Aided INS/GPS/SAR navigation with other platforms

The need for geo-registered features is avoided by a system for estimating a motion of a first sensor during a time interval. The system has a second sensor where the first sensor and the second sensor sense the same geo-location during the time interval. The first sensor computes a first target location error from sensing the geo-location. The second sensor also computes a second target location error from sensing the geo-location. A data link interconnects the first sensor and the second sensor, the data link transmitting the second target location error computed by the second sensor to the first sensor during the time interval. A processor at the first sensor combines the first target location error and the second target location error in a first sensor observation model, where the sensor observation model is descriptive of the motion of the first sensor. The observation model is used with a Kalman filter to update the position of the first sensor. This combination of the first sensor observation model and the second sensor observation model generates a more accurate target location error at the first sensor. The principle is extended to a plurality of platforms.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention is in the field of improved sensor motion (position, velocity, acceleration) accuracy during GPS unavailability using multiple sensors locating a particular geo-target in a common time frame.

2. Description of the Related Art

Synthetic Aperture Radar (SAR) is used for ground mapping as well as target identification. The general principle behind SAR is to coherently combine the amplitude and phase information of radar returns from a plurality of sequentially transmitted pulses. These pulses are from a relatively small antenna on a moving platform. As the platform moves, the information contained in the pulses is coherently combined to arrive at a high resolution SAR image.

The plurality of returns creating a SAR image generated by the transmitted pulses along a presumed known path of the platform make up an array. Theoretically, during the array, amplitude as well as phase information returned from each of the pulses, for each of many range bins, is preserved. The SAR image is formed from the coherent combination of the amplitude and phase of return(s) within each range bin, motion compensated for spatial displacement of the moving platform during the acquisition of the returns for the duration of the array.

The clarity of a SAR image is in many respects dependent on the quality of the motion compensation applied to each radar return contributing to the coherent SAR image computation. Motion compensation shifts the phase of each radar sample (typically an I+jQ complex quantity derived from an analog to digital converter) in accordance with the motion in space of the moving platform with respect to a reference point. The SAR imaging process depends on the coherent, phase accurate summing of all radar returns expected within an array. These principles are detailed by W. G. Carrara, R. S. Goodman and R. M. Majewski inSpotlight Synthetic Radar, Boston, Artech House, 1995, incorporated herein in its entirety by reference.

Thus, the accuracy of the motion compensation for phase coherence applied to each radar A/D sample is critical to SAR imaging. Typically, an inertial navigation system (INS) using accelerometers and gyroscopes derives velocity, acceleration and position information for use in radar motion compensation. The INS is updated from various sources, such as satellite based Global Positioning Systems (GPS) or pre-stored geo registered features of the terrain in the vicinity of the path of the moving radar. Using an INS aided by GPS may subject the GPS to jamming, corrupting the GPS signal. Consequently, the GPS jamming may induce a position error that may manifest itself in certain applications as a blurring of SAR images, reducing SAR utility.

Using a plurality of pre-stored geo registered features (position references) instead of GPS updates of the INS requires added memory and interfacing within the radar, increasing parts count and reducing reliability. The concept of using pre-stored geo registered features for increased position accuracy is described in U.S. Pat. No. 5,485,384, titled On Board Navigation System For An Aerial Craft Including a Synthetic Aperture Sideways Looking Radar issued Jan. 16, 1996 to B. Falconnet and U.S. Pat. No. 5,432,520 titled SAR/GPS Inertial Method of Range Measurement, issued Jul. 11, 1995 to Schneider et al., both incorporated herein in their entirety by reference. An alternative to using pre-stored geo registered features is thus desirable to avoid generating an accurate geo registered feature database, updating it, and interfacing it to a sensor, such as a radar system.

SUMMARY OF THE INVENTION

The need for geo-registered features is avoided and above limitations reduced by a system for estimating a motion of a first sensor during a time interval, said system comprising a second sensor, said first sensor and said second sensor sensing the same geo-location during said time interval. The first sensor computes a first target location error from sensing the geo-location. The second sensor also computing a second target location error from sensing the same geo-location. A data link interconnects the first sensor and the second sensor, the data link transmitting the second target location error computed by the second sensor to the first sensor during the time interval. A processor at said first sensor combines the first target location error and the second target location error in a first sensor observation model, where the sensor observation model is descriptive of the motion of the first sensor. The observation model is used with a Kalman filter to update the position of the first sensor.

The geo-location is not pre-registered, nor known in advance.

DETAILED DESCRIPTION OF THE INVENTION

The present disclosure describes a method and apparatus for geo-locating the position of a sensor when Global Positioning Satellite (GPS) transmission is jammed, or unavailable. Instead of using GPS, the position of the sensor is computed by combining a plurality of TLEs derived from sensing a geo-location by a plurality of sensors. The TLEs thus derived are transmitted using a data link from independent sensors motion measurements, where the sensors may be separated in space and not co-located. The geo-location is not known in advance, nor is it pre-registered.

As shown inFIG. 1, in the prior art, sensor motion is initially measured by an inertial measurement unit110. The output from inertial measurement unit110is used by inertial navigation system processor106to update a Kalman filter102in conjunction with GPS signal from processor108within INS/GPS integrator100. If however, GPS jamming detector104determines that the GPS signal is jammed or unavailable, then guidance process118directs a SAR/FLIR sensor116to perform location measurements on a geo-registered feature120. The output from SAR/FLIR sensor116is examined in image processor114and compared with contents of Catalog of Registered Features112. Position of SAR/FLIR sensor116is extracted from data provided from image processor114in Extract Position118. This yields the position of sensor116with respect to the geo-registered feature120. The position of SAR/FLIR sensor116thus derived from image processor114and Extract Position118is used within Kalman filter102to augment inertial navigation information, instead of the unavailable GPS information. The limitation of this prior art approach is that a catalog of geo registered features112has to exist for SAR/FLIR processor sensor116for its current geographical position.

The motion of sensor116(position, velocity and acceleration) is updated and projected by a motion navigator. An example of a motion navigator used with this disclosure is the classical Kalman filter, (Kalman and Bucy, 1960) well known in the art, and described by A. Gelb inApplied Optimal Estimation,1974, The Analytic Science Corporation, The MIT Press, incorporated herein in its entirety by reference. The function of the motion navigator in this disclosure, exemplified by the Kalman filter, is to (optimally) predict the position, velocity and acceleration of a platform containing a sensor at known time intervals between inputs from a position sensor, such as, for example, a Synthetic Aperture Radar (SAR), Forward Looking Infrared (FLIR), and/or SONAR.

As shown inFIG. 1A, further detailingFIG. 1, the estimation of motion is made from a position sensor generating input data101at time t=1. SAR/FLIR position sensor116measures position during an update time interval, and presents results at the end of the time interval. The Kalman filter evaluates changes in position measured by the position sensor over many previous intervals to estimate future motion, or trajectory of the sensor during the next measuring interval.

Continuing withFIG. 1A, in computing the estimation of sensor motion within a Kalman filter, an error covariance matrix103is computed along with an observation model105, typically made up of the Observation Matrix Hkand Measurement Noise Matrix Rk. Based on the observation model, optimal gains for particular parameters are computed in Compute Optimal Gains Kk107and used by Update Sensor Position and Filter Parameters111. The cycle is repeated during the next time interval, t=2.

The input data is presented to the Kalman filter, described by the Gelb reference above, and described as follows:
{right arrow over (x)}k=Φk−1{right arrow over (x)}k−1+{right arrow over (w)}k−1, {right arrow over (w)}k˜N({right arrow over (0)}, Qk)
{right arrow over (z)}k=Hk{right arrow over (x)}k+{right arrow over (v)}k, {right arrow over (v)}k˜N({right arrow over (0)}, Rk)
E[{right arrow over (x)}(0)]={right arrow over (x)}0, E[{right arrow over (x)}0{right arrow over (x)}0T]=P0, E[{right arrow over (w)}j{right arrow over (v)}kT]={right arrow over (0)}∀j,k
Pk−=Φk−1Pk−1+Φk−1T+Qk−1
Pk+=(I−KkHk)Pk−
Kk=Pk−HkT[HkPk−HkT+Rk]−1Equation 1
where Φkis the transition matrix for interval k.

The error covariance propagation matrix Pk+103, Kalman filter gain Kk107, measurement model105(observation matrix Hk, and observation noise matrix Rk) are shown inFIG. 1A.

A typical target location error (TLE) ellipsoid202derived from computations inFIG. 1andFIG. 1Ais shown inFIG. 2. The TLE is due to uncertainty in the position of the sensor (or its associated platform), with respect to a coordinate system. Thus, the TLE represents an error independent of sensor capabilities or accuracy in detecting or tracking a target. There are three perpendicular quantities that define the extent of a TLE: vertical track204, cross track206and down-track208error.

Equation 1 depends on only one sensor (or platform) to derive target location and update the trajectory estimation of the target from data at t=1 to be used for the time interval k until the next update at t=2.

In contrast, this disclosure derives an improved (measurement) noise matrix Rkand an observation matrix Hkfor use within a sensor navigator, e.g. Kalman filter. This disclosure combines a plurality of independent common geo-location measuring sensors (independent sources of a target location), each having its own independent TLE for overall measurement. The combination of TLEs provide a more accurate estimate of target position as compared to any one of the contributing sensors. That is, a plurality of measurements from individual, independent sensors on separate, or the same platform(s), are combined to obtain a lower, new TLE. The new TLE is of higher accuracy, lesser extent, lesser volume, as compared to the TLE from any one of the sensors used to form the combined, new TLE. In some applications, the more accurate TLE obtained from combining observation models from SAR and/or FLIR sensors avoids the need for the inclusion of geo-registered features in target location computations. The same concept may be applied to sonar in an ocean environment.

Reducing Target Location Errors (TLE).

Errors in computed target geo-location using a single platform can be primarily attributed to three major sources:

sensor position errors

sensor bearing errors and

Digital Terrain Elevation Data (DTED) errors.

For this disclosure, above three errors are being treated as being statistically independent, i.e. fully de-correlated, and have a zero mean Gaussian distribution. Other errors, not cited, are assumed insignificantly small compared to the above three errors, and thus are not considered. It is further assumed that the target to be tracked is acquired, that is, its position is detected at time intervals used to compute its new position during the next time interval. DTED noise is treated as part of the measurement noise in the Z direction using the Earth Center Earth Fixed (ECEF) coordinate frame.

Errors in a target position sensor directly transform to the slant coordinate frame. These errors are converted into the platform coordinate system using the angle ψ described in the parent application.

As detailed in the parent application, the slant plane consists of vectors {right arrow over (V)}Dand {right arrow over (R)}. The slant coordinate frame is defined by:

xsis along the vehicle velocity axis {right arrow over (V)};

zsis perpendicular to the slant plane;

ysforms a right hand coordinate system with xsand zs.

The platform coordinate frame (sensor body coordinate frame) is defined by:

zpforms a right hand coordinate system with xpand yp.

The relationship between the slant coordinate frame and the platform coordinate system is given by:

{right arrow over (V)} is the velocity vector of the sensor platform (vehicle);

{right arrow over (R)} is the range vector between the vehicle position and a geo-location; and

φ is the angle between the sensor platform (vehicle) flight path and the line of sight between the sensor platform (vehicle) and the geo-location sensed by a plurality of sensors.

{right arrow over (r)} and Δ{right arrow over (V)} are the first six Kalman filter error states defined as
Δ{right arrow over (r)}=(δrx,δry,δrz)T
and
Δ{right arrow over (V)}=(δVx,δVy,δVz)T

in the platform coordinate frame and subscript T denotes the transpose of the vector.

If Δ{right arrow over (r)} and Δ{right arrow over (V)} are defined in the ECEF coordinate frame, then these error states are transformed into the platform reference frame where the error equations are defined. The Kalman filter error states {right arrow over (x)}k, observation matrix Hkand measurement noise matrix Rkare defined as:

Assume that the vectors

Therefore, the target location error (TLE), as derived in the parent application can be written in the following form:

Note that the dxp(down-track), dyp(cross-track), and dzpvertical track components form an ellipsoid of TLE.

The following observation matrix is applicable,

Now the measurement noise is derived. The measurement noises are determined by the TLE of each platform. An example of the measurement noise matrix is described using a two dimensional observation model and two sensors, followed by more general scenarios.

It is assumed that all the sensors (platforms) in each scenario are in a common time frame, observing the same geo-location (target(s)), and sharing navigation information instantaneously via a data link system. The scenarios considered are examples of the teachings herein, and are as follows.

a. Platform0is updated from platform1with two dimensional measurement noise matrix.

c. Platform0is updated from all other platforms i where i=1, 2 . . . n−1 with three dimensional measurement noise matrix.

Case Ia Embodiment

Platform0is updated from Platform1with two dimensional measurement noise matrix.

In this case Platform1has higher navigation accuracy than that of Platform 0. The navigation accuracy of Platform0is updated with independent observations (target measurements), separate and distinct from those obtained in Platform1via the data link system. The error state vector, the observation matrix and the measurement noise matrices of the Kalman filter for Platform0are:

The derivation of r00and r11is shown inFIG. 5. InFIG. 5, the lengths OP0(denoted as a0) is the down track error while OQ0(denoted as b0) is the cross track error of the TLE obtained from platform0. The lengths OP1(denoted as a1) is the down track error while OQ1(denoted as b1) is the cross track error of the TLE obtained from platform1. The TLE for platform0(namely E0) is an ellipsoid which is formed by the semi-major axis a0and semi minor axis b0Similarly, the TLE for platform1(namely E1) is an ellipsoid which is formed by the semi-major axis a1and semi minor axis b1.

Since platform0can obtain the TLE information from platform1, the intersection of these two ellipsoids, E0∩ E1, becomes a more accurate TLE for platform0. Therefore, for platform1, the down track error a1will be reduced to rDR1, the length of OA1. Similarly, for platform0, the down track error a0will be reduced to rDR0, the length of OA0. This information is used to update and to bind the navigation errors for platform0. The minimum of rDR0and a1is the standard deviation of the measurement noise for the down-track. Similarly, the minimum of rCR0and b1is the standard deviation of the measurement noise for the down-track. The two dimensional measurement noise matrix of the Kalman filter for platform0is as follows:

Now, we will derive rDR0and rCR. The length of OA0and OA1can be computed as follows.

The general two-dimensional elliptic equation is

For platform0and platform i, the general forms for rDRiand rCRiare denoted as

Vx0and Vy0are the x and y component of the vehicle velocity for platform0. Vxiand Vyiare the x and y component of the vehicle velocity for platform i.

VH0and VHiare the magnitudes of vectors {right arrow over (VH0)} and {right arrow over (VHi)} respectively. θ is the angle between the semi-major axes of platform0and i.

Case Ib

We will choose the down-track and vertical-track of the TLE as two dimensional elliptic axes. Thusb1=cross-trackc1=vertical-track

The general elliptic equation for two dimension is

Note that we also can obtain rCR1from the above equations. However, this rCR1is the same as rCR1that was derived in Case Ia.

Note that the rVR1can also be derived from the vertical-track and cross-track of the TLE ellipsoid by using the above method.

The hij(i=0,1,2 j=0,1,3,4,5) are defined in Equation 2 which are derived from the TLE for platform0.

In one embodiment, as shown inFIG. 3, Sensor0301is connected to all other sensors, sensor1303, sensor i307and sensor (n−1)305using bidirectional data link309. Sensor0, an example of a typical sensor, is also described inFIG. 4, as sensor0,400. The structure of sensor0is applicable to sensor1303, sensor i307and sensor (n−1)305. Thus TLEs are exchanged among all platforms for a particular geo-location (target).

For each pair, (0,i), which is platforms0and i, compute rCR(i-1), rDR(i-1), and rVR(i-1)from Case Ib above. Thus the H and R matrices can be derived as follows,

Case II

Sensor i is updated from other sensors j (≠i) at the same time where j=0, 1, . . . , n-1 for a fixed i where I=0, 1, . . . , n-1. All sensors, including sensor0, are sensing the same geo-location A, typically a conveniently discernable target.

This case is illustrated inFIG. 4. Here, sensor0400has a GPS receiver402for receiving navigation signals from a constellation of GPS satellites. GPS Jamming Detector414detects a jammed or unavailable GPS signal. If the GPS navigation signal is valid, the GPS location information is passed to Kalman filter412, which in turn supplies position information to Update Guidance Position, Velocity and Attitude416within processor420.

Conversely, if GPS Jamming Detector414determines that the GPS signal is unusable, that is, jammed or corrupted, an alternative source of navigation information is activated. Inertial Navigation System SAR, FLIR Platform motion404determines the location of a sensor (on a platform) and geo-location A, typically using a SAR or FLIR sensor such as sensor116inFIG. 1. Note that geo-location A is not cataloged, nor pre-stored or geo-registered in a data base. Returning toFIG. 4, sensor400uses Generates TLE equations406to compute its own TLE. These TLE from sensor0400are sent to other sensor (platforms) using two way link418.

In receiving TLE from other sensors using two way link418, a coordinate transformation408is performed on incoming TLE from sensors1,2. . . (n-1) to match their TLE to the current position of sensor0400. This and the data from sensor0, is input into observation model for sensor0400(Compute Observation Matrix H and Measurement Noise Matrix410).

The observation matrix H and Measurement Noise Matrix are part of the input into Kalman Filter412to substitute for the missing GPS information.

This case is an extension of the Case Ic from sensor (platform)0to any sensor (platform) i. In this case, the observation model is as follows.

Note that the classical Kalman filter has a restriction on the cross-correlation between process (matrix Q in equation 1) and measurement noise (matrix R in equation 1). A modified filter is thus used in this disclosure.

To preserve uncorrelated relationships between observation model and dynamic model in the Kalman filter for platform i, it is necessary to exclude the down track, cross track and vertical track information obtained from Platform i for the computation of rjjand RKmatixes. Thus, the observation model is modified as follows.

x→k=(δ⁢⁢rx,δ⁢⁢ry,δ⁢⁢rz,δ⁢⁢Vx,δ⁢⁢Vy,δ⁢⁢Vz,0,…⁢,0)T,⁢Hk=(h00,h01,h02,h03,h04,h05,0,…⁢,0h10,h11,h12,h13,h14,h15,0,…⁢,0h20,h21,h22,h23,h24,h25,0,…⁢,0),⁢⁢andRk=(r00,0,00,r11,00,0,r22)r01=r02=r10=r12=r20=r21=0,⁢r00=rDi⁢⁢1,r11=rCi⁢⁢1,r22=rVi⁢⁢1whererDi⁢⁢1⁢=denote⁢min⁢{rDR⁢⁢0,rDR⁢⁢1,…⁢,rDR⁡(i-1),rDR⁡(i+1),…⁢,rDR⁡(n-1)},⁢rCi⁢⁢1⁢=denote⁢min⁢{rCR⁢⁢0,rCR⁢⁢1,…⁢,rCR⁡(i-1),rCR⁡(i+1),…⁢,rCR⁡(n-1)}andrVi⁢⁢1⁢=denote⁢min⁢{rVR⁢⁢0,rVR⁢⁢1,…⁢,rVR⁡(i-1),rVR⁡(i+1),…⁢,rVR⁡(n-1)}
A Typical Method

As shown inFIG. 6, above analytical analysis describes a method for estimating the motion of a first sensor, typically on a platform, during a time interval, comprising the following steps:

a) sensing a geo location using sense geo-location602for the first sensor, sense geo-location604for the second sensor, and sense geo-location606for the Nthsensor during the time interval;

b)computing a first TLE in Compute TLE1608using the first sensor, a second TLE in Compute TLE2610using the second sensor; a third TLE in Compute TLE N612using the Nthsensor;

c) interconnecting the first sensor, the second sensor and the Nthsensor using a data link, the data link transmitting the second location error TLE2from second sensor2using Send TLE2, and the Nth sensor using Send TLE N to the first sensor during said time interval;

e) combining the first target location error (TLE1) associated with the first sensor the second target location error (TLE2) and the Nthtarget location errors in a first sensor observation model within Combine TLE1, and TLE2. . . N in Sensor Observation Model 620;

f) Using the combined TLE gained from the combination of TLEs from the second and Nthseparate, de-correlated measurements within Update Kalman Filter622associated with sensor1, thereby reducing the TLE for sensor1.

The first, or second sensor, or both, is a synthetic aperture radar, a FLIR infrared sensor, or a SONAR. The only requirement is that the sensor supplying a TLE observe, or take position measurements with respect to the same reference geo-location.

The first sensor and the second sensor sense the geo-location to be used as a reference independently, during the same time interval, or common time frame. It is understood that geo-location sensing can be adjusted in time to insure that reported position observations are synchronized to the exact same time.

Application Example

Above principles are typically applied for the described cases using a 15 error state Kalman filter defined as having 3 position errors, 3 velocity errors, 3 attitude errors, 3 gyro biases, and 3 accelerometer biases. In this example, a typical 1σ error budget is defined as follows:

Using above operating figures, the size of the navigation error using the teachings herein is substantially reduced especially over longer time intervals, as compared to the single sensor case. For example, where GPS measurements are lost and updates are received via the two way data link every 100 seconds from a second sensor over a 1000 second interval, the navigation position error is reduced from about 4000 meters to 200 meters and the velocity error is reduced from 4 meter/sec to about 1 meter/sec.

All references cited in this document are incorporated herein in their entirety by reference.

Although presented in exemplary fashion employing specific embodiments, the disclosed structures are not intended to be so limited. For example, although the target location accuracy improvement herein is described in the context of a radar sensor for target position, the disclosure is also applicable for sonar TLE, or other target locating methods, where a location of a target (or scatterers) is independently determined by a plurality or target measuring platforms, each platform having its own, independent TLE.

Those skilled in the art will also appreciate that numerous changes and modifications could be made to the embodiment described herein without departing in any way from the invention.