and external circuit board. Still, such an ambition performance target may call for a (possibly expensive) GPS receiver, and most likely intensive computations as well, in order to fuse the sensor data (i.e.,. more sophisticated Bayesian tracking methods). Map information may reduce the search space (computations).