Avionics, in the scope of the project, implies all electrical hardware and software components necessary to achieve the project objectives using the model helicopter as the flight test platform. Maybeck (1999) provides a pleasant introduction to stochastic processes and estimation and, together with Levy (2002), helps to understand the operation of the Kalman filter.
Overview
General model helicopter information
Overview
Key functional requirements
Interconnections between elements indicate functional components that depend on or communicate with each other in some way.
Hardware
Hardware overview
Processing unit
Instrumentation
- Inertial measurement unit
- Global positioning system
- Barometer
- Magnetic compass
Communication units
- Wireless data transceiver
- Model helicopter radio system
Actuation and flight switch
Power requirements and power supply design
Ground station
Software
Embedded software
- Design methodology
- Embedded application overview
- Timing and execution schedule
- Telemetry, logging and remote operation
The DSP falls into the DSP/BIOS "idle loop" after setup and initialization which is coded into the DSP software entry point - the C main() function. Essentially, when sending telemetry (sensor data, navigation conditions etc.), the full transmission packet must be sent in the time available between IMU samples (approximately 15.6 ms).
Ground station software
- Design methodology
- Functionality and possible operations
The primary purpose of the MDI window for data log files is to visualize telemetry. The MDI window contains tools for navigating data files by variable category (eg accelerations, angular velocities, INS states, etc.) and time/sample number.
Overview
Navigation system architecture
Fusion configurations
Both methods propose to estimate the errors of the inertial system which are the consequence of the states of the corresponding Kalman filters. These corrections are the outputs of the Kalman filter resulting from an estimation of the inertial system errors.
Coupling approaches
Farell and Barth (1999) offer a slightly different interpretation where the INS provides the pseudo satellite array tool and the GPS receiver generates the corresponding measurements that are processed by the Kalman filter. Farell and Barth (1999) consider assisting the carrier tracking loops with data from the INS solution as essential for tight coupling.
Strap down INS
Introductory concepts
Weston and Titterton (2000) refer to the belt-down system as the electronic analogue of the mechanized platform system. In terms of size, the mechanized platform is usually larger than the belt-down system due to the characteristic actuated platform.
Helicopter orientation
- Reference frames
- Orientation problem
Britting (1971) notes that the origin of the body frame and the origin of the navigation reference frame rarely coincide. Because the body frame is attached to the helicopter's center of mass, its orientation changes with respect to the navigation reference frame.
Kalman filtering overview
- Introductory theory and concepts
- Applicability to the navigation problem
- Filter structure
- Non linear implementation
- Linearised Kalman filter
- Extended Kalman filter
- Obtaining total quantities
- Linearised versus extended Kalman filtering
Consequently, the subsequent discussion of the Kalman filter will focus on discrete time aspects and application. For a treatment of the continuous Kalman filter see Brown and Hwang (1992) or Grewal and Andrews (2001). The Kalman filter takes on the challenge of determining the state xk ϵ Rn of the system.
Since the extended Kalman filter is an adaptation of the linearized Kalman filter, it is appropriate to start with the linearized Kalman filter. Representative image of actual versus nominal trajectory for linearized Kalman filter (after Brown and Hwang, 1992). The extended Kalman filter differs from the linearized Kalman filter only in the determination of the nominal path.
With the extended Kalman filter it may be more suitable for tracking total estimates. As the subsequent discussion shows, the preference of the linearized Kalman filter over the extended Kalman filter (or vice versa) is difficult to justify.
Navigation filter design
Anatomy of the fusion Kalman filter
The Kalman filter that estimates these conditions relies on measurements mostly provided by the GPS receiver. GPS position readings are quoted in longitude, latitude and altitude with speeds given in the north, east and up frame. Conversions given in Section 4.3.2.2.3 result in the GPS receiver effectively providing positions in the north, east and down system.
A barometer is also included, the output from which is converted to altitude and pre-combined with the GPS vertical position, thus providing a fused down position and covariance (Section 4.5.2.2.1).
Development of the Kalman filter process and measurement models
- Navigation state mechanisation equations
- Measurement models
In Equation 4.54, the denominators of the main diagonal elements in A represent the radii (in meters) of the arcs spanned by latitude and longitude changes (in radians). The cos(lat) term in the longitude equation is used to account for the shortening of the cross-sectional East-West radius conversion term at latitudes away from the equator. The skew symmetric matrix Ωne representing the relative rotation of the navigation frame with respect to the Earth frame.
The IMU provides accelerations in the helicopter's body coordinates, but application of the DCM body to navigation frame transformation (section will result in accelerations being expressed as desired. The discussion thus far has assumed that the IMU's accelerometers and rate gyros are silent It is assumed that these noise terms are not correlated with each other, as the IMU design includes independent detection elements for each displayed channel (common mode noise, for example from a power supply, is neglected).
Regarding the sensors used, only the GPS down position measurement and the barometric altimeter have been pre-combined as described in Section 4.5.2.2.1. Finally, the inaccuracies present in the GPS position and velocity solutions must be taken into account.
Kalman filter parameters and setup
- Use of the extended Kalman filter
- Determination of process and measurement noise covariances
- Navigation system initialisation and alignment
Qk, the process noise covariance, is determined by calculating the covariance of the noise terms associated with the process dynamics (Equation 4.65). E ( nnT) is the expectation of nnT, which for zero-mean signals is the covariance matrix with elements representing individual covariances along the main diagonal (Equation 4.74). The RMS, mean and covariance can be related by Equation 4.75, where x is a random variable and the top bar denotes mean.
Once the conversion from velocity increase to acceleration has been made, Equation 4.75 can be applied to produce the acceleration noise covariances of Equation 4.77. In general, if from one 64 Hz sample to the next the incremental output angle is α rad, the angular velocity, ρ, can be given by Equation 4.78, which is applied to convert the incremental angular noise into angular velocity RMS noise. Once this conversion is done, Equation 4.75 is applied to arrive at the noise covariance.
The last six elements of equation 4.74 describe the statistics of sounds associated with the IMU bias model included in the state mechanization equations. Applying the method of equation 4.81 and assuming that the initial bias is uniformly distributed between ±5 mg and ±0.5.
Navigation filter computation cycle
As such, the computation of Equations 4.94 is iteratively processed over a period of time so that the average results for the initial ϕ and θ can be found. Furthermore, it should be noted that the gravity, as seen by the IMU, is also calculated iteratively during this process and the average of these results is used to determine the gravity in terms of the hardware used. Azimuth alignment, relative to the compass, involves measuring the rotation of the Earth to determine the initial turn.
As such, the output of the two-axis magnetic compass, with the INS nearly level (as was usually the start position), was used to determine the initial turn. Again, an averaging process over multiple samples was used to obtain an initial mean curve and covariance. The residual accelerometer and slew rate biases are known to be 5 mg and 0.5 °/s, respectively.
According to Figure 4.22, it should be noted that in the absence of an external update of the measurement, the filter works only with a prediction. Instead, the filter is performed by prediction only, with Equations 4.96 facilitating the continuation of the feedback loop.
Matlab filter implementation
- Baseline implementation
- Initial filter test
The operation of the filter from section 4.5.5.1 was initially validated by capturing the raw IMU and GPS inputs from the helicopter and passing them offline through the Matlab setup. Adjusting parameters and initialization quantities was done for testing the embedded INS solution (section 4.5.6). The compass was used only for yaw initialization, which, in the absence of the CMPS03, was done using an external magnetic compass, the reading of which was manually entered into the system.
The flights in Table 4.2 did not follow a strict trajectory, as the pilot was still honing his skills at this stage of the project. As such, the tests here were more intended to validate the 'shape' of the solution and to avoid unforeseen numerical pitfalls. In flight test 2, the forward flight pattern is clearly shown in Figure 4.42, with the down position channel (Figure 4.41) showing takeoff and altitude during flight, as well as questionable GPS sampling making the estimate poor after landing (more than about 50 degrees). seconds).
A more detailed analysis of the filter is given when considering the embedded test flight results.
Embedded implementation
- Matrix operations
- Filter alignment
- Numerical considerations
- Embedded filter tests
These Matlab versions were used to validate the correct functioning of the developed matrix operations. Inversion conditioning was assessed by calculating the condition number of the matrix, [HkPk−HkT + Rk]. Several issues raised by Grewal and Andrews (2001) appear to demonstrate acceptable behavior in terms of the navigation solution.
As such, the down position estimate was validated by reviewing video log recordings. This was recorded in an attempt to determine the effect of the filter versus the model, i.e. examination of the video footage (Appendix 3) shows that the end of the flight path was exceeded, leading to the inconsistent length.
Based on the layout of the flight test field and flight paths, Test 4 showed that the course along the test varied between 325° and 0°. Furthermore, the yaw result for flight test 5 shows three turns of approx. 90° - indicative of the square that was followed. It was expected, due to the benign nature of the flight maneuvers, that the maximum required sensor bandwidth would be between 5 and 10 Hz.
The avionics were custom designed to support the navigation system and eventually the autonomous flight of the helicopter.
Avionics hardware schematics
Minimum variance estimator
Applying these results to Equations A2.3 and A2.5 produces the minimum variance estimate and variance, respectively (Equations A2.11). In the case where there are two measurements to be combined, it is necessary to find a linear estimator (Eq. A2.12) with coefficients a1 and a2 so that the variance of the estimate is as small as possible subject to the constraint a1+ a2 = 1. The variance of the estimate in Eq. A2.13 must be minimized and the aforementioned constraint follows naturally from A.
Using these results in Equations A2.12 and A2.14 produces the minimum estimate and variance, respectively (Equations A2.20).
Software, datasheets and other digital content
