GB2555806A

GB2555806A - A navigation system

Info

Publication number: GB2555806A
Application number: GB1618941.7A
Authority: GB
Inventors: R Wilkinson Nicholas
Original assignee: Atlantic Inertial Systems Ltd
Current assignee: Atlantic Inertial Systems Ltd
Priority date: 2016-11-09
Filing date: 2016-11-09
Publication date: 2018-05-16
Also published as: EP3321631B1; KR20180052075A; EP3321631A1; US20180128645A1; KR102432116B1; US11015957B2

Abstract

A navigation system comprises: an inertial navigation system (INS) 110 outputting a first position estimate; a terrain based navigation unit 120 outputting a second position estimate; a stored gravity map 130 arranged to receive a position and output gravity information for that position; and an iterative algorithm unit 140 arranged to determine an INS error state 45. The iterative algorithm unit receives the first and second position estimate; determines a gravity corrected position estimate based on the first position estimate, the INS error state and the gravity information; and updates the next INS error state. The terrain based navigation unit may comprise a radar altimeter or laser altimeter arranged to determine a positional estimate based on a terrain profile data. The gravitational information may comprise three-dimensional gravitational field strength and/or a tensor of the gravity field strength data. The position estimate received by the stored gravity map may be the first or second position estimate or the first position estimate as corrected by the INS error state. The iterative algorithm unit may comprise a Kalman filter that, in each iteration, outputs an error corrected position estimate based on the INS error state for the next iteration and the first position estimate.

Description

(54) Title of the Invention: A navigation system

Abstract Title: Inertial navigation system with terrain and gravitational error correction (57) A navigation system comprises: an inertial navigation system (INS) 110 outputting a first position estimate; a terrain based navigation unit 120 outputting a second position estimate; a stored gravity map 130 arranged to receive a position and output gravity information for that position; and an iterative algorithm unit 140 arranged to determine an INS error state 45. The iterative algorithm unit receives the first and second position estimate; determines a gravity corrected position estimate based on the first position estimate, the INS error state and the gravity information; and updates the next INS error state. The terrain based navigation unit may comprise a radar altimeter or laser altimeter arranged to determine a positional estimate based on a terrain profile data. The gravitational information may comprise three-dimensional gravitational field strength and/or a tensor of the gravity field strength data. The position estimate received by the stored gravity map may be the first or second position estimate or the first position estimate as corrected by the INS error state. The iterative algorithm unit may comprise a Kalman filter that, in each iteration, outputs an error corrected position estimate based on the INS error state for the next iteration and the first position estimate.

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- 1 A Navigation System

Technical field

The present disclosure relates to a navigation system, a vehicle comprising the navigation system, a method, a computer-readable medium, and an apparatus for reducing the amount of uncertainty in an inertial navigation system, particularly in the presence of a gravitational anomaly.

Background

Terrain Referenced Navigation (TRN) systems which integrate aircraft navigation data, radar altimeter data and digital terrain elevation data to generate a navigation solution are in service on a number of airborne platforms and provide a navigation solution and an uncertainty estimate for the navigation solution. Such systems often use the navigation solution from an Inertial Navigation System (INS) as a key input and use INS error calibrating Kalman Filters as a means of integrating the terrain based position measurements with the INS data.

Inertial navigation systems (INS) are often used by vehicles (e.g. aeroplanes, ships, submarines and cars) as part of the vehicle’s navigation system to determine the vehicle’s navigational data (e.g. position, velocity, acceleration and attitude of the vehicle). The navigational data may for example be used to check whether the vehicle is navigating along a desired route and to determine suitable course corrections when off-route. An estimate of the uncertainty in the data will often also be monitored.

There are situations where the INS will provide the primary source of navigation data for the vehicle. Such situations may arise where other navigation aids such as GPS are unavailable or cannot be trusted (e.g. when they are jammed or there is a suspicion that they may be spoofed). The INS navigates by dead reckoning based on the onboard sensors which cannot so easily be jammed or spoofed.

Typically, the vehicle’s acceleration and rotation are measured using inertial sensors such as accelerometers and gyroscopes, and the INS derives the vehicle’s

- 2velocity and location information from the outputs of these sensors. Small errors in the measuring capabilities of the accelerometers or in the balance of the gyroscopes can overtime lead to build up of large errors in the outputs of the INS. Such errors can lead to significant errors in estimates of vehicle location (and/or velocity, attitude, etc.) and can be problematic for navigation decisions, for example resulting in false course corrections. Typically, the errors in the INS position estimates drift at a rate of around 2 nautical miles per hour due to the integration over time of errors within the accelerometer and gyroscope sensors within the INS.

In addition, the output from the INS can also be severely degraded in the region of gravity anomalies. Typically systems in service today have no knowledge of where gravity anomalies occur. In the region of such anomalies the accelerometers in the INS sense an acceleration change due to a gravity anomaly (e.g. a local change in the gravitational field strength/gradient). Such acceleration measurements may be erroneously attributed by the INS to aircraft motion and integrate the acceleration into the INS navigation solution leading to erroneous position, velocity, acceleration and attitude outputs. In the case of TRN based systems, this in turn severely degrades the navigation solution output of the Terrain Referenced Navigation system and can also make the uncertainty output unrepresentative of the likely error in the navigation solution making the navigation solution and uncertainty unsafe to use.

To compensate for such erroneous readings some existing systems have attempted to correct the INS measurements directly based on measurements or maps of the gravitational anomaly. However, the resulting INS performance, although much improved, continues to exhibit navigation errors.

Many vehicles employ Kalman Filter type algorithms within their navigation systems to calibrate the errors within the INS using navigation data from other sources such as GPS, Terrain Referenced Navigation, etc. together with an INS error model that understands the relationship between the inertial sensor errors and the navigation errors produced by the INS. Such INS error estimating algorithms may typically then make a set of corrections available to other systems that use the INS navigation solution.

- 3The present disclosure seeks to provide an improved INS.

Summary

According to a first aspect, this disclosure provides a navigation system comprising: an inertial navigation system arranged to output a first position estimate; a terrain based navigation unit arranged to output a second position estimate; a stored gravity map arranged to receive a position and to output gravity information for that position; and an iterative algorithm unit arranged to determine an INS error state in each iteration; wherein in each iteration the iterative algorithm unit is arranged to: receive the first position estimate and the second position estimate; determine a gravity corrected position estimate based on the first position estimate, the INS error state and the gravity information; and update the INS error state for the next iteration based on the INS error state, the gravity corrected position estimate and the second position estimate.

The INS error state represents the estimated error in the position estimate from the inertial navigation system (INS). The navigation system may combine the INS position estimate with the INS error state to provide an error corrected position estimate. That is, the navigation system may use the INS error state as a correction function (which may include a plurality of correction values) for correcting the position estimate from the INS.

The INS error state may also comprise data representative of the error in the INS sensor measurements (e.g. accelerometer and gyroscope measurements), attitude errors, and velocity error. Accordingly, it will be appreciated that the INS error state may be used to correct the overall navigation solution provided by the INS.

The gravity information from the gravity map can be used to determine the components of the INS’s accelerometer and gyroscope outputs that are due to the local gravity field, and in particular can take account of the spatial variations in the local gravity field. The remaining components of the sensor outputs are assumed to be due to vehicle movement. Therefore by taking into account the local gravity field information, together with the INS error state of the current iteration and the first position estimate from the INS, the navigation system can correct the first position estimate to provide a gravity corrected position estimate.

- 4The accuracy of the INS error state estimate in each iteration is improved by updating the INS error state for the next iteration based on the INS error state of the current iteration, the gravity corrected position estimate and the second position estimate. In this way, it will be appreciated that as a result of the updating step the next iteration of the iterative algorithm unit is arranged to inherit an INS error state based on the parameters and calculations of the preceding iteration. In particular, it will be appreciated that the next iteration of the iterative algorithm unit will use an INS error state based on the INS error state of the current iteration, the gravity corrected position estimate and the second position estimate.

It will be appreciated that the gravity corrections are not simply applied directly as corrections to the INS outputs, but the gravity corrected position estimate can instead be used simply as another position estimate, alongside the second position estimate. By monitoring the uncertainties in each estimate the iterative algorithm can weight the different position estimates according to their estimated uncertainties, placing more weight on position estimates that have lower uncertainty.

It will be appreciated that the architecture can be extended to include additional sources of navigation information such as GPS. For example, GPS could be used as an additional (e.g. third) position estimate alongside the gravity corrected position estimate and the second position estimate.

In examples, the iterative algorithm unit comprises a Kalman filter or other type of “predictor corrector” algorithm. The Kalman filter may be a modified Kalman filter such as an extended Kalman filter. The Kalman filter includes an error model that models and propagates the INS error state. The Kalman filter preferably models the relationship between the inertial sensors and the navigation errors produced by the INS. In each iteration, the Kalman filter preferably updates the propagated error state based on the INS error state, the gravity corrected position estimate and the second position estimate. As the iterative algorithm unit may predict the growth in the INS error state from one iteration to the next iteration, the contribution from gravity is monitored and taken into account. It will be appreciated that Kalman filters are a type of “predictor corrector” iterative algorithm that uses least squares

- 5estimation within the correction or measurement step (i.e. update step). As with a Kalman filter, such least squares estimators provide an estimate of a subsequent state based on prior states. Thus, it will be appreciated that in some examples the iterative algorithm unit may comprise a least squares estimator.

The terrain based navigation unit (TNU) may be arranged to determine the second position estimate based on a correlation between measured terrain profile data and stored terrain profile data in a terrain map (e.g. digital terrain elevation data). The measured terrain profile data may be obtained using any suitable sensor or detection equipment. However, in some preferred examples, a radar altimeter or laser altimeter is used. The terrain profile data may comprise surface topology measurements such as surface height measurements. In traditional TRN systems the INS output is used to provide a coarse position estimate. The TRN algorithms then generate a correction to the INS position based on the matching of the radar (or laser) altimeter data with the terrain elevation data.

The second position estimate provides an external and independent measurement of position. The inventors have found that the accuracy of the INS error state may be further improved by taking the second position estimate into account when updating the INS error state based on the gravity corrected position. This is because the second position estimate constrains the growth in the error of the gravity corrected INS output. In examples where the iterative algorithm unit comprises a Kalman filter or other type of “predictor corrector” algorithm, the second position estimate binds the growth in the error of the INS output by integrating the gravity corrected position estimate with the second position estimate.

It will be appreciated that the gravity map may take any of a number of forms. However, in some preferred examples, the gravity information may comprise threedimensional gravity field strength/gradient data, and/or a second or a third order tensor of the gravity field strength/gradient. It is advantageous to use gravity gradient data as it is computationally easier to determine the effect of a gravity anomaly on the INS sensor measurements. For example, the gravity gradient can be fed directly into non-linear equations of motion to determine the components of accelerometer and gyroscope output that are due to the gravity gradient. The computational process is made even quicker using tensors. Such increases in

- 6speed are of course desirable for “real-time” navigation, particularly when travelling at high speeds of greater than 200 miles per hour. 3D gravity information enables the effects of a gravity anomaly on the INS sensor to be determined more accurately than 2D or 1D gravity information.

The first and the second position estimates may comprise three dimensional coordinates.

The error, and hence accuracy, in the INS position estimates drift over time, typically at a rate of up to 2 nautical miles per hour (as errors in the inertial sensor measurements integrate into velocity and attitude errors, which in turn integrate into position errors).

TNU position estimates are typically accurate to within around 20 meters when there is sufficient information in the terrain map data and the terrain measurements for a good correlation. However, when there is insufficient information in the terrain map data and the terrain measurements for a good correlation (e.g. when travelling over flat terrain) the error in the TNU position estimate may increase.

It will be appreciated that following a period without sufficient information in the terrain map data and the terrain measurements for a good correlation, should sufficient information then become available, the error in the TNU position estimate will typically return to within a 20 meter accuracy level once the TNU has correlated the information.

The error in position estimate from the navigation system may also drift but it will drift at a lower rate than the 2 nautical miles per hour exhibited by the INS solution, and, in general, the position estimate from the navigation system will be more accurate than the individual INS, TNU and GNU position estimates. This is because the navigation system position estimate benefits from the correction applied by the updated INS Error State.

In examples, the position estimate received by the stored gravity map may be the first position estimate as corrected by the INS error state. In other examples it may be the first or the second position estimate. In some other examples, the first

- 7position estimate may be used when the estimated accuracy in the INS is better than a predetermined threshold for the x, y and/or z position coordinates. In some examples, the second position estimate may be used when the estimated accuracy of the second position estimate is better than a predetermined threshold. Selecting which position estimate to use in this way ensures that the gravity information is determined at the most accurate location estimate available. Most preferably, the position estimate received by the stored gravity map is the first position estimate as corrected by the INS error state. In normal operation this is expected to be the most accurate position estimate available. In some examples, the threshold level may be set according to the estimated accuracy of the terrain based navigation unit or INS (e.g. based on the estimated uncertainties discussed above).

In some examples, in each iteration of the iterative algorithm unit, the iterative algorithm unit may be further arranged to output an error corrected position estimate based on the INS error state for the next iteration and the first position estimate from the INS. The error corrected position estimate provides a position estimate that more accurately accounts for changes in the gravity field by correcting the first position estimate with the INS error state for the next iteration.

This disclosure also extends to a vehicle comprising a navigation system according to any of the above examples (optionally including any or all of the preferred or optional features described above).

According to a further aspect, this disclosure provides an iterative method of determining an INS error state, each iteration of the method comprising: receiving a first position estimate from an inertial navigation system and a second position estimate from a terrain based navigation unit; determining gravity information at a received position from a stored gravity map; determining a gravity corrected position estimate based on the first position estimate, the INS error state and the gravity information; and updating the INS error state for the next iteration based on the INS error state, the gravity corrected position estimate and the second position estimate.

The features described above in relation to the system, including the preferred and optional features, apply equally to the iterative method.

- 8Accordingly, for example, the INS error state may be updated using a Kalman filter.

The second position estimate may be determined based on a correlation between measured terrain profile data and stored terrain profile data in a terrain map.

The gravity information from the stored gravity map is determined based on the first position estimate as corrected by the INS error state, the first position estimate or the second position estimate.

Each iteration of the iterative method may further comprise outputting an error corrected position estimate based on the INS error state for the next iteration and the first position estimate.

This disclosure also extends to a computer-readable medium comprising instructions that are executable by a processor to perform any of the abovedescribed methods.

This disclosure also extends to apparatus comprising a processor and a memory, the memory storing instructions that are executable by the processor to perform any of the above-described methods.

Brief description of drawings

One or more non-limiting examples will now be described, with reference to the accompanying drawings, in which Fig. 1 illustrates a schematic flow block diagram of a navigation system 100 in accordance with the present disclosure.

The navigation system 100 shown in Fig. 1 is for a vehicle such as an aeroplane, a car, a boat or a rocket. The navigation system 100 comprises an iterative algorithm unit (IAU) 140 in communication with an inertial navigation system (INS) 110, a terrain based navigation unit (TNU) 120, and a stored gravity map 130. It will be appreciated that existing navigation systems use an IAU comprising a Kalman filter, together with an INS and optionally TNU to determine the error in the INS vehicle

- 9position estimate and, by correcting for the determined error, provide a better vehicle position estimate.

In the system according to examples of this disclosure, the IAU 140 comprises processing blocks 20 and 40. Processing block 20 comprises an INS error state 22 and a Kalman filter propagation unit wherein INS error states and covariances are propagated based on INS Error Model and acceleration due to gravity derived from the gravity map 130. Processing block 40 updates (e.g. the INS error state) based on position measurements generated from best fit of terrain sensor measurements (e.g. radar altimeter (Radalt)) with map data (e.g. terrain map data) and estimated positions (e.g. gravity corrected position estimate 35).

More specifically, the IAU 140 is arranged to determine an updated INS error state 45. The updated INS error state 45 is determined based on the INS error state 22, the gravity corrected position estimate 35 and the second position estimate 55. The result of this is that the INS error state 45 accounts for the error associated with the effect of gravitational anomalies on the INS position estimate 10, and that the growth in the error of the INS output is bound by the TNU position estimate 55. Preferably, the navigation system 100 also determines an error corrected position estimate 60. The error corrected position estimate 60 relates to the INS’s position estimate 10 as corrected by the updated INS error state 45.

As the gravity corrections are applied as part of the iterative algorithm alongside the second position estimate, rather than simply being applied directly to the INS output, the uncertainty in those corrections can be monitored in the same way as the uncertainty in the second position estimate is monitored. Thus the accuracy of those corrections can be suitably taken into account when updating the error state.

The INS 110 is a standard INS that estimates the location of the vehicle using suitable sensors such as accelerometers and gyroscopes. The INS 110 may of course provide other navigation data such as the velocity, roll, pitch, and yaw of the vehicle based on the accelerometer and/or gyroscope readings.

The TNU 120 comprises a digital terrain map 125 and a terrain profiling sensor 126 such as a radar altimeter. The digital terrain map 125 comprises information on the

- 10surface topology which includes terrain elevation information above a reference surface (e.g. above a geoid or other reference surface) and possibly other such terrain profile data. Such digital terrain maps 125 may be obtained from, for example, government survey agencies. The terrain profiling sensor 126 is positioned to measure the elevation of the surface topology. An estimate of the vehicle position is determined by correlating the measured terrain profile data with the terrain profile data in the terrain map. The position on the terrain map that is associated with the highest correlation strength provides an estimate of the vehicle’s position.

The stored gravity map 130 comprises a 3D spatial map of information on the gravity gradient.

The IAU 140 comprises an INS error state calculating iterative algorithm (such as a Kalman filter which may be a modified Kalman filter such as an extended Kalman filter) arranged to determine an updated INS error state 45 based on the current INS error state 22, a gravity corrected position estimate 35 and the TNU position estimate 55. It will be appreciated that the INS error state calculating iterative algorithm is processed at processing blocks 20 and 40.

In a given iteration of the navigation system 100, the INS 110 and the TNU 120 each determine a current position estimate 10, 55 of the vehicle. At processing block 20, the IAU 140 receives the INS and TNU position estimates 10, 55 and determines the gravitational field strength based on the 3D spatial map information 15 received from the gravity map 130 at a location corresponding to the INS position estimate 10 as corrected by the INS error state 22. However, in other examples, if the TNU 120 is estimated to have an accuracy for the x, y and/or z position coordinates better than a predetermined threshold, then the IAU 140 may determine the gravitational field strength based on the 3D spatial map information 15 in the gravity map 130 at a location corresponding to the TNU position estimate 55. Thus, it will be appreciated that the IAU 140 may select which position estimate 10, 55 to use depending on the estimated accuracy of various position estimates. This is beneficial as it ensures that the gravity information is determined at the most accurate location estimate available.

- 11 The IAU140 is configured to correct the INS error state 22 based on the gravitational field strength to provide a gravity corrected INS error state 30. In addition, the I AU 140 is also configured to correct the INS position estimate 10 based on the gravity corrected INS error state 30 to provide a gravity corrected position estimate 35. For example, the I AU 140 may correct the INS position estimate 10 by correcting the associated INS sensor data (e.g. the data from the INS’s accelerometer and gyroscope) with the gravity corrected INS error state 30.

In other examples, the gravity corrected position estimate 35 may be determined by another component of the navigation system 100.

At processing block 40, the INS error state 22 is updated based on the gravity corrected position estimate 35, the INS error state 22, and the TNU position estimate 55. For example, the gravity corrected position estimate 35 is used with the INS error state 22 and the TNU position estimate 55 in a Kalman filter to provide an updated INS error state 45. It will be appreciated that the TNU position estimate 55 acts as a secondary navigation aid that constrains the growth in the error of the INS output in, for example, a Kalman filter. It will also be appreciated that the updated INS error state 45 is fed forward 50 for use in the next iteration of the I AU 140. However, on the whole, it will be appreciated that updating the INS error state 45 for the next iteration based on the INS error state 22 of the current iteration, the gravity corrected position estimate 35 and the TNU position estimate 55 improves the accuracy of the updated INS error state 45.

It will also be appreciated that, as a result of feeding forward the updated INS error state 45, the I AU 140 predicts and propagates the growth in the INS error state in each iteration based on the updated INS error state. In this way, the I AU 140 considers the effect of gravity in the growth of the INS error state.

At step 56, the I AU 140 is configured to correct the INS position estimate 10 based on the updated INS error state 45 to provide an error corrected position estimate 60.

Additionally or alternatively, the IAU 140 may also update covariances associated with the INS error state 22 based on the INS error state 22 of the current iteration, the gravity corrected position estimate 35 and the TNU position estimate 55.

- 12In some examples, the IAU 140 may receive the digital terrain map 125 information and the terrain profiling sensor 126 measurements from the TNU 120 and perform a correlation to determine the TNU position estimate 55 at, for example, processing block 40.

It will thus be appreciated that with the above examples, a gravity map can be integrated into a terrain referenced navigation system. Information from the gravity map at the vehicle’s location may be used by the Terrain Referenced Navigation system’s Kalman Filter’s error Propagation as follows:

(1) The error growth in the Inertial Navigation System’s navigation solution due to the effect of gravity anomalies will be estimated. The three dimensional acceleration sensed due to the local gravity anomaly at the vehicle location will be calculated from the gravity map. This additional acceleration will be accounted for by the INS error model embodied within the Kalman Filter and used to update the Kalman Filter error states.

(2) Additional uncertainty may be added to the Kalman Filter via the Process Noise matrix, proportional to the magnitude of the local gravity anomaly as read from the gravity map, to account for any errors or limitations in the acceleration estimates derived in (1) above.

The various methods described herein may be implemented by one or more computer program products or computer readable media provided on one or more devices. The computer program product or computer readable media may include computer code arranged to instruct a computer or a plurality of computers to perform the functions of one or more of the various methods described herein. The computer program and/or the code for performing such methods may be provided to an apparatus, such as a computer, on a computer readable medium or computer program product. The computer readable medium may be transitory or nontransitory. The computer readable medium could be, for example, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, ora propagation medium for data transmission, for example for downloading the code over the Internet. Alternatively, the computer readable medium could take the form

- 13of a physical computer readable medium such as semiconductor or solid state memory, magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disc, and an optical disk, such as a CD-ROM, CD-R/Wor DVD. An apparatus such as a computer may be configured in accordance with such code to perform one or more processes in accordance with the various methods discussed herein. Such an apparatus may take the form of a data processing system. Such a data processing system may be a distributed system. For example, such a data processing system may be distributed across a network. Some of the processes may be performed by software on a user device, while other processes may be performed by software on a server, or a combination thereof.

Claims

1. A navigation system comprising:

an inertial navigation system arranged to output a first position estimate; a terrain based navigation unit arranged to output a second position estimate;

a stored gravity map arranged to receive a position and to output gravity information for that position; and an iterative algorithm unit arranged to determine an INS error state in each iteration;

wherein in each iteration the iterative algorithm unit is arranged to: receive the first position estimate and the second position estimate; determine a gravity corrected position estimate based on the first position estimate, the INS error state and the gravity information; and update the INS error state for the next iteration based on the INS error state, the gravity corrected position estimate and the second position estimate.

2. A navigation system according to claim 1, wherein the iterative algorithm comprises a Kalman filter.

3. A navigation system according to claim 1 or 2, wherein the terrain based navigation unit is arranged to determine the second position estimate based on a correlation between measured terrain profile data and stored terrain profile data in a terrain map.

4. A navigation system according to claim 3, wherein the terrain based navigation unit comprises a radar altimeter or laser altimeter arranged to measure the terrain profile data.

5. A navigation system according to any preceding claim, wherein the gravity information comprises three-dimensional gravity field strength/gradient data, and/or a second or a third order tensor of the gravity field strength/gradient.

6. A navigation system according to any preceding claim, wherein the position estimate received by the stored gravity map is the first position estimate as

- 15corrected by the INS error state, the first position estimate or the second position estimate.

7. A navigation system according to any preceding claim, wherein in each iteration the iterative algorithm unit is further arranged to output an error corrected position estimate based on the INS error state for the next iteration and the first position estimate.

8. A vehicle comprising the navigation system according to any of claims 1-7.

9. An iterative method of determining an INS error state, each iteration of the method comprising:

receiving a first position estimate from an inertial navigation system and a second position estimate from a terrain based navigation unit;

determining gravity information at a received position from a stored gravity map;

determining a gravity corrected position estimate based on the first position estimate, the INS error state and the gravity information; and updating the INS error state for the next iteration based on the INS error state, the gravity corrected position estimate and the second position estimate.

10. An iterative method according to claim 9, wherein the INS error state is updated using a Kalman filter.

11. An iterative method according to claim 9 or 10, wherein the second position estimate is determined based on a correlation between measured terrain profile data and stored terrain profile data in a terrain map.

12. An iterative method according to any of claims 9-11, wherein the gravity information from the stored gravity map is determined based on the first position estimate as corrected by the INS error state, the first position estimate or the second position estimate.

- 1613. The iterative method according to any of claims 9-12, wherein each iteration of the iterative method further comprises outputting an error corrected position estimate based on the INS error state for the next iteration and the first position estimate.

14. A computer-readable medium comprising instructions that are executable by a processor to perform the method of any of claims 9 to 13.

15. Apparatus comprising a processor and a memory, the memory storing

10 instructions that are executable by the processor to perform the method of any of claims 9 to 13.

Intellectual

Property

Office

Application No: GB1618941.7 Examiner: Mr Chris Davidson